Efficient Wideband Numerical Simulations for Nanostructures Employing a Drude-Critical Points (DCP) Dispersive Model.

PubMed

Ren, Qiang; Nagar, Jogender; Kang, Lei; Bian, Yusheng; Werner, Ping; Werner, Douglas H

2017-05-18

A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements. The collocated E-J scheme facilitates solving the auxiliary equations by converting the inversions of matrices to simpler vector manipulations. A new hybrid time stepping approach, which couples the Runge-Kutta and Newmark methods, is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency. The advantages of this new approach, in terms of computational resource overhead and accuracy, are validated through comparison with well-known commercial software for three diverse cases, which cover both near-field and far-field properties with plane wave and lumped port sources. The presented work provides the missing link between DCP dispersive models and FETD and/or SETD based algorithms. It is a competitive candidate for numerically studying the wideband plasmonic properties of DCP media.

Teaching the Literature Review: A Practical Approach for College Instructors

ERIC Educational Resources Information Center

Cisco, Jonathan

2014-01-01

Instructors across the disciplines require their students to write literature reviews. Although numerous sources describe the literature review process, instructors and students face difficulty when approaching the structure of a literature review. This paper presents a straightforward, efficient approach for teaching students how to write a…

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

A third-order approximation method for three-dimensional wheel-rail contact

NASA Astrophysics Data System (ADS)

Negretti, Daniele

2012-03-01

Multibody train analysis is used increasingly by railway operators whenever a reliable and time-efficient method to evaluate the contact between wheel and rail is needed; particularly, the wheel-rail contact is one of the most important aspects that affects a reliable and time-efficient vehicle dynamics computation. The focus of the approach proposed here is to carry out such tasks by means of online wheel-rail elastic contact detection. In order to improve efficiency and save time, a main analytical approach is used for the definition of wheel and rail surfaces as well as for contact detection, then a final numerical evaluation is used to locate contact. The final numerical procedure consists in finding the zeros of a nonlinear function in a single variable. The overall method is based on the approximation of the wheel surface, which does not influence the contact location significantly, as shown in the paper.

A pertinent approach to solve nonlinear fuzzy integro-differential equations.

PubMed

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

On continuous and discontinuous approaches for modeling groundwater flow in heterogeneous media using the Numerical Manifold Method: Model development and comparison

NASA Astrophysics Data System (ADS)

Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny

2015-06-01

One major challenge in modeling groundwater flow within heterogeneous geological media is that of modeling arbitrarily oriented or intersected boundaries and inner material interfaces. The Numerical Manifold Method (NMM) has recently emerged as a promising method for such modeling, in its ability to handle boundaries, its flexibility in constructing physical cover functions (continuous or with gradient jump), its meshing efficiency with a fixed mathematical mesh (covers), its convenience for enhancing approximation precision, and its integration precision, achieved by simplex integration. In this paper, we report on developing and comparing two new approaches for boundary constraints using the NMM, namely a continuous approach with jump functions and a discontinuous approach with Lagrange multipliers. In the discontinuous Lagrange multiplier method (LMM), the material interfaces are regarded as discontinuities which divide mathematical covers into different physical covers. We define and derive stringent forms of Lagrange multipliers to link the divided physical covers, thus satisfying the continuity requirement of the refraction law. In the continuous Jump Function Method (JFM), the material interfaces are regarded as inner interfaces contained within physical covers. We briefly define jump terms to represent the discontinuity of the head gradient across an interface to satisfy the refraction law. We then make a theoretical comparison between the two approaches in terms of global degrees of freedom, treatment of multiple material interfaces, treatment of small area, treatment of moving interfaces, the feasibility of coupling with mechanical analysis and applicability to other numerical methods. The newly derived boundary-constraint approaches are coded into a NMM model for groundwater flow analysis, and tested for precision and efficiency on different simulation examples. We first test the LMM for a Dirichlet boundary and then test both LMM and JFM for an idealized heterogeneous model, comparing the numerical results with analytical solutions. Then we test both approaches for a heterogeneous model and compare the results of hydraulic head and specific discharge. We show that both approaches are suitable for modeling material boundaries, considering high accuracy for the boundary constraints, the capability to deal with arbitrarily oriented or complexly intersected boundaries, and their efficiency using a fixed mathematical mesh.

An efficient approach for computing the geometrical optics field reflected from a numerically specified surface

NASA Technical Reports Server (NTRS)

Mittra, R.; Rushdi, A.

1979-01-01

An approach for computing the geometrical optic fields reflected from a numerically specified surface is presented. The approach includes the step of deriving a specular point and begins with computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Then, a cluster of three adjacent rays are chosen to define a 'mean ray' and the divergence factor associated with this mean ray. Finally, the ampilitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.

Communication: An efficient approach to compute state-specific nuclear gradients for a generic state-averaged multi-configuration self consistent field wavefunction.

PubMed

Granovsky, Alexander A

2015-12-21

We present a new, very efficient semi-numerical approach for the computation of state-specific nuclear gradients of a generic state-averaged multi-configuration self consistent field wavefunction. Our approach eliminates the costly coupled-perturbed multi-configuration Hartree-Fock step as well as the associated integral transformation stage. The details of the implementation within the Firefly quantum chemistry package are discussed and several sample applications are given. The new approach is routinely applicable to geometry optimization of molecular systems with 1000+ basis functions using a standalone multi-core workstation.

Communication: An efficient approach to compute state-specific nuclear gradients for a generic state-averaged multi-configuration self consistent field wavefunction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Granovsky, Alexander A., E-mail: alex.granovsky@gmail.com

We present a new, very efficient semi-numerical approach for the computation of state-specific nuclear gradients of a generic state-averaged multi-configuration self consistent field wavefunction. Our approach eliminates the costly coupled-perturbed multi-configuration Hartree-Fock step as well as the associated integral transformation stage. The details of the implementation within the Firefly quantum chemistry package are discussed and several sample applications are given. The new approach is routinely applicable to geometry optimization of molecular systems with 1000+ basis functions using a standalone multi-core workstation.

Magnetohydrodynamic Simulations of Black Hole Accretion Flows Using PATCHWORK, a Multi-Patch, multi-code approach

NASA Astrophysics Data System (ADS)

Avara, Mark J.; Noble, Scott; Shiokawa, Hotaka; Cheng, Roseanne; Campanelli, Manuela; Krolik, Julian H.

2017-08-01

A multi-patch approach to numerical simulations of black hole accretion flows allows one to robustly match numerical grid shape and equations solved to the natural structure of the physical system. For instance, a cartesian gridded patch can be used to cover coordinate singularities on a spherical-polar grid, increasing computational efficiency and better capturing the physical system through natural symmetries. We will present early tests, initial applications, and first results from the new MHD implementation of the PATCHWORK framework.

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

Advancing Efficient All-Electron Electronic Structure Methods Based on Numeric Atom-Centered Orbitals for Energy Related Materials

NASA Astrophysics Data System (ADS)

Blum, Volker

This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.

Fast globally optimal segmentation of cells in fluorescence microscopy images.

PubMed

Bergeest, Jan-Philip; Rohr, Karl

2011-01-01

Accurate and efficient segmentation of cells in fluorescence microscopy images is of central importance for the quantification of protein expression in high-throughput screening applications. We propose a new approach for segmenting cell nuclei which is based on active contours and convex energy functionals. Compared to previous work, our approach determines the global solution. Thus, the approach does not suffer from local minima and the segmentation result does not depend on the initialization. We also suggest a numeric approach for efficiently computing the solution. The performance of our approach has been evaluated using fluorescence microscopy images of different cell types. We have also performed a quantitative comparison with previous segmentation approaches.

Performance estimation of a Venturi scrubber using a computational model for capturing dust particles with liquid spray.

PubMed

Pak, S I; Chang, K S

2006-12-01

A Venturi scrubber has dispersed three-phase flow of gas, dust, and liquid. Atomization of a liquid jet and interaction between the phases has a large effect on the performance of Venturi scrubbers. In this study, a computational model for the interactive three-phase flow in a Venturi scrubber has been developed to estimate pressure drop and collection efficiency. The Eulerian-Lagrangian method is used to solve the model numerically. Gas flow is solved using the Eulerian approach by using the Navier-Stokes equations, and the motion of dust and liquid droplets, described by the Basset-Boussinesq-Oseen (B-B-O) equation, is solved using the Lagrangian approach. This model includes interaction between gas and droplets, atomization of a liquid jet, droplet deformation, breakup and collision of droplets, and capture of dust by droplets. A circular Pease-Anthony Venturi scrubber was simulated numerically with this new model. The numerical results were compared with earlier experimental data for pressure drop and collection efficiency, and gave good agreements.

Multiscale Modeling and Uncertainty Quantification for Nuclear Fuel Performance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Estep, Donald; El-Azab, Anter; Pernice, Michael

2017-03-23

In this project, we will address the challenges associated with constructing high fidelity multiscale models of nuclear fuel performance. We (*) propose a novel approach for coupling mesoscale and macroscale models, (*) devise efficient numerical methods for simulating the coupled system, and (*) devise and analyze effective numerical approaches for error and uncertainty quantification for the coupled multiscale system. As an integral part of the project, we will carry out analysis of the effects of upscaling and downscaling, investigate efficient methods for stochastic sensitivity analysis of the individual macroscale and mesoscale models, and carry out a posteriori error analysis formore » computed results. We will pursue development and implementation of solutions in software used at Idaho National Laboratories on models of interest to the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program.« less

An efficient approach to suppress the negative role of contrarian oscillators in synchronization

NASA Astrophysics Data System (ADS)

Zhang, Xiyun; Ruan, Zhongyuan; Liu, Zonghua

2013-09-01

It has been found that contrarian oscillators usually take a negative role in the collective behaviors formed by conformist oscillators. However, experiments revealed that it is also possible to achieve a strong coherence even when there are contrarians in the system such as neuron networks with both excitable and inhibitory neurons. To understand the underlying mechanism of this abnormal phenomenon, we here consider a complex network of coupled Kuramoto oscillators with mixed positive and negative couplings and present an efficient approach, i.e., tit-for-tat strategy, to suppress the negative role of contrarian oscillators in synchronization and thus increase the order parameter of synchronization. Two classes of contrarian oscillators are numerically studied and a brief theoretical analysis is provided to explain the numerical results.

A method for development of efficient 3D models for neutronic calculations of ASTRA critical facility using experimental information

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balanin, A. L.; Boyarinov, V. F.; Glushkov, E. S.

The application of experimental information on measured axial distributions of fission reaction rates for development of 3D numerical models of the ASTRA critical facility taking into account azimuthal asymmetry of the assembly simulating a HTGR with annular core is substantiated. Owing to the presence of the bottom reflector and the absence of the top reflector, the application of 2D models based on experimentally determined buckling is impossible for calculation of critical assemblies of the ASTRA facility; therefore, an alternative approach based on the application of the extrapolated assembly height is proposed. This approach is exemplified by the numerical analysis ofmore » experiments on measurement of efficiency of control rods mockups and protection system (CPS).« less

The evolution of cosmic-ray-mediated magnetohydrodynamic shocks: A two-fluid approach

NASA Astrophysics Data System (ADS)

Jun, Byung-Il; Clarke, David A.; Norman, Michael L.

1994-07-01

We study the shock structure and acceleration efficiency of cosmic-ray mediated Magnetohydrodynamic (MHD) shocks both analytically and numerically by using a two-fluid model. Our model includes the dynamical effect of magnetic fields and cosmic rays on a background thermal fluid. The steady state solution is derived by following the technique of Drury & Voelk (1981) and compared to numerical results. We explore the time evolution of plane-perpendicular, piston-driven shocks. From the results of analytical and numerical studies, we conclude that the mean magnetic field plays an important role in the structure and acceleration efficiency of cosmic-ray mediated MHD shocks. The acceleration of cosmic-ray particles becomes less efficient in the presence of strong magnetic pressure since the field makes the shock less compressive. This feature is more prominent at low Mach numbers than at high Mach numbers.

The evolution of cosmic-ray-mediated magnetohydrodynamic shocks: A two-fluid approach

NASA Technical Reports Server (NTRS)

Jun, Byung-Il; Clarke, David A.; Norman, Michael L.

1994-01-01

We study the shock structure and acceleration efficiency of cosmic-ray mediated Magnetohydrodynamic (MHD) shocks both analytically and numerically by using a two-fluid model. Our model includes the dynamical effect of magnetic fields and cosmic rays on a background thermal fluid. The steady state solution is derived by following the technique of Drury & Voelk (1981) and compared to numerical results. We explore the time evolution of plane-perpendicular, piston-driven shocks. From the results of analytical and numerical studies, we conclude that the mean magnetic field plays an important role in the structure and acceleration efficiency of cosmic-ray mediated MHD shocks. The acceleration of cosmic-ray particles becomes less efficient in the presence of strong magnetic pressure since the field makes the shock less compressive. This feature is more prominent at low Mach numbers than at high Mach numbers.

A linear circuit analysis program with stiff systems capability

NASA Technical Reports Server (NTRS)

Cook, C. H.; Bavuso, S. J.

1973-01-01

Several existing network analysis programs have been modified and combined to employ a variable topological approach to circuit translation. Efficient numerical integration techniques are used for transient analysis.

On a turbulent wall model to predict hemolysis numerically in medical devices

NASA Astrophysics Data System (ADS)

Lee, Seunghun; Chang, Minwook; Kang, Seongwon; Hur, Nahmkeon; Kim, Wonjung

2017-11-01

Analyzing degradation of red blood cells is very important for medical devices with blood flows. The blood shear stress has been recognized as the most dominant factor for hemolysis in medical devices. Compared to laminar flows, turbulent flows have higher shear stress values in the regions near the wall. In case of predicting hemolysis numerically, this phenomenon can require a very fine mesh and large computational resources. In order to resolve this issue, the purpose of this study is to develop a turbulent wall model to predict the hemolysis more efficiently. In order to decrease the numerical error of hemolysis prediction in a coarse grid resolution, we divided the computational domain into two regions and applied different approaches to each region. In the near-wall region with a steep velocity gradient, an analytic approach using modeled velocity profile is applied to reduce a numerical error to allow a coarse grid resolution. We adopt the Van Driest law as a model for the mean velocity profile. In a region far from the wall, a regular numerical discretization is applied. The proposed turbulent wall model is evaluated for a few turbulent flows inside a cannula and centrifugal pumps. The results present that the proposed turbulent wall model for hemolysis improves the computational efficiency significantly for engineering applications. Corresponding author.

A Metalens with a Near-Unity Numerical Aperture.

PubMed

Paniagua-Domínguez, Ramón; Yu, Ye Feng; Khaidarov, Egor; Choi, Sumin; Leong, Victor; Bakker, Reuben M; Liang, Xinan; Fu, Yuan Hsing; Valuckas, Vytautas; Krivitsky, Leonid A; Kuznetsov, Arseniy I

2018-03-14

The numerical aperture (NA) of a lens determines its ability to focus light and its resolving capability. Having a large NA is a very desirable quality for applications requiring small light-matter interaction volumes or large angular collections. Traditionally, a large NA lens based on light refraction requires precision bulk optics that ends up being expensive and is thus also a specialty item. In contrast, metasurfaces allow the lens designer to circumvent those issues producing high-NA lenses in an ultraflat fashion. However, so far, these have been limited to numerical apertures on the same order of magnitude as traditional optical components, with experimentally reported NA values of <0.9. Here we demonstrate, both numerically and experimentally, a new approach that results in a diffraction-limited flat lens with a near-unity numerical aperture (NA > 0.99) and subwavelength thickness (∼λ/3), operating with unpolarized light at 715 nm. To demonstrate its imaging capability, the designed lens is applied in a confocal configuration to map color centers in subdiffractive diamond nanocrystals. This work, based on diffractive elements that can efficiently bend light at angles as large as 82°, represents a step beyond traditional optical elements and existing flat optics, circumventing the efficiency drop associated with the standard, phase mapping approach.

A Metalens with a Near-Unity Numerical Aperture

NASA Astrophysics Data System (ADS)

Paniagua-Domínguez, Ramón; Yu, Ye Feng; Khaidarov, Egor; Choi, Sumin; Leong, Victor; Bakker, Reuben M.; Liang, Xinan; Fu, Yuan Hsing; Valuckas, Vytautas; Krivitsky, Leonid A.; Kuznetsov, Arseniy I.

2018-03-01

The numerical aperture (NA) of a lens determines its ability to focus light and its resolving capability. Having a large NA is a very desirable quality for applications requiring small light-matter interaction volumes or large angular collections. Traditionally, a large NA lens based on light refraction requires precision bulk optics that ends up being expensive and is thus also a specialty item. In contrast, metasurfaces allow the lens designer to circumvent those issues producing high NA lenses in an ultra-flat fashion. However, so far, these have been limited to numerical apertures on the same order of traditional optical components, with experimentally reported values of NA <0.9. Here we demonstrate, both numerically and experimentally, a new approach that results in a diffraction limited flat lens with a near-unity numerical aperture (NA>0.99) and sub-wavelength thickness (~{\\lambda}/3), operating with unpolarized light at 715 nm. To demonstrate its imaging capability, the designed lens is applied in a confocal configuration to map color centers in sub-diffractive diamond nanocrystals. This work, based on diffractive elements able to efficiently bend light at angles as large as 82{\\deg}, represents a step beyond traditional optical elements and existing flat optics, circumventing the efficiency drop associated to the standard, phase mapping approach.

On-line Bayesian model updating for structural health monitoring

NASA Astrophysics Data System (ADS)

Rocchetta, Roberto; Broggi, Matteo; Huchet, Quentin; Patelli, Edoardo

2018-03-01

Fatigue induced cracks is a dangerous failure mechanism which affects mechanical components subject to alternating load cycles. System health monitoring should be adopted to identify cracks which can jeopardise the structure. Real-time damage detection may fail in the identification of the cracks due to different sources of uncertainty which have been poorly assessed or even fully neglected. In this paper, a novel efficient and robust procedure is used for the detection of cracks locations and lengths in mechanical components. A Bayesian model updating framework is employed, which allows accounting for relevant sources of uncertainty. The idea underpinning the approach is to identify the most probable crack consistent with the experimental measurements. To tackle the computational cost of the Bayesian approach an emulator is adopted for replacing the computationally costly Finite Element model. To improve the overall robustness of the procedure, different numerical likelihoods, measurement noises and imprecision in the value of model parameters are analysed and their effects quantified. The accuracy of the stochastic updating and the efficiency of the numerical procedure are discussed. An experimental aluminium frame and on a numerical model of a typical car suspension arm are used to demonstrate the applicability of the approach.

Efficient globally optimal segmentation of cells in fluorescence microscopy images using level sets and convex energy functionals.

PubMed

Bergeest, Jan-Philip; Rohr, Karl

2012-10-01

In high-throughput applications, accurate and efficient segmentation of cells in fluorescence microscopy images is of central importance for the quantification of protein expression and the understanding of cell function. We propose an approach for segmenting cell nuclei which is based on active contours using level sets and convex energy functionals. Compared to previous work, our approach determines the global solution. Thus, the approach does not suffer from local minima and the segmentation result does not depend on the initialization. We consider three different well-known energy functionals for active contour-based segmentation and introduce convex formulations of these functionals. We also suggest a numeric approach for efficiently computing the solution. The performance of our approach has been evaluated using fluorescence microscopy images from different experiments comprising different cell types. We have also performed a quantitative comparison with previous segmentation approaches. Copyright © 2012 Elsevier B.V. All rights reserved.

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.

1973-01-01

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

An efficient implementation of semi-numerical computation of the Hartree-Fock exchange on the Intel Phi processor

NASA Astrophysics Data System (ADS)

Liu, Fenglai; Kong, Jing

2018-07-01

Unique technical challenges and their solutions for implementing semi-numerical Hartree-Fock exchange on the Phil Processor are discussed, especially concerning the single- instruction-multiple-data type of processing and small cache size. Benchmark calculations on a series of buckyball molecules with various Gaussian basis sets on a Phi processor and a six-core CPU show that the Phi processor provides as much as 12 times of speedup with large basis sets compared with the conventional four-center electron repulsion integration approach performed on the CPU. The accuracy of the semi-numerical scheme is also evaluated and found to be comparable to that of the resolution-of-identity approach.

Formulation of a dynamic analysis method for a generic family of hoop-mast antenna systems

NASA Technical Reports Server (NTRS)

Gabriele, A.; Loewy, R.

1981-01-01

Analytical studies of mast-cable-hoop-membrane type antennas were conducted using a transfer matrix numerical analysis approach. This method, by virtue of its specialization and the inherently easy compartmentalization of the formulation and numerical procedures, can be significantly more efficient in computer time required and in the time needed to review and interpret the results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hewett, D.W.; Yu-Jiuan Chen

The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously.

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

PubMed Central

Kerfriden, P.; Goury, O.; Rabczuk, T.; Bordas, S.P.A.

2013-01-01

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. PMID:23750055

Realization of the Najafi-Golestanian microswimmer

NASA Astrophysics Data System (ADS)

Grosjean, Galien; Hubert, Maxime; Lagubeau, Guillaume; Vandewalle, Nicolas

2016-08-01

A paradigmatic microswimmer is the three-linked-spheres model, which follows a minimalist approach for propulsion by shape shifting. As such, it has been the subject of numerous analytical and numerical studies. In this Rapid Communication, an experimental three-linked-spheres swimmer is created by self-assembling ferromagnetic particles at an air-water interface. It is powered by a uniform oscillating magnetic field. A model, using two harmonic oscillators, reproduces the experimental findings. Because the model remains general, the same approach could be used to design a variety of efficient microswimmers.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows

NASA Technical Reports Server (NTRS)

Moitra, Stuti; Gatski, Thomas B.

1997-01-01

A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.

Spectral method for pricing options in illiquid markets

NASA Astrophysics Data System (ADS)

Pindza, Edson; Patidar, Kailash C.

2012-09-01

We present a robust numerical method to solve a problem of pricing options in illiquid markets. The governing equation is described by a nonlinear Black-Scholes partial differential equation (BS-PDE) of the reaction-diffusion-advection type. To discretise this BS-PDE numerically, we use a spectral method in the asset (spatial) direction and couple it with a fifth order RADAU method for the discretisation in the time direction. Numerical experiments illustrate that our approach is very efficient for pricing financial options in illiquid markets.

Integrated approaches to the application of advanced modeling technology in process development and optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allgor, R.J.; Feehery, W.F.; Tolsma, J.E.

The batch process development problem serves as good candidate to guide the development of process modeling environments. It demonstrates that very robust numerical techniques are required within an environment that can collect, organize, and maintain the data and models required to address the batch process development problem. This paper focuses on improving the robustness and efficiency of the numerical algorithms required in such a modeling environment through the development of hybrid numerical and symbolic strategies.

Hierarchical matrices implemented into the boundary integral approaches for gravity field modelling

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Vipiana, Francesca

2017-04-01

Boundary integral approaches applied for gravity field modelling have been recently developed to solve the geodetic boundary value problems numerically, or to process satellite observations, e.g. from the GOCE satellite mission. In order to obtain numerical solutions of "cm-level" accuracy, such approaches require very refined level of the disretization or resolution. This leads to enormous memory requirements that need to be reduced. An implementation of the Hierarchical Matrices (H-matrices) can significantly reduce a numerical complexity of these approaches. A main idea of the H-matrices is based on an approximation of the entire system matrix that is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation. This allows reducing memory requirements significantly while improving the efficiency. The poster presents our preliminary results of implementations of the H-matrices into the existing boundary integral approaches based on the boundary element method or the method of fundamental solution.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

On the use of reverse Brownian motion to accelerate hybrid simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategiesmore » for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.« less

Numerical difficulties and computational procedures for thermo-hydro-mechanical coupled problems of saturated porous media

NASA Astrophysics Data System (ADS)

Simoni, L.; Secchi, S.; Schrefler, B. A.

2008-12-01

This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.

Toward topology-based characterization of small-scale mixing in compressible turbulence

NASA Astrophysics Data System (ADS)

Suman, Sawan; Girimaji, Sharath

2011-11-01

Turbulent mixing rate at small scales of motion (molecular mixing) is governed by the steepness of the scalar-gradient field which in turn is dependent upon the prevailing velocity gradients. Thus motivated, we propose a velocity-gradient topology-based approach for characterizing small-scale mixing in compressible turbulence. We define a mixing efficiency metric that is dependent upon the topology of the solenoidal and dilatational deformation rates of a fluid element. The mixing characteristics of solenoidal and dilatational velocity fluctuations are clearly delineated. We validate this new approach by employing mixing data from direct numerical simulations (DNS) of compressible decaying turbulence with passive scalar. For each velocity-gradient topology, we compare the mixing efficiency predicted by the topology-based model with the corresponding conditional scalar variance obtained from DNS. The new mixing metric accurately distinguishes good and poor mixing topologies and indeed reasonably captures the numerical values. The results clearly demonstrate the viability of the proposed approach for characterizing and predicting mixing in compressible flows.

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Nonadiabatic dynamics of photo-induced proton-coupled electron transfer reactions via ring-polymer surface hopping

NASA Astrophysics Data System (ADS)

Shakib, Farnaz; Huo, Pengfei

Photo-induced proton-coupled electron transfer reactions (PCET) are at the heart of energy conversion reactions in photocatalysis. Here, we apply the recently developed ring-polymer surface-hopping (RPSH) approach to simulate the nonadiabatic dynamics of photo-induced PCET. The RPSH method incorporates ring-polymer (RP) quantization of the proton into the fewest-switches surface-hopping (FSSH) approach. Using two diabatic electronic states, corresponding to the electron donor and acceptor states, we model photo-induced PCET with the proton described by a classical isomorphism RP. From the RPSH method, we obtain numerical results that are comparable to those obtained when the proton is treated quantum mechanically. This accuracy stems from incorporating exact quantum statistics, such as proton tunnelling, into approximate quantum dynamics. Additionally, RPSH offers the numerical accuracy along with the computational efficiency. Namely, compared to the FSSH approach in vibronic representation, there is no need to calculate a massive number of vibronic states explicitly. This approach opens up the possibility to accurately and efficiently simulate photo-induced PCET with multiple transferring protons or electrons.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

On the numerical modeling of sliding beams: A comparison of different approaches

NASA Astrophysics Data System (ADS)

Steinbrecher, Ivo; Humer, Alexander; Vu-Quoc, Loc

2017-11-01

The transient analysis of sliding beams represents a challenging problem of structural mechanics. Typically, the sliding motion superimposed by large flexible deformation requires numerical methods as, e.g., finite elements, to obtain approximate solutions. By means of the classical sliding spaghetti problem, the present paper provides a guideline to the numerical modeling with conventional finite element codes. For this purpose, two approaches, one using solid elements and one using beam elements, respectively, are employed in the analysis, and the characteristics of each approach are addressed. The contact formulation realizing the interaction of the beam with its support demands particular attention in the context of sliding structures. Additionally, the paper employs the sliding-beam formulation as a third approach, which avoids the numerical difficulties caused by the large sliding motion through a suitable coordinate transformation. The present paper briefly outlines the theoretical fundamentals of the respective approaches for the modeling of sliding structures and gives a detailed comparison by means of the sliding spaghetti serving as a representative example. The specific advantages and limitations of the different approaches with regard to accuracy and computational efficiency are discussed in detail. Through the comparison, the sliding-beam formulation, which proves as an effective approach for the modeling, can be validated for the general problem of a sliding structure subjected to large deformation.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography.

PubMed

Shaw, Calvin B; Prakash, Jaya; Pramanik, Manojit; Yalavarthy, Phaneendra K

2013-08-01

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison.

Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

NASA Technical Reports Server (NTRS)

Fink, Patrick W.; Wilton, Donald R.; Khayat, Michael A.

2007-01-01

Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries.

PubMed

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries

PubMed Central

Ge, Liang; Sotiropoulos, Fotis

2008-01-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533

Experimenting with galaxies

NASA Technical Reports Server (NTRS)

Miller, Richard H.

1992-01-01

A study to demonstrate how the dynamics of galaxies may be investigated through the creation of galaxies within a computer model is presented. The numerical technique for simulating galaxies is shown to be both highly efficient and highly robust. Consideration is given to the anatomy of a galaxy, the gravitational N-body problem, numerical approaches to the N-body problem, use of the Poisson equation, and the symplectic integrator.

First- and second-order sensitivity analysis of linear and nonlinear structures

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Mroz, Z.

1986-01-01

This paper employs the principle of virtual work to derive sensitivity derivatives of structural response with respect to stiffness parameters using both direct and adjoint approaches. The computations required are based on additional load conditions characterized by imposed initial strains, body forces, or surface tractions. As such, they are equally applicable to numerical or analytical solution techniques. The relative efficiency of various approaches for calculating first and second derivatives is assessed. It is shown that for the evaluation of second derivatives the most efficient approach is one that makes use of both the first-order sensitivities and adjoint vectors. Two example problems are used for demonstrating the various approaches.

An efficient numerical method for solving the Boltzmann equation in multidimensions

NASA Astrophysics Data System (ADS)

Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

2018-01-01

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

NASA Astrophysics Data System (ADS)

Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

2015-03-01

We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

Numerical approach of the quantum circuit theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.

2017-03-15

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency formore » a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.« less

Vectorized Jiles-Atherton hysteresis model

NASA Astrophysics Data System (ADS)

Szymański, Grzegorz; Waszak, Michał

2004-01-01

This paper deals with vector hysteresis modeling. A vector model consisting of individual Jiles-Atherton components placed along principal axes is proposed. The cross-axis coupling ensures general vector model properties. Minor loops are obtained using scaling method. The model is intended for efficient finite element method computations defined in terms of magnetic vector potential. Numerical efficiency is ensured by differential susceptibility approach.

An Embedded 3D Fracture Modeling Approach for Simulating Fracture-Dominated Fluid Flow and Heat Transfer in Geothermal Reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnston, Henry; Wang, Cong; Winterfeld, Philip

An efficient modeling approach is described for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks of representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added tomore » the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while keeps sufficient accuracy. Several numeral simulations are present to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to simulation of fractured geothermal reservoirs with both artificial and natural fractures.« less

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Secure Multiparty Quantum Computation for Summation and Multiplication.

PubMed

Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2016-01-21

As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics.

Secure Multiparty Quantum Computation for Summation and Multiplication

PubMed Central

Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2016-01-01

As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics. PMID:26792197

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

Accurate complex scaling of three dimensional numerical potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cerioni, Alessandro; Genovese, Luigi; Duchemin, Ivan

2013-05-28

The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is desirable to apply the complex scaling to investigate resonances in physical systems defined on numerical discrete grids, the most direct approach relies on the application of a similarity transformation to the original, unscaled Hamiltonian. We show that such an approach can be conveniently implemented in the Daubechies wavelet basis set, featuring a very promising level of generality, high accuracy, and no need for artificial convergence parameters. Complex scalingmore » of three dimensional numerical potentials can be efficiently and accurately performed. By carrying out an illustrative resonant state computation in the case of a one-dimensional model potential, we then show that our wavelet-based approach may disclose new exciting opportunities in the field of computational non-Hermitian quantum mechanics.« less

Partition method and experimental validation for impact dynamics of flexible multibody system

NASA Astrophysics Data System (ADS)

Wang, J. Y.; Liu, Z. Y.; Hong, J. Z.

2018-06-01

The impact problem of a flexible multibody system is a non-smooth, high-transient, and strong-nonlinear dynamic process with variable boundary. How to model the contact/impact process accurately and efficiently is one of the main difficulties in many engineering applications. The numerical approaches being used widely in impact analysis are mainly from two fields: multibody system dynamics (MBS) and computational solid mechanics (CSM). Approaches based on MBS provide a more efficient yet less accurate analysis of the contact/impact problems, while approaches based on CSM are well suited for particularly high accuracy needs, yet require very high computational effort. To bridge the gap between accuracy and efficiency in the dynamic simulation of a flexible multibody system with contacts/impacts, a partition method is presented considering that the contact body is divided into two parts, an impact region and a non-impact region. The impact region is modeled using the finite element method to guarantee the local accuracy, while the non-impact region is modeled using the modal reduction approach to raise the global efficiency. A three-dimensional rod-plate impact experiment is designed and performed to validate the numerical results. The principle for how to partition the contact bodies is proposed: the maximum radius of the impact region can be estimated by an analytical method, and the modal truncation orders of the non-impact region can be estimated by the highest frequency of the signal measured. The simulation results using the presented method are in good agreement with the experimental results. It shows that this method is an effective formulation considering both accuracy and efficiency. Moreover, a more complicated multibody impact problem of a crank slider mechanism is investigated to strengthen this conclusion.

Phase Space Approach to Dynamics of Interacting Fermions

NASA Astrophysics Data System (ADS)

Davidson, Shainen; Sels, Dries; Kasper, Valentin; Polkovnikov, Anatoli

Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of this. Already in equilibrium, fermions are notoriously hard to handle due to the sign problem. Out of equilibrium, an important outstanding problem is the efficient numerical simulation of the dynamics of these systems. In this work we develop a new semiclassical phase-space approach (a.k.a. the truncated Wigner approximation) for simulating the dynamics of interacting lattice fermions in arbitrary dimensions. We demonstrate the strength of the method by comparing the results to exact diagonalization (ED) on small 1D and 2D systems. We furthermore present results on Many-Body Localized (MBL) systems in 1D and 2D, and demonstrate how the method can be used to determine the MBL transition.

Numerical investigation of multichannel laser beam phase locking in turbulent atmosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Volkov, V A; Volkov, M V; Garanin, S G

2015-12-31

The efficiency of coherent multichannel beam combining under focusing through a turbulent medium on a target in the cases of phase conjugation and target irradiation in the feedback loop is investigated numerically in various approximations. The conditions of efficient focusing of multichannel radiation on the target are found. It is shown that the coherent beam combining with target irradiation in the feedback loop, which does not require a reference beam and wavefront measurements, is as good as the phase conjugation approach in the efficiency of focusing. It is found that the main effect of focusing is provided by properly chosenmore » phase shifts in the channels, whereas taking into account local wavefront tip tilts weakly affects the result. (control of laser radiation parameters)« less

A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund-Potsdam-Jena (LPJ) model as an example

NASA Astrophysics Data System (ADS)

Sun, Guodong; Mu, Mu

2017-05-01

An important source of uncertainty, which causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. Therefore, finding a subset among numerous physical parameters in numerical models in the atmospheric and oceanic sciences, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach in China. The results imply that nonlinear interactions among parameters play a key role in the identification of sensitive parameters in arid and semi-arid regions of China compared to those in northern, northeastern, and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.

Efficient, massively parallel eigenvalue computation

NASA Technical Reports Server (NTRS)

Huo, Yan; Schreiber, Robert

1993-01-01

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-07-01

The study of the electrodynamics of static, axisymmetric, and force-free Kerr magnetospheres relies vastly on solutions of the so-called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give a detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established set-ups (split-monopole, paraboloidal, BH disc, uniform).

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: Numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-04-01

The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, paraboloidal, BH-disk, uniform).

Numerical simulation of turbulent stratified flame propagation in a closed vessel

NASA Astrophysics Data System (ADS)

Gruselle, Catherine; Lartigue, Ghislain; Pepiot, Perrine; Moureau, Vincent; D'Angelo, Yves

2012-11-01

Reducing pollutants emissions while keeping a high combustion efficiency and a low fuel consumption is an important challenge for both gas turbine (GT) and internal combustion engines (ICE). To fulfill these new constraints, stratified combustion may constitute an efficient strategy. A tabulated chemistry approach based on FPI combined to a low-Mach number method is applied in the analysis of a turbulent propane-air flame with equivalence ratio (ER) stratification, which has been studied experimentally by Balusamy [S. Balusamy, Ph.D Thesis, INSA-Rouen (2010)]. Flame topology, along with flame velocity statistics, are well reproduced in the simulation, even if time-history effects are not accounted for in the tabulated approach. However, these effects may become significant when exhaust gas recirculation (EGR) is introduced. To better quantify them, both ER and EGR-stratified two-dimensional flames are simulated using finite-rate chemistry and a semi-detailed mechanism for propane oxidation. The numerical implementation is first investigated in terms of efficiency and accuracy, with a focus on splitting errors. The resulting flames are then analyzed to investigate potential extensions of the FPI technique to EGR stratification.

Local Orthogonal Cutting Method for Computing Medial Curves and Its Biomedical Applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiao, Xiangmin; Einstein, Daniel R.; Dyedov, Volodymyr

2010-03-24

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stabilitymore » and consistency tests. These concepts lend themselves to robust numerical techniques including eigenvalue analysis, weighted least squares approximations, and numerical minimization, resulting in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods.« less

A gradient enhanced plasticity-damage microplane model for concrete

NASA Astrophysics Data System (ADS)

Zreid, Imadeddin; Kaliske, Michael

2018-03-01

Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

Mixing Efficiency in the Ocean.

PubMed

Gregg, M C; D'Asaro, E A; Riley, J J; Kunze, E

2018-01-03

Mixing efficiency is the ratio of the net change in potential energy to the energy expended in producing the mixing. Parameterizations of efficiency and of related mixing coefficients are needed to estimate diapycnal diffusivity from measurements of the turbulent dissipation rate. Comparing diffusivities from microstructure profiling with those inferred from the thickening rate of four simultaneous tracer releases has verified, within observational accuracy, 0.2 as the mixing coefficient over a 30-fold range of diapycnal diffusivities. Although some mixing coefficients can be estimated from pycnocline measurements, at present mixing efficiency must be obtained from channel flows, laboratory experiments, and numerical simulations. Reviewing the different approaches demonstrates that estimates and parameterizations for mixing efficiency and coefficients are not converging beyond the at-sea comparisons with tracer releases, leading to recommendations for a community approach to address this important issue.

Mixing Efficiency in the Ocean

NASA Astrophysics Data System (ADS)

Gregg, M. C.; D'Asaro, E. A.; Riley, J. J.; Kunze, E.

2018-01-01

Mixing efficiency is the ratio of the net change in potential energy to the energy expended in producing the mixing. Parameterizations of efficiency and of related mixing coefficients are needed to estimate diapycnal diffusivity from measurements of the turbulent dissipation rate. Comparing diffusivities from microstructure profiling with those inferred from the thickening rate of four simultaneous tracer releases has verified, within observational accuracy, 0.2 as the mixing coefficient over a 30-fold range of diapycnal diffusivities. Although some mixing coefficients can be estimated from pycnocline measurements, at present mixing efficiency must be obtained from channel flows, laboratory experiments, and numerical simulations. Reviewing the different approaches demonstrates that estimates and parameterizations for mixing efficiency and coefficients are not converging beyond the at-sea comparisons with tracer releases, leading to recommendations for a community approach to address this important issue.

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

NASA Astrophysics Data System (ADS)

Cheng, Qing; Yang, Xiaofeng; Shen, Jie

2017-07-01

In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

Tempest - Efficient Computation of Atmospheric Flows Using High-Order Local Discretization Methods

NASA Astrophysics Data System (ADS)

Ullrich, P. A.; Guerra, J. E.

2014-12-01

The Tempest Framework composes several compact numerical methods to easily facilitate intercomparison of atmospheric flow calculations on the sphere and in rectangular domains. This framework includes the implementations of Spectral Elements, Discontinuous Galerkin, Flux Reconstruction, and Hybrid Finite Element methods with the goal of achieving optimal accuracy in the solution of atmospheric problems. Several advantages of this approach are discussed such as: improved pressure gradient calculation, numerical stability by vertical/horizontal splitting, arbitrary order of accuracy, etc. The local numerical discretization allows for high performance parallel computation and efficient inclusion of parameterizations. These techniques are used in conjunction with a non-conformal, locally refined, cubed-sphere grid for global simulations and standard Cartesian grids for simulations at the mesoscale. A complete implementation of the methods described is demonstrated in a non-hydrostatic setting.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces

NASA Technical Reports Server (NTRS)

Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John

2011-01-01

Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

Evaluation of radiation loading on finite cylindrical shells using the fast Fourier transform: A comparison with direct numerical integration.

PubMed

Liu, S X; Zou, M S

2018-03-01

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration.

The admissible portfolio selection problem with transaction costs and an improved PSO algorithm

NASA Astrophysics Data System (ADS)

Chen, Wei; Zhang, Wei-Guo

2010-05-01

In this paper, we discuss the portfolio selection problem with transaction costs under the assumption that there exist admissible errors on expected returns and risks of assets. We propose a new admissible efficient portfolio selection model and design an improved particle swarm optimization (PSO) algorithm because traditional optimization algorithms fail to work efficiently for our proposed problem. Finally, we offer a numerical example to illustrate the proposed effective approaches and compare the admissible portfolio efficient frontiers under different constraints.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Transonic Navier-Stokes wing solutions using a zonal approach. Part 2: High angle-of-attack simulation

NASA Technical Reports Server (NTRS)

Chaderjian, N. M.

1986-01-01

A computer code is under development whereby the thin-layer Reynolds-averaged Navier-Stokes equations are to be applied to realistic fighter-aircraft configurations. This transonic Navier-Stokes code (TNS) utilizes a zonal approach in order to treat complex geometries and satisfy in-core computer memory constraints. The zonal approach has been applied to isolated wing geometries in order to facilitate code development. Part 1 of this paper addresses the TNS finite-difference algorithm, zonal methodology, and code validation with experimental data. Part 2 of this paper addresses some numerical issues such as code robustness, efficiency, and accuracy at high angles of attack. Special free-stream-preserving metrics proved an effective way to treat H-mesh singularities over a large range of severe flow conditions, including strong leading-edge flow gradients, massive shock-induced separation, and stall. Furthermore, lift and drag coefficients have been computed for a wing up through CLmax. Numerical oil flow patterns and particle trajectories are presented both for subcritical and transonic flow. These flow simulations are rich with complex separated flow physics and demonstrate the efficiency and robustness of the zonal approach.

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Nonlinear mechanics of non-rigid origami: an efficient computational approach

NASA Astrophysics Data System (ADS)

Liu, K.; Paulino, G. H.

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on `bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Nonlinear mechanics of non-rigid origami: an efficient computational approach.

PubMed

Liu, K; Paulino, G H

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on 'bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

3-D parallel program for numerical calculation of gas dynamics problems with heat conductivity on distributed memory computational systems (CS)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sofronov, I.D.; Voronin, B.L.; Butnev, O.I.

1997-12-31

The aim of the work performed is to develop a 3D parallel program for numerical calculation of gas dynamics problem with heat conductivity on distributed memory computational systems (CS), satisfying the condition of numerical result independence from the number of processors involved. Two basically different approaches to the structure of massive parallel computations have been developed. The first approach uses the 3D data matrix decomposition reconstructed at temporal cycle and is a development of parallelization algorithms for multiprocessor CS with shareable memory. The second approach is based on using a 3D data matrix decomposition not reconstructed during a temporal cycle.more » The program was developed on 8-processor CS MP-3 made in VNIIEF and was adapted to a massive parallel CS Meiko-2 in LLNL by joint efforts of VNIIEF and LLNL staffs. A large number of numerical experiments has been carried out with different number of processors up to 256 and the efficiency of parallelization has been evaluated in dependence on processor number and their parameters.« less

An efficient numerical model for multicomponent compressible flow in fractured porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2014-12-01

An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant-Freidricks-Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20-130 times in 2D. In 3D, one may expect even a higher computational efficiency.

Reliability-Based Control Design for Uncertain Systems

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.

2005-01-01

This paper presents a robust control design methodology for systems with probabilistic parametric uncertainty. Control design is carried out by solving a reliability-based multi-objective optimization problem where the probability of violating design requirements is minimized. Simultaneously, failure domains are optimally enlarged to enable global improvements in the closed-loop performance. To enable an efficient numerical implementation, a hybrid approach for estimating reliability metrics is developed. This approach, which integrates deterministic sampling and asymptotic approximations, greatly reduces the numerical burden associated with complex probabilistic computations without compromising the accuracy of the results. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Multi-dimensional upwinding-based implicit LES for the vorticity transport equations

NASA Astrophysics Data System (ADS)

Foti, Daniel; Duraisamy, Karthik

2017-11-01

Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.

Computational methods for reactive transport modeling: A Gibbs energy minimization approach for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg

2016-02-01

We present a numerical method for multiphase chemical equilibrium calculations based on a Gibbs energy minimization approach. The method can accurately and efficiently determine the stable phase assemblage at equilibrium independently of the type of phases and species that constitute the chemical system. We have successfully applied our chemical equilibrium algorithm in reactive transport simulations to demonstrate its effective use in computationally intensive applications. We used FEniCS to solve the governing partial differential equations of mass transport in porous media using finite element methods in unstructured meshes. Our equilibrium calculations were benchmarked with GEMS3K, the numerical kernel of the geochemical package GEMS. This allowed us to compare our results with a well-established Gibbs energy minimization algorithm, as well as their performance on every mesh node, at every time step of the transport simulation. The benchmark shows that our novel chemical equilibrium algorithm is accurate, robust, and efficient for reactive transport applications, and it is an improvement over the Gibbs energy minimization algorithm used in GEMS3K. The proposed chemical equilibrium method has been implemented in Reaktoro, a unified framework for modeling chemically reactive systems, which is now used as an alternative numerical kernel of GEMS.

Numerical Comparison of Nasal Aerosol Administration Systems for Efficient Nose-to-Brain Drug Delivery.

PubMed

Dong, Jingliang; Shang, Yidan; Inthavong, Kiao; Chan, Hak-Kim; Tu, Jiyuan

2017-12-29

Nose-to-brain drug administration along the olfactory and trigeminal nerve pathways offers an alternative route for the treatment of central nervous system (CNS) disorders. The characterization of particle deposition remains difficult to achieve in experiments. Alternative numerical approach is applied to identify suitable aerosol particle size with maximized inhaled doses. This study numerically compared the drug delivery efficiency in a realistic human nasal cavity between two aerosol drug administration systems targeting the olfactory region: the aerosol mask system and the breath-powered bi-directional system. Steady inhalation and exhalation flow rates were applied to both delivery systems. The discrete phase particle tracking method was employed to capture the aerosol drug transport and deposition behaviours in the nasal cavity. Both overall and regional deposition characteristics were analysed in detail. The results demonstrated the breath-powered drug delivery approach can produce superior olfactory deposition with peaking olfactory deposition fractions for diffusive 1 nm particles and inertial 10 μm. While for particles in the range of 10 nm to 2 μm, no significant olfactory deposition can be found, indicating the therapeutic agents should avoid this size range when targeting the olfactory deposition. The breath-powered bi-directional aerosol delivery approach shows better drug delivery performance globally and locally, and improved drug administration doses can be achieved in targeted olfactory region.

ADVANCED COMPUTATIONAL METHODS IN DOSE MODELING: APPLICATION OF COMPUTATIONAL BIOPHYSICAL TRANSPORT, COMPUTATIONAL CHEMISTRY, AND COMPUTATIONAL BIOLOGY

EPA Science Inventory

Computational toxicology (CompTox) leverages the significant gains in computing power and computational techniques (e.g., numerical approaches, structure-activity relationships, bioinformatics) realized over the last few years, thereby reducing costs and increasing efficiency i...

Improved Filon-type asymptotic methods for highly oscillatory differential equations with multiple time scales

NASA Astrophysics Data System (ADS)

Wang, Bin; Wu, Xinyuan

2014-11-01

In this paper we consider multi-frequency highly oscillatory second-order differential equations x″ (t) + Mx (t) = f (t , x (t) ,x‧ (t)) where high-frequency oscillations are generated by the linear part Mx (t), and M is positive semi-definite (not necessarily nonsingular). It is known that Filon-type methods are effective approach to numerically solving highly oscillatory problems. Unfortunately, however, existing Filon-type asymptotic methods fail to apply to the highly oscillatory second-order differential equations when M is singular. We study and propose an efficient improvement on the existing Filon-type asymptotic methods, so that the improved Filon-type asymptotic methods can be able to numerically solving this class of multi-frequency highly oscillatory systems with a singular matrix M. The improved Filon-type asymptotic methods are designed by combining Filon-type methods with the asymptotic methods based on the variation-of-constants formula. We also present one efficient and practical improved Filon-type asymptotic method which can be performed at lower cost. Accompanying numerical results show the remarkable efficiency.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

PubMed Central

Cilfone, Nicholas A.; Kirschner, Denise E.; Linderman, Jennifer J.

2015-01-01

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level. PMID:26366228

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

NASA Astrophysics Data System (ADS)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

NASA Astrophysics Data System (ADS)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

Structured Overlapping Grid Simulations of Contra-rotating Open Rotor Noise

NASA Technical Reports Server (NTRS)

Housman, Jeffrey A.; Kiris, Cetin C.

2015-01-01

Computational simulations using structured overlapping grids with the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for predicting tonal noise generated by a contra-rotating open rotor (CROR) propulsion system. A coupled Computational Fluid Dynamics (CFD) and Computational AeroAcoustics (CAA) numerical approach is applied. Three-dimensional time-accurate hybrid Reynolds Averaged Navier-Stokes/Large Eddy Simulation (RANS/LES) CFD simulations are performed in the inertial frame, including dynamic moving grids, using a higher-order accurate finite difference discretization on structured overlapping grids. A higher-order accurate free-stream preserving metric discretization with discrete enforcement of the Geometric Conservation Law (GCL) on moving curvilinear grids is used to create an accurate, efficient, and stable numerical scheme. The aeroacoustic analysis is based on a permeable surface Ffowcs Williams-Hawkings (FW-H) approach, evaluated in the frequency domain. A time-step sensitivity study was performed using only the forward row of blades to determine an adequate time-step. The numerical approach is validated against existing wind tunnel measurements.

A heuristic approach using multiple criteria for environmentally benign 3PLs selection

NASA Astrophysics Data System (ADS)

Kongar, Elif

2005-11-01

Maintaining competitiveness in an environment where price and quality differences between competing products are disappearing depends on the company's ability to reduce costs and supply time. Timely responses to rapidly changing market conditions require an efficient Supply Chain Management (SCM). Outsourcing logistics to third-party logistics service providers (3PLs) is one commonly used way of increasing the efficiency of logistics operations, while creating a more "core competency focused" business environment. However, this alone may not be sufficient. Due to recent environmental regulations and growing public awareness regarding environmental issues, 3PLs need to be not only efficient but also environmentally benign to maintain companies' competitiveness. Even though an efficient and environmentally benign combination of 3PLs can theoretically be obtained using exhaustive search algorithms, heuristics approaches to the selection process may be superior in terms of the computational complexity. In this paper, a hybrid approach that combines a multiple criteria Genetic Algorithm (GA) with Linear Physical Weighting Algorithm (LPPW) to be used in efficient and environmentally benign 3PLs is proposed. A numerical example is also provided to illustrate the method and the analyses.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

Adaptive [theta]-methods for pricing American options

NASA Astrophysics Data System (ADS)

Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran

2008-12-01

We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.

Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

PubMed Central

Bruno, Oscar P.; Turc, Catalin; Venakides, Stephanos

2016-01-01

This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach. PMID:27493573

Modelling radionuclide transport in fractured media with a dynamic update of K d values

DOE PAGES

Trinchero, Paolo; Painter, Scott L.; Ebrahimi, Hedieh; ...

2015-10-13

Radionuclide transport in fractured crystalline rocks is a process of interest in evaluating long term safety of potential disposal systems for radioactive wastes. Given their numerical efficiency and the absence of numerical dispersion, Lagrangian methods (e.g. particle tracking algorithms) are appealing approaches that are often used in safety assessment (SA) analyses. In these approaches, many complex geochemical retention processes are typically lumped into a single parameter: the distribution coefficient (Kd). Usually, the distribution coefficient is assumed to be constant over the time frame of interest. However, this assumption could be critical under long-term geochemical changes as it is demonstrated thatmore » the distribution coefficient depends on the background chemical conditions (e.g. pH, Eh, and major chemistry). In this study, we provide a computational framework that combines the efficiency of Lagrangian methods with a sound and explicit description of the geochemical changes of the site and their influence on the radionuclide retention properties.« less

An efficient multi-dimensional implementation of VSIAM3 and its applications to free surface flows

NASA Astrophysics Data System (ADS)

Yokoi, Kensuke; Furuichi, Mikito; Sakai, Mikio

2017-12-01

We propose an efficient multidimensional implementation of VSIAM3 (volume/surface integrated average-based multi-moment method). Although VSIAM3 is a highly capable fluid solver based on a multi-moment concept and has been used for a wide variety of fluid problems, VSIAM3 could not simulate some simple benchmark problems well (for instance, lid-driven cavity flows) due to relatively high numerical viscosity. In this paper, we resolve the issue by using the efficient multidimensional approach. The proposed VSIAM3 is shown to capture lid-driven cavity flows of the Reynolds number up to Re = 7500 with a Cartesian grid of 128 × 128, which was not capable for the original VSIAM3. We also tested the proposed framework in free surface flow problems (droplet collision and separation of We = 40 and droplet splashing on a superhydrophobic substrate). The numerical results by the proposed VSIAM3 showed reasonable agreements with these experiments. The proposed VSIAM3 could capture droplet collision and separation of We = 40 with a low numerical resolution (8 meshes for the initial diameter of droplets). We also simulated free surface flows including particles toward non-Newtonian flow applications. These numerical results have showed that the proposed VSIAM3 can robustly simulate interactions among air, particles (solid), and liquid.

Directional Slack-Based Measure for the Inverse Data Envelopment Analysis

PubMed Central

Abu Bakar, Mohd Rizam; Lee, Lai Soon; Jaafar, Azmi B.; Heydar, Maryam

2014-01-01

A novel technique has been introduced in this research which lends its basis to the Directional Slack-Based Measure for the inverse Data Envelopment Analysis. In practice, the current research endeavors to elucidate the inverse directional slack-based measure model within a new production possibility set. On one occasion, there is a modification imposed on the output (input) quantities of an efficient decision making unit. In detail, the efficient decision making unit in this method was omitted from the present production possibility set but substituted by the considered efficient decision making unit while its input and output quantities were subsequently modified. The efficiency score of the entire DMUs will be retained in this approach. Also, there would be an improvement in the efficiency score. The proposed approach was investigated in this study with reference to a resource allocation problem. It is possible to simultaneously consider any upsurges (declines) of certain outputs associated with the efficient decision making unit. The significance of the represented model is accentuated by presenting numerical examples. PMID:24883350

A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1976-01-01

The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

Efficient numerical method of freeform lens design for arbitrary irradiance shaping

NASA Astrophysics Data System (ADS)

Wojtanowski, Jacek

2018-05-01

A computational method to design a lens with a flat entrance surface and a freeform exit surface that can transform a collimated, generally non-uniform input beam into a beam with a desired irradiance distribution of arbitrary shape is presented. The methodology is based on non-linear elliptic partial differential equations, known as Monge-Ampère PDEs. This paper describes an original numerical algorithm to solve this problem by applying the Gauss-Seidel method with simplified boundary conditions. A joint MATLAB-ZEMAX environment is used to implement and verify the method. To prove the efficiency of the proposed approach, an exemplary study where the designed lens is faced with the challenging illumination task is shown. An analysis of solution stability, iteration-to-iteration ray mapping evolution (attached in video format), depth of focus and non-zero étendue efficiency is performed.

Cost-of-illness studies based on massive data: a prevalence-based, top-down regression approach.

PubMed

Stollenwerk, Björn; Welchowski, Thomas; Vogl, Matthias; Stock, Stephanie

2016-04-01

Despite the increasing availability of routine data, no analysis method has yet been presented for cost-of-illness (COI) studies based on massive data. We aim, first, to present such a method and, second, to assess the relevance of the associated gain in numerical efficiency. We propose a prevalence-based, top-down regression approach consisting of five steps: aggregating the data; fitting a generalized additive model (GAM); predicting costs via the fitted GAM; comparing predicted costs between prevalent and non-prevalent subjects; and quantifying the stochastic uncertainty via error propagation. To demonstrate the method, it was applied to aggregated data in the context of chronic lung disease to German sickness funds data (from 1999), covering over 7.3 million insured. To assess the gain in numerical efficiency, the computational time of the innovative approach has been compared with corresponding GAMs applied to simulated individual-level data. Furthermore, the probability of model failure was modeled via logistic regression. Applying the innovative method was reasonably fast (19 min). In contrast, regarding patient-level data, computational time increased disproportionately by sample size. Furthermore, using patient-level data was accompanied by a substantial risk of model failure (about 80 % for 6 million subjects). The gain in computational efficiency of the innovative COI method seems to be of practical relevance. Furthermore, it may yield more precise cost estimates.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

NASA Astrophysics Data System (ADS)

Grenier, Christophe; Anbergen, Hauke; Bense, Victor; Chanzy, Quentin; Coon, Ethan; Collier, Nathaniel; Costard, François; Ferry, Michel; Frampton, Andrew; Frederick, Jennifer; Gonçalvès, Julio; Holmén, Johann; Jost, Anne; Kokh, Samuel; Kurylyk, Barret; McKenzie, Jeffrey; Molson, John; Mouche, Emmanuel; Orgogozo, Laurent; Pannetier, Romain; Rivière, Agnès; Roux, Nicolas; Rühaak, Wolfram; Scheidegger, Johanna; Selroos, Jan-Olof; Therrien, René; Vidstrand, Patrik; Voss, Clifford

2018-04-01

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. This issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatial and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution ofmore » dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.« less

Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Havu, V.; Fritz Haber Institute of the Max Planck Society, Berlin; Blum, V.

2009-12-01

We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as themore » more rigorous bottom-up approaches.« less

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

NASA Astrophysics Data System (ADS)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Numerical simulation of deformation and failure processes of a complex technical object under impact loading

NASA Astrophysics Data System (ADS)

Kraus, E. I.; Shabalin, I. I.; Shabalin, T. I.

2018-04-01

The main points of development of numerical tools for simulation of deformation and failure of complex technical objects under nonstationary conditions of extreme loading are presented. The possibility of extending the dynamic method for construction of difference grids to the 3D case is shown. A 3D realization of discrete-continuum approach to the deformation and failure of complex technical objects is carried out. The efficiency of the existing software package for 3D modelling is shown.

Propagation of diffuse light in a turbid medium with multiple spherical inhomogeneities.

PubMed

Pustovit, Vitaliy N; Markel, Vadim A

2004-01-01

We develop a fast and accurate solver for the forward problem of diffusion tomography in the case of several spherical inhomogeneities. The approach allows one to take into account multiple scattering of diffuse waves between different inhomogeneities. Theoretical results are illustrated with numerical examples; excellent numerical convergence and efficiency are demonstrated. The method is generalized for the case of additional planar diffuse-nondiffuse interfaces and is therefore applicable to the half-space and slab imaging geometries.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

Heat transfer of phase-change materials in two-dimensional cylindrical coordinates

NASA Technical Reports Server (NTRS)

Labdon, M. B.; Guceri, S. I.

1981-01-01

Two-dimensional phase-change problem is numerically solved in cylindrical coordinates (r and z) by utilizing two Taylor series expansions for the temperature distributions in the neighborhood of the interface location. These two expansions form two polynomials in r and z directions. For the regions sufficiently away from the interface the temperature field equations are numerically solved in the usual way and the results are coupled with the polynomials. The main advantages of this efficient approach include ability to accept arbitrarily time dependent boundary conditions of all types and arbitrarily specified initial temperature distributions. A modified approach using a single Taylor series expansion in two variables is also suggested.

A highly efficient approach to protein interactome mapping based on collaborative filtering framework.

PubMed

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-09

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

PubMed Central

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly. PMID:25572661

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

NASA Astrophysics Data System (ADS)

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

AN INTEGRAL EQUATION REPRESENTATION OF WIDE-BAND ELECTROMAGNETIC SCATTERING BY THIN SHEETS

EPA Science Inventory

An efficient, accurate numerical modeling scheme has been developed, based on the integral equation solution to compute electromagnetic (EM) responses of thin sheets over a wide frequency band. The thin-sheet approach is useful for simulating the EM response of a fracture system ...

A non-linear steady state characteristic performance curve for medium temperature solar energy collectors

NASA Astrophysics Data System (ADS)

Eames, P. C.; Norton, B.

A numerical simulation model was employed to investigate the effects of ambient temperature and insolation on the efficiency of compound parabolic concentrating solar energy collectors. The limitations of presently-used collector performance characterization curves were investigated and a new approach proposed.

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.; Leser, William P.; Leser, Patrick E.; Newman, John A

2016-01-01

This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.

Spectrum splitting using multi-layer dielectric meta-surfaces for efficient solar energy harvesting

NASA Astrophysics Data System (ADS)

Yao, Yuhan; Liu, He; Wu, Wei

2014-06-01

We designed a high-efficiency dispersive mirror based on multi-layer dielectric meta-surfaces. By replacing the secondary mirror of a dome solar concentrator with this dispersive mirror, the solar concentrator can be converted into a spectrum-splitting photovoltaic system with higher energy harvesting efficiency and potentially lower cost. The meta-surfaces are consisted of high-index contrast gratings (HCG). The structures and parameters of the dispersive mirror (i.e. stacked HCG) are optimized based on finite-difference time-domain and rigorous coupled-wave analysis method. Our numerical study shows that the dispersive mirror can direct light with different wavelengths into different angles in the entire solar spectrum, maintaining very low energy loss. Our approach will not only improve the energy harvesting efficiency, but also lower the cost by using single junction cells instead of multi-layer tandem solar cells. Moreover, this approach has the minimal disruption to the existing solar concentrator infrastructures.

Efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber laser.

PubMed

Wang, P; Cooper, L J; Sahu, J K; Clarkson, W A

2006-01-15

A novel approach to achieving robust single-spatial-mode operation of cladding-pumped fiber lasers with multimode cores is reported. The approach is based on the use of a fiber geometry in which the core has a helical trajectory within the inner cladding to suppress laser oscillation on higher-order modes. In a preliminary proof-of-principle study, efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber laser with a 30 microm diameter core and a numerical aperture of 0.087 has been demonstrated. The laser yielded 60.4 W of output at 1043 nm in a beam with M2 < 1.4 for 92.6 W launched pump power from a diode stack at 976 nm. The slope efficiency at pump powers well above threshold was approximately 84%, which compares favorably with the slope efficiencies achievable with conventional straight-core Yb-doped double-clad fiber lasers.

Application of identified sensitive physical parameters in reducing the uncertainty of numerical simulation

NASA Astrophysics Data System (ADS)

Sun, Guodong; Mu, Mu

2016-04-01

An important source of uncertainty, which then causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. There are many physical parameters in numerical models in the atmospheric and oceanic sciences, and it would cost a great deal to reduce uncertainties in all physical parameters. Therefore, finding a subset of these parameters, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach. The results imply that nonlinear interactions among parameters play a key role in the uncertainty of numerical simulations in arid and semi-arid regions of China compared to those in northern, northeastern and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method

NASA Astrophysics Data System (ADS)

Zhang, Hong; Zegeling, Paul Andries

2017-09-01

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow in porous media incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behavior. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.

Reactive transport modeling in the subsurface environment with OGS-IPhreeqc

NASA Astrophysics Data System (ADS)

He, Wenkui; Beyer, Christof; Fleckenstein, Jan; Jang, Eunseon; Kalbacher, Thomas; Naumov, Dimitri; Shao, Haibing; Wang, Wenqing; Kolditz, Olaf

2015-04-01

Worldwide, sustainable water resource management becomes an increasingly challenging task due to the growth of population and extensive applications of fertilizer in agriculture. Moreover, climate change causes further stresses to both water quantity and quality. Reactive transport modeling in the coupled soil-aquifer system is a viable approach to assess the impacts of different land use and groundwater exploitation scenarios on the water resources. However, the application of this approach is usually limited in spatial scale and to simplified geochemical systems due to the huge computational expense involved. Such computational expense is not only caused by solving the high non-linearity of the initial boundary value problems of water flow in the unsaturated zone numerically with rather fine spatial and temporal discretization for the correct mass balance and numerical stability, but also by the intensive computational task of quantifying geochemical reactions. In the present study, a flexible and efficient tool for large scale reactive transport modeling in variably saturated porous media and its applications are presented. The open source scientific software OpenGeoSys (OGS) is coupled with the IPhreeqc module of the geochemical solver PHREEQC. The new coupling approach makes full use of advantages from both codes: OGS provides a flexible choice of different numerical approaches for simulation of water flow in the vadose zone such as the pressure-based or mixed forms of Richards equation; whereas the IPhreeqc module leads to a simplification of data storage and its communication with OGS, which greatly facilitates the coupling and code updating. Moreover, a parallelization scheme with MPI (Message Passing Interface) is applied, in which the computational task of water flow and mass transport is partitioned through domain decomposition, whereas the efficient parallelization of geochemical reactions is achieved by smart allocation of computational workload over multiple compute nodes. The plausibility of the new coupling is verified by several benchmark tests. In addition, the efficiency of the new coupling approach is demonstrated by its application in a large scale scenario, in which the environmental fate of pesticides in a complex soil-aquifer system is studied.

Reactive transport modeling in variably saturated porous media with OGS-IPhreeqc

NASA Astrophysics Data System (ADS)

He, W.; Beyer, C.; Fleckenstein, J. H.; Jang, E.; Kalbacher, T.; Shao, H.; Wang, W.; Kolditz, O.

2014-12-01

Worldwide, sustainable water resource management becomes an increasingly challenging task due to the growth of population and extensive applications of fertilizer in agriculture. Moreover, climate change causes further stresses to both water quantity and quality. Reactive transport modeling in the coupled soil-aquifer system is a viable approach to assess the impacts of different land use and groundwater exploitation scenarios on the water resources. However, the application of this approach is usually limited in spatial scale and to simplified geochemical systems due to the huge computational expense involved. Such computational expense is not only caused by solving the high non-linearity of the initial boundary value problems of water flow in the unsaturated zone numerically with rather fine spatial and temporal discretization for the correct mass balance and numerical stability, but also by the intensive computational task of quantifying geochemical reactions. In the present study, a flexible and efficient tool for large scale reactive transport modeling in variably saturated porous media and its applications are presented. The open source scientific software OpenGeoSys (OGS) is coupled with the IPhreeqc module of the geochemical solver PHREEQC. The new coupling approach makes full use of advantages from both codes: OGS provides a flexible choice of different numerical approaches for simulation of water flow in the vadose zone such as the pressure-based or mixed forms of Richards equation; whereas the IPhreeqc module leads to a simplification of data storage and its communication with OGS, which greatly facilitates the coupling and code updating. Moreover, a parallelization scheme with MPI (Message Passing Interface) is applied, in which the computational task of water flow and mass transport is partitioned through domain decomposition, whereas the efficient parallelization of geochemical reactions is achieved by smart allocation of computational workload over multiple compute nodes. The plausibility of the new coupling is verified by several benchmark tests. In addition, the efficiency of the new coupling approach is demonstrated by its application in a large scale scenario, in which the environmental fate of pesticides in a complex soil-aquifer system is studied.

DNS of Low-Pressure Turbine Cascade Flows with Elevated Inflow Turbulence Using a Discontinuous-Galerkin Spectral-Element Method

NASA Technical Reports Server (NTRS)

Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.

2016-01-01

Recent progress towards developing a new computational capability for accurate and efficient high-fidelity direct numerical simulation (DNS) and large-eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy- stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in a computationally efficient manner on a modern high performance computer architecture. An inflow turbulence generation procedure based on a linear forcing approach has been incorporated in this framework and DNS conducted to study the effect of inflow turbulence on the suction- side separation bubble in low-pressure turbine (LPT) cascades. The T106 series of airfoil cascades in both lightly (T106A) and highly loaded (T106C) configurations at exit isentropic Reynolds numbers of 60,000 and 80,000, respectively, are considered. The numerical simulations are performed using 8th-order accurate spatial and 4th-order accurate temporal discretization. The changes in separation bubble topology due to elevated inflow turbulence is captured by the present method and the physical mechanisms leading to the changes are explained. The present results are in good agreement with prior numerical simulations but some expected discrepancies with the experimental data for the T106C case are noted and discussed.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Simulation-Based Approach to Determining Electron Transfer Rates Using Square-Wave Voltammetry.

PubMed

Dauphin-Ducharme, Philippe; Arroyo-Currás, Netzahualcóyotl; Kurnik, Martin; Ortega, Gabriel; Li, Hui; Plaxco, Kevin W

2017-05-09

The efficiency with which square-wave voltammetry differentiates faradic and charging currents makes it a particularly sensitive electroanalytical approach, as evidenced by its ability to measure nanomolar or even picomolar concentrations of electroactive analytes. Because of the relative complexity of the potential sweep it uses, however, the extraction of detailed kinetic and mechanistic information from square-wave data remains challenging. In response, we demonstrate here a numerical approach by which square-wave data can be used to determine electron transfer rates. Specifically, we have developed a numerical approach in which we model the height and the shape of voltammograms collected over a range of square-wave frequencies and amplitudes to simulated voltammograms as functions of the heterogeneous rate constant and the electron transfer coefficient. As validation of the approach, we have used it to determine electron transfer kinetics in both freely diffusing and diffusionless surface-tethered species, obtaining electron transfer kinetics in all cases in good agreement with values derived using non-square-wave methods.

Irreversible Brownian Heat Engine

NASA Astrophysics Data System (ADS)

Taye, Mesfin Asfaw

2017-10-01

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4}. It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.

An indirect approach to the extensive calculation of relationship coefficients

PubMed Central

Colleau, Jean-Jacques

2002-01-01

A method was described for calculating population statistics on relationship coefficients without using corresponding individual data. It relied on the structure of the inverse of the numerator relationship matrix between individuals under investigation and ancestors. Computation times were observed on simulated populations and were compared to those incurred with a conventional direct approach. The indirect approach turned out to be very efficient for multiplying the relationship matrix corresponding to planned matings (full design) by any vector. Efficiency was generally still good or very good for calculating statistics on these simulated populations. An extreme implementation of the method is the calculation of inbreeding coefficients themselves. Relative performances of the indirect method were good except when many full-sibs during many generations existed in the population. PMID:12270102

Improved transition path sampling methods for simulation of rare events

NASA Astrophysics Data System (ADS)

Chopra, Manan; Malshe, Rohit; Reddy, Allam S.; de Pablo, J. J.

2008-04-01

The free energy surfaces of a wide variety of systems encountered in physics, chemistry, and biology are characterized by the existence of deep minima separated by numerous barriers. One of the central aims of recent research in computational chemistry and physics has been to determine how transitions occur between deep local minima on rugged free energy landscapes, and transition path sampling (TPS) Monte-Carlo methods have emerged as an effective means for numerical investigation of such transitions. Many of the shortcomings of TPS-like approaches generally stem from their high computational demands. Two new algorithms are presented in this work that improve the efficiency of TPS simulations. The first algorithm uses biased shooting moves to render the sampling of reactive trajectories more efficient. The second algorithm is shown to substantially improve the accuracy of the transition state ensemble by introducing a subset of local transition path simulations in the transition state. The system considered in this work consists of a two-dimensional rough energy surface that is representative of numerous systems encountered in applications. When taken together, these algorithms provide gains in efficiency of over two orders of magnitude when compared to traditional TPS simulations.

Numerical dissipation vs. subgrid-scale modelling for large eddy simulation

NASA Astrophysics Data System (ADS)

Dairay, Thibault; Lamballais, Eric; Laizet, Sylvain; Vassilicos, John Christos

2017-05-01

This study presents an alternative way to perform large eddy simulation based on a targeted numerical dissipation introduced by the discretization of the viscous term. It is shown that this regularisation technique is equivalent to the use of spectral vanishing viscosity. The flexibility of the method ensures high-order accuracy while controlling the level and spectral features of this purely numerical viscosity. A Pao-like spectral closure based on physical arguments is used to scale this numerical viscosity a priori. It is shown that this way of approaching large eddy simulation is more efficient and accurate than the use of the very popular Smagorinsky model in standard as well as in dynamic version. The main strength of being able to correctly calibrate numerical dissipation is the possibility to regularise the solution at the mesh scale. Thanks to this property, it is shown that the solution can be seen as numerically converged. Conversely, the two versions of the Smagorinsky model are found unable to ensure regularisation while showing a strong sensitivity to numerical errors. The originality of the present approach is that it can be viewed as implicit large eddy simulation, in the sense that the numerical error is the source of artificial dissipation, but also as explicit subgrid-scale modelling, because of the equivalence with spectral viscosity prescribed on a physical basis.

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

Computationally efficient method for optical simulation of solar cells and their applications

NASA Astrophysics Data System (ADS)

Semenikhin, I.; Zanuccoli, M.; Fiegna, C.; Vyurkov, V.; Sangiorgi, E.

2013-01-01

This paper presents two novel implementations of the Differential method to solve the Maxwell equations in nanostructured optoelectronic solid state devices. The first proposed implementation is based on an improved and computationally efficient T-matrix formulation that adopts multiple-precision arithmetic to tackle the numerical instability problem which arises due to evanescent modes. The second implementation adopts the iterative approach that allows to achieve low computational complexity O(N logN) or better. The proposed algorithms may work with structures with arbitrary spatial variation of the permittivity. The developed two-dimensional numerical simulator is applied to analyze the dependence of the absorption characteristics of a thin silicon slab on the morphology of the front interface and on the angle of incidence of the radiation with respect to the device surface.

Efficient dynamic modeling of manipulators containing closed kinematic loops

NASA Astrophysics Data System (ADS)

Ferretti, Gianni; Rocco, Paolo

An approach to efficiently solve the forward dynamics problem for manipulators containing closed chains is proposed. The two main distinctive features of this approach are: the dynamics of the equivalent open loop tree structures (any closed loop can be in general modeled by imposing some additional kinematic constraints to a suitable tree structure) is computed through an efficient Newton Euler formulation; the constraint equations relative to the most commonly adopted closed chains in industrial manipulators are explicitly solved, thus, overcoming the redundancy of Lagrange's multipliers method while avoiding the inefficiency due to a numerical solution of the implicit constraint equations. The constraint equations considered for an explicit solution are those imposed by articulated gear mechanisms and planar closed chains (pantograph type structures). Articulated gear mechanisms are actually used in all industrial robots to transmit motion from actuators to links, while planar closed chains are usefully employed to increase the stiffness of the manipulators and their load capacity, as well to reduce the kinematic coupling of joint axes. The accuracy and the efficiency of the proposed approach are shown through a simulation test.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

All-optical nanomechanical heat engine.

PubMed

Dechant, Andreas; Kiesel, Nikolai; Lutz, Eric

2015-05-08

We propose and theoretically investigate a nanomechanical heat engine. We show how a levitated nanoparticle in an optical trap inside a cavity can be used to realize a Stirling cycle in the underdamped regime. The all-optical approach enables fast and flexible control of all thermodynamical parameters and the efficient optimization of the performance of the engine. We develop a systematic optimization procedure to determine optimal driving protocols. Further, we perform numerical simulations with realistic parameters and evaluate the maximum power and the corresponding efficiency.

All-Optical Nanomechanical Heat Engine

NASA Astrophysics Data System (ADS)

Dechant, Andreas; Kiesel, Nikolai; Lutz, Eric

2015-05-01

We propose and theoretically investigate a nanomechanical heat engine. We show how a levitated nanoparticle in an optical trap inside a cavity can be used to realize a Stirling cycle in the underdamped regime. The all-optical approach enables fast and flexible control of all thermodynamical parameters and the efficient optimization of the performance of the engine. We develop a systematic optimization procedure to determine optimal driving protocols. Further, we perform numerical simulations with realistic parameters and evaluate the maximum power and the corresponding efficiency.

Prediction of daily sea surface temperature using efficient neural networks

NASA Astrophysics Data System (ADS)

Patil, Kalpesh; Deo, Makaranad Chintamani

2017-04-01

Short-term prediction of sea surface temperature (SST) is commonly achieved through numerical models. Numerical approaches are more suitable for use over a large spatial domain than in a specific site because of the difficulties involved in resolving various physical sub-processes at local levels. Therefore, for a given location, a data-driven approach such as neural networks may provide a better alternative. The application of neural networks, however, needs a large experimentation in their architecture, training methods, and formation of appropriate input-output pairs. A network trained in this manner can provide more attractive results if the advances in network architecture are additionally considered. With this in mind, we propose the use of wavelet neural networks (WNNs) for prediction of daily SST values. The prediction of daily SST values was carried out using WNN over 5 days into the future at six different locations in the Indian Ocean. First, the accuracy of site-specific SST values predicted by a numerical model, ROMS, was assessed against the in situ records. The result pointed out the necessity for alternative approaches. First, traditional networks were tried and after noticing their poor performance, WNN was used. This approach produced attractive forecasts when judged through various error statistics. When all locations were viewed together, the mean absolute error was within 0.18 to 0.32 °C for a 5-day-ahead forecast. The WNN approach was thus found to add value to the numerical method of SST prediction when location-specific information is desired.

Characterization of Meta-Materials Using Computational Electromagnetic Methods

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Shin, Joon

2005-01-01

An efficient and powerful computational method is presented to synthesize a meta-material to specified electromagnetic properties. Using the periodicity of meta-materials, the Finite Element Methodology (FEM) is developed to estimate the reflection and transmission through the meta-material structure for a normal plane wave incidence. For efficient computations of the reflection and transmission over a wide band frequency range through a meta-material a Finite Difference Time Domain (FDTD) approach is also developed. Using the Nicholson-Ross method and the Genetic Algorithms, a robust procedure to extract electromagnetic properties of meta-material from the knowledge of its reflection and transmission coefficients is described. Few numerical examples are also presented to validate the present approach.

Wave steering effects in anisotropic composite structures: Direct calculation of the energy skew angle through a finite element scheme.

PubMed

Chronopoulos, D

2017-01-01

A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors. Copyright © 2016 Elsevier B.V. All rights reserved.

AN EFFICIENT HIGHER-ORDER FAST MULTIPOLE BOUNDARY ELEMENT SOLUTION FOR POISSON-BOLTZMANN BASED MOLECULAR ELECTROSTATICS

PubMed Central

Bajaj, Chandrajit; Chen, Shun-Chuan; Rand, Alexander

2011-01-01

In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy. PMID:21660123

Estimation of cardiac conductivities in ventricular tissue by a variational approach

NASA Astrophysics Data System (ADS)

Yang, Huanhuan; Veneziani, Alessandro

2015-11-01

The bidomain model is the current standard model to simulate cardiac potential propagation. The numerical solution of this system of partial differential equations strongly depends on the model parameters and in particular on the cardiac conductivities. Unfortunately, it is quite problematic to measure these parameters in vivo and even more so in clinical practice, resulting in no common agreement in the literature. In this paper we consider a variational data assimilation approach to estimating those parameters. We consider the parameters as control variables to minimize the mismatch between the computed and the measured potentials under the constraint of the bidomain system. The existence of a minimizer of the misfit function is proved with the phenomenological Rogers-McCulloch ionic model, that completes the bidomain system. We significantly improve the numerical approaches in the literature by resorting to a derivative-based optimization method with settlement of some challenges due to discontinuity. The improvement in computational efficiency is confirmed by a 2D test as a direct comparison with approaches in the literature. The core of our numerical results is in 3D, on both idealized and real geometries, with the minimal ionic model. We demonstrate the reliability and the stability of the conductivity estimation approach in the presence of noise and with an imperfect knowledge of other model parameters.

Multi-rendezvous low-thrust trajectory optimization using costate transforming and homotopic approach

NASA Astrophysics Data System (ADS)

Chen, Shiyu; Li, Haiyang; Baoyin, Hexi

2018-06-01

This paper investigates a method for optimizing multi-rendezvous low-thrust trajectories using indirect methods. An efficient technique, labeled costate transforming, is proposed to optimize multiple trajectory legs simultaneously rather than optimizing each trajectory leg individually. Complex inner-point constraints and a large number of free variables are one main challenge in optimizing multi-leg transfers via shooting algorithms. Such a difficulty is reduced by first optimizing each trajectory leg individually. The results may be, next, utilized as an initial guess in the simultaneous optimization of multiple trajectory legs. In this paper, the limitations of similar techniques in previous research is surpassed and a homotopic approach is employed to improve the convergence efficiency of the shooting process in multi-rendezvous low-thrust trajectory optimization. Numerical examples demonstrate that newly introduced techniques are valid and efficient.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Zeng, Lingzao; Chen, Cheng; Chen, Dingjiang; Wu, Laosheng

2015-01-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

Leveraging Gibbs Ensemble Molecular Dynamics and Hybrid Monte Carlo/Molecular Dynamics for Efficient Study of Phase Equilibria.

PubMed

Gartner, Thomas E; Epps, Thomas H; Jayaraman, Arthi

2016-11-08

We describe an extension of the Gibbs ensemble molecular dynamics (GEMD) method for studying phase equilibria. Our modifications to GEMD allow for direct control over particle transfer between phases and improve the method's numerical stability. Additionally, we found that the modified GEMD approach had advantages in computational efficiency in comparison to a hybrid Monte Carlo (MC)/MD Gibbs ensemble scheme in the context of the single component Lennard-Jones fluid. We note that this increase in computational efficiency does not compromise the close agreement of phase equilibrium results between the two methods. However, numerical instabilities in the GEMD scheme hamper GEMD's use near the critical point. We propose that the computationally efficient GEMD simulations can be used to map out the majority of the phase window, with hybrid MC/MD used as a follow up for conditions under which GEMD may be unstable (e.g., near-critical behavior). In this manner, we can capitalize on the contrasting strengths of these two methods to enable the efficient study of phase equilibria for systems that present challenges for a purely stochastic GEMC method, such as dense or low temperature systems, and/or those with complex molecular topologies.

Moving microphone arrays to reduce spatial aliasing in the beamforming technique: theoretical background and numerical investigation.

PubMed

Cigada, Alfredo; Lurati, Massimiliano; Ripamonti, Francesco; Vanali, Marcello

2008-12-01

This paper introduces a measurement technique aimed at reducing or possibly eliminating the spatial aliasing problem in the beamforming technique. Beamforming main disadvantages are a poor spatial resolution, at low frequency, and the spatial aliasing problem, at higher frequency, leading to the identification of false sources. The idea is to move the microphone array during the measurement operation. In this paper, the proposed approach is theoretically and numerically investigated by means of simple sound propagation models, proving its efficiency in reducing the spatial aliasing. A number of different array configurations are numerically investigated together with the most important parameters governing this measurement technique. A set of numerical results concerning the case of a planar rotating array is shown, together with a first experimental validation of the method.

High-Order Methods for Incompressible Fluid Flow

NASA Astrophysics Data System (ADS)

Deville, M. O.; Fischer, P. F.; Mund, E. H.

2002-08-01

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

NASA Astrophysics Data System (ADS)

Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko

2017-09-01

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

DOE PAGES

Grenier, Christophe; Anbergen, Hauke; Bense, Victor; ...

2018-02-26

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. Here in this paper, this issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatialmore » and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.« less

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

NASA Astrophysics Data System (ADS)

Trinkle, Dallas R.

2017-10-01

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grenier, Christophe; Anbergen, Hauke; Bense, Victor

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. Here in this paper, this issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatialmore » and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.« less

Design of a high-power, high-brightness Nd:YAG solar laser.

PubMed

Liang, Dawei; Almeida, Joana; Garcia, Dário

2014-03-20

A simple high-power, high-brightness Nd:YAG solar laser pumping approach is presented in this paper. The incoming solar radiation is both collected and concentrated by four Fresnel lenses and redirected toward a Nd:YAG laser head by four plane-folding mirrors. A fused-silica secondary concentrator is used to compress the highly concentrated solar radiation to a laser rod. Optimum pumping conditions and laser resonator parameters are found through ZEMAX and LASCAD numerical analysis. Solar laser power of 96 W is numerically calculated, corresponding to the collection efficiency of 24  W/m². A record-high solar laser beam brightness figure of merit of 9.6 W is numerically achieved.

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

NASA Astrophysics Data System (ADS)

Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel

2017-07-01

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) [13], we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

Dynamics of Coupled Electron-Boson Systems with the Multiple Davydov D1 Ansatz and the Generalized Coherent State.

PubMed

Chen, Lipeng; Borrelli, Raffaele; Zhao, Yang

2017-11-22

The dynamics of a coupled electron-boson system is investigated by employing a multitude of the Davydov D 1 trial states, also known as the multi-D 1 Ansatz, and a second trial state based on a superposition of the time-dependent generalized coherent state (GCS Ansatz). The two Ansätze are applied to study population dynamics in the spin-boson model and the Holstein molecular crystal model, and a detailed comparison with numerically exact results obtained by the (multilayer) multiconfiguration time-dependent Hartree method and the hierarchy equations of motion approach is drawn. It is found that the two methodologies proposed here have significantly improved over that with the single D 1 Ansatz, yielding quantitatively accurate results even in the critical cases of large energy biases and large transfer integrals. The two methodologies provide new effective tools for accurate, efficient simulation of many-body quantum dynamics thanks to a relatively small number of parameters which characterize the electron-nuclear wave functions. The wave-function-based approaches are capable of tracking explicitly detailed bosonic dynamics, which is absent by construct in approaches based on the reduced density matrix. The efficiency and flexibility of our methods are also advantages as compared with numerically exact approaches such as QUAPI and HEOM, especially at low temperatures and in the strong coupling regime.

Parallel implementation of geometrical shock dynamics for two dimensional converging shock waves

NASA Astrophysics Data System (ADS)

Qiu, Shi; Liu, Kuang; Eliasson, Veronica

2016-10-01

Geometrical shock dynamics (GSD) theory is an appealing method to predict the shock motion in the sense that it is more computationally efficient than solving the traditional Euler equations, especially for converging shock waves. However, to solve and optimize large scale configurations, the main bottleneck is the computational cost. Among the existing numerical GSD schemes, there is only one that has been implemented on parallel computers, with the purpose to analyze detonation waves. To extend the computational advantage of the GSD theory to more general applications such as converging shock waves, a numerical implementation using a spatial decomposition method has been coupled with a front tracking approach on parallel computers. In addition, an efficient tridiagonal system solver for massively parallel computers has been applied to resolve the most expensive function in this implementation, resulting in an efficiency of 0.93 while using 32 HPCC cores. Moreover, symmetric boundary conditions have been developed to further reduce the computational cost, achieving a speedup of 19.26 for a 12-sided polygonal converging shock.

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Numerical simulation of active track tensioning system for autonomous hybrid vehicle

NASA Astrophysics Data System (ADS)

Mȩżyk, Arkadiusz; Czapla, Tomasz; Klein, Wojciech; Mura, Gabriel

2017-05-01

One of the most important components of a high speed tracked vehicle is an efficient suspension system. The vehicle should be able to operate both in rough terrain for performance of engineering tasks as well as on the road with high speed. This is especially important for an autonomous platform that operates either with or without human supervision, so that the vibration level can rise compared to a manned vehicle. In this case critical electronic and electric parts must be protected to ensure the reliability of the vehicle. The paper presents a dynamic parameters determination methodology of suspension system for an autonomous high speed tracked platform with total weight of about 5 tonnes and hybrid propulsion system. Common among tracked vehicles suspension solutions and cost-efficient, the torsion-bar system was chosen. One of the most important issues was determining optimal track tensioning - in this case an active hydraulic system was applied. The selection of system parameters was performed with using numerical model based on multi-body dynamic approach. The results of numerical analysis were used to define parameters of active tensioning control system setup. LMS Virtual.Lab Motion was used for multi-body dynamics numerical calculation and Matlab/SIMULINK for control system simulation.

Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mohebbi, Akbar

2018-02-01

In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

Predicting multi-level drug response with gene expression profile in multiple myeloma using hierarchical ordinal regression.

PubMed

Zhang, Xinyan; Li, Bingzong; Han, Huiying; Song, Sha; Xu, Hongxia; Hong, Yating; Yi, Nengjun; Zhuang, Wenzhuo

2018-05-10

Multiple myeloma (MM), like other cancers, is caused by the accumulation of genetic abnormalities. Heterogeneity exists in the patients' response to treatments, for example, bortezomib. This urges efforts to identify biomarkers from numerous molecular features and build predictive models for identifying patients that can benefit from a certain treatment scheme. However, previous studies treated the multi-level ordinal drug response as a binary response where only responsive and non-responsive groups are considered. It is desirable to directly analyze the multi-level drug response, rather than combining the response to two groups. In this study, we present a novel method to identify significantly associated biomarkers and then develop ordinal genomic classifier using the hierarchical ordinal logistic model. The proposed hierarchical ordinal logistic model employs the heavy-tailed Cauchy prior on the coefficients and is fitted by an efficient quasi-Newton algorithm. We apply our hierarchical ordinal regression approach to analyze two publicly available datasets for MM with five-level drug response and numerous gene expression measures. Our results show that our method is able to identify genes associated with the multi-level drug response and to generate powerful predictive models for predicting the multi-level response. The proposed method allows us to jointly fit numerous correlated predictors and thus build efficient models for predicting the multi-level drug response. The predictive model for the multi-level drug response can be more informative than the previous approaches. Thus, the proposed approach provides a powerful tool for predicting multi-level drug response and has important impact on cancer studies.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach

NASA Astrophysics Data System (ADS)

Pinto, Rafael S.; Saa, Alberto

2015-12-01

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function ωTL ω , where ω stands for the vector of the natural frequencies of the oscillators and L for the network Laplacian matrix. Many recently obtained numerical results can be reobtained analytically and in a simpler way from our maximization condition. A computationally efficient hill climb rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner.

Thermodynamic efficiency limits of classical and bifacial multi-junction tandem solar cells: An analytical approach

NASA Astrophysics Data System (ADS)

Alam, Muhammad Ashraful; Khan, M. Ryyan

2016-10-01

Bifacial tandem cells promise to reduce three fundamental losses (i.e., above-bandgap, below bandgap, and the uncollected light between panels) inherent in classical single junction photovoltaic (PV) systems. The successive filtering of light through the bandgap cascade and the requirement of current continuity make optimization of tandem cells difficult and accessible only to numerical solution through computer modeling. The challenge is even more complicated for bifacial design. In this paper, we use an elegantly simple analytical approach to show that the essential physics of optimization is intuitively obvious, and deeply insightful results can be obtained with a few lines of algebra. This powerful approach reproduces, as special cases, all of the known results of conventional and bifacial tandem cells and highlights the asymptotic efficiency gain of these technologies.

Multi-Item Multiperiodic Inventory Control Problem with Variable Demand and Discounts: A Particle Swarm Optimization Algorithm

PubMed Central

Mousavi, Seyed Mohsen; Niaki, S. T. A.; Bahreininejad, Ardeshir; Musa, Siti Nurmaya

2014-01-01

A multi-item multiperiod inventory control model is developed for known-deterministic variable demands under limited available budget. Assuming the order quantity is more than the shortage quantity in each period, the shortage in combination of backorder and lost sale is considered. The orders are placed in batch sizes and the decision variables are assumed integer. Moreover, all unit discounts for a number of products and incremental quantity discount for some other items are considered. While the objectives are to minimize both the total inventory cost and the required storage space, the model is formulated into a fuzzy multicriteria decision making (FMCDM) framework and is shown to be a mixed integer nonlinear programming type. In order to solve the model, a multiobjective particle swarm optimization (MOPSO) approach is applied. A set of compromise solution including optimum and near optimum ones via MOPSO has been derived for some numerical illustration, where the results are compared with those obtained using a weighting approach. To assess the efficiency of the proposed MOPSO, the model is solved using multi-objective genetic algorithm (MOGA) as well. A large number of numerical examples are generated at the end, where graphical and statistical approaches show more efficiency of MOPSO compared with MOGA. PMID:25093195

A new hybrid numerical scheme for simulating fault ruptures with near-fault bulk inhomogeneities

NASA Astrophysics Data System (ADS)

Hajarolasvadi, S.; Elbanna, A. E.

2017-12-01

The Finite Difference (FD) and Boundary Integral (BI) Method have been extensively used to model spontaneously propagating shear cracks, which can serve as a useful idealization of natural earthquakes. While FD suffers from artificial dispersion and numerical dissipation and has a large computational cost as it requires the discretization of the whole volume of interest, it can be applied to a wider range of problems including ones with bulk nonlinearities and heterogeneities. On the other hand, in the BI method, the numerical consideration is confined to the crack path only, with the elastodynamic response of the bulk expressed in terms of integral relations between displacement discontinuities and tractions along the crack. Therefore, this method - its spectral boundary integral (SBI) formulation in particular - is much faster and more computationally efficient than other bulk methods such as FD. However, its application is restricted to linear elastic bulk and planar faults. This work proposes a novel hybrid numerical scheme that combines FD and the SBI to enable treating fault zone nonlinearities and heterogeneities with unprecedented resolution and in a more computationally efficient way. The main idea of the method is to enclose the inhomgeneities in a virtual strip that is introduced for computational purposes only. This strip is then discretized using a volume-based numerical method, chosen here to be the finite difference method while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low velocity layer and the other in which off-fault plasticity is permitted. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art.

Higher-order compositional modeling of three-phase flow in 3D fractured porous media based on cross-flow equilibrium

NASA Astrophysics Data System (ADS)

Moortgat, Joachim; Firoozabadi, Abbas

2013-10-01

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

Modelling and analysis of solar cell efficiency distributions

NASA Astrophysics Data System (ADS)

Wasmer, Sven; Greulich, Johannes

2017-08-01

We present an approach to model the distribution of solar cell efficiencies achieved in production lines based on numerical simulations, metamodeling and Monte Carlo simulations. We validate our methodology using the example of an industrial feasible p-type multicrystalline silicon “passivated emitter and rear cell” process. Applying the metamodel, we investigate the impact of each input parameter on the distribution of cell efficiencies in a variance-based sensitivity analysis, identifying the parameters and processes that need to be improved and controlled most accurately. We show that if these could be optimized, the mean cell efficiencies of our examined cell process would increase from 17.62% ± 0.41% to 18.48% ± 0.09%. As the method relies on advanced characterization and simulation techniques, we furthermore introduce a simplification that enhances applicability by only requiring two common measurements of finished cells. The presented approaches can be especially helpful for ramping-up production, but can also be applied to enhance established manufacturing.

Dispersion of speckle suppression efficiency for binary DOE structures: spectral domain and coherent matrix approaches.

PubMed

Lapchuk, Anatoliy; Prygun, Olexandr; Fu, Minglei; Le, Zichun; Xiong, Qiyuan; Kryuchyn, Andriy

2017-06-26

We present the first general theoretical description of speckle suppression efficiency based on an active diffractive optical element (DOE). The approach is based on spectral analysis of diffracted beams and a coherent matrix. Analytical formulae are obtained for the dispersion of speckle suppression efficiency using different DOE structures and different DOE activation methods. We show that a one-sided 2D DOE structure has smaller speckle suppression range than a two-sided 1D DOE structure. Both DOE structures have sufficient speckle suppression range to suppress low-order speckles in the entire visible range, but only the two-sided 1D DOE can suppress higher-order speckles. We also show that a linear shift 2D DOE in a laser projector with a large numerical aperture has higher effective speckle suppression efficiency than the method using switching or step-wise shift DOE structures. The generalized theoretical models elucidate the mechanism and practical realization of speckle suppression.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stubos, A.K.; Caseiras, C.P.; Buchlin, J.M.

The transient two-phase flow and phase change heat transfer processes in porous media are investigated. Based on an enthalpic approach, a one-domain formulation of the problem is developed, avoiding explicit internal boundary tracking between single- and two-phase regions. An efficient numerical scheme is applied to obtain the solution on a fixed two-dimensional grid. The transient response of a liquid-saturated, self-heated porous bed is examined in detail. A physical interpretation of a liquid-saturated, self-heated porous bed is examined in detail. A physical interpretation of the computed response to fast power transients is attempted. Comparisons with experimental data are made regarding themore » average void fraction and the limiting dryout heat flux. The numerical approach is extended, keeping the one-domain formulation, to include the surrounding wall structure in the calculation.« less

Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

2017-07-01

The paper considers a generalized functional and algorithmic construction of direct computational experiments in fluid dynamics. Notation of tensor mathematics is naturally embedded in the finite - element operation in the construction of numerical schemes. Large fluid particle, which have a finite size, its own weight, internal displacement and deformation is considered as an elementary computing object. Tensor representation of computational objects becomes strait linear and uniquely approximation of elementary volumes and fluid particles inside them. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. It is shown that advantages of the proposed approach are achieved among them by considering representation of large particles of a continuous medium motion in dual coordinate systems and computing operations in the projections of these two coordinate systems with direct and inverse transformations. So new method for mathematical representation and synthesis of computational experiment based on large particle method is proposed.

Computation of the sound generated by isotropic turbulence

NASA Technical Reports Server (NTRS)

Sarkar, S.; Hussaini, M. Y.

1993-01-01

The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.

Airfoil Design and Optimization by the One-Shot Method

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Taasan, Shlomo; Salas, M. D.

1995-01-01

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Lagrange multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Airfoil optimization by the one-shot method

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Taasan, Shlomo; Salas, M. D.

1994-01-01

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Nonlinear interferometry approach to photonic sequential logic

NASA Astrophysics Data System (ADS)

Mabuchi, Hideo

2011-10-01

Motivated by rapidly advancing capabilities for extensive nanoscale patterning of optical materials, I propose an approach to implementing photonic sequential logic that exploits circuit-scale phase coherence for efficient realizations of fundamental components such as a NAND-gate-with-fanout and a bistable latch. Kerr-nonlinear optical resonators are utilized in combination with interference effects to drive the binary logic. Quantum-optical input-output models are characterized numerically using design parameters that yield attojoule-scale energy separation between the latch states.

Queueing Network Models for Parallel Processing of Task Systems: an Operational Approach

NASA Technical Reports Server (NTRS)

Mak, Victor W. K.

1986-01-01

Computer performance modeling of possibly complex computations running on highly concurrent systems is considered. Earlier works in this area either dealt with a very simple program structure or resulted in methods with exponential complexity. An efficient procedure is developed to compute the performance measures for series-parallel-reducible task systems using queueing network models. The procedure is based on the concept of hierarchical decomposition and a new operational approach. Numerical results for three test cases are presented and compared to those of simulations.

Assessment of the temperature cut-off point by a commercial intravaginal device to predict parturition in piedmontese beef cows

USDA-ARS?s Scientific Manuscript database

Dystocic parturitions have an adverse impact on animal productivity, and therefore the profitability of the farm. In this regard, an accurate calving prediction is essential since it allows for efficient and prompt assistance for the dam and the calf. Numerous approaches to predict parturition have ...

Machine learning action parameters in lattice quantum chromodynamics

NASA Astrophysics Data System (ADS)

Shanahan, Phiala E.; Trewartha, Daniel; Detmold, William

2018-05-01

Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. The high information content and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.

Mathematical modeling of the Stirling engine in terms of applying the composition of the power complex containing non-conventional and renewable energy

NASA Astrophysics Data System (ADS)

Gaponenko, A. M.; Kagramanova, A. A.

2017-11-01

The opportunity of application of Stirling engine with non-conventional and renewable sources of energy. The advantage of such use. The resulting expression for the thermal efficiency of the Stirling engine. It is shown that the work per cycle is proportional to the quantity of matter, and hence the pressure of the working fluid, the temperature difference and, to a lesser extent, depends on the expansion coefficient; efficiency of ideal Stirling cycle coincides with the efficiency of an ideal engine working on the Carnot cycle, which distinguishes a Stirling cycle from the cycles of Otto and Diesel underlying engine. It has been established that the four input parameters, the only parameter which can be easily changed during operation, and which effectively affects the operation of the engine is the phase difference. Dependence of work per cycle of the phase difference, called the phase characteristic, visually illustrates mode of operation of Stirling engine. The mathematical model of the cycle of Schmidt and the analysis of operation of Stirling engine in the approach of Schmidt with the aid of numerical analysis. To conduct numerical experiments designed program feature in the language MathLab. The results of numerical experiments are illustrated by graphical charts.

The analytical and numerical approaches to the theory of the Moon's librations: Modern analysis and results

NASA Astrophysics Data System (ADS)

Petrova, N.; Zagidullin, A.; Nefedyev, Y.; Kosulin, V.; Andreev, A.

2017-11-01

Observing physical librations of celestial bodies and the Moon represents one of the astronomical methods of remotely assessing the internal structure of a celestial body without conducting expensive space experiments. The paper contains a review of recent advances in studying the Moon's structure using various methods of obtaining and applying the lunar physical librations (LPhL) data. In this article LPhL simulation methods of assessing viscoelastic and dissipative properties of the lunar body and lunar core parameters, whose existence has been recently confirmed during the seismic data reprocessing of ;Apollo; space mission, are described. Much attention is paid to physical interpretation of the free librations phenomenon and the methods for its determination. In the paper the practical application of the most accurate analytical LPhL tables (Rambaux and Williams, 2011) is discussed. The tables were built on the basis of complex analytical processing of the residual differences obtained when comparing long-term series of laser observations with the numerical ephemeris DE421. In the paper an efficiency analysis of two approaches to LPhL theory is conducted: the numerical and the analytical ones. It has been shown that in lunar investigation both approaches complement each other in various aspects: the numerical approach provides high accuracy of the theory, which is required for the proper processing of modern observations, the analytical approach allows to comprehend the essence of the phenomena in the lunar rotation, predict and interpret new effects in the observations of lunar body and lunar core parameters.

More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators?

PubMed Central

Palmer, T. N.

2014-01-01

This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. In this approach, the conventionally hard boundary between the dynamical core and the sub-grid parametrizations is blurred. This approach is motivated by the relatively shallow power-law spectrum for atmospheric energy on scales of hundreds of kilometres and less. It is first argued that, because of this, the closure schemes for weather and climate simulators should be based on stochastic–dynamic systems rather than deterministic formulae. Second, as high-wavenumber elements of the dynamical core will necessarily inherit this stochasticity during time integration, it is argued that the dynamical core will be significantly over-engineered if all computations, regardless of scale, are performed completely deterministically and if all variables are represented with maximum numerical precision (in practice using double-precision floating-point numbers). As the era of exascale computing is approached, an energy- and computationally efficient approach to cloud-resolved weather and climate simulation is described where determinism and numerical precision are focused on the largest scales only. PMID:24842038

More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators?

PubMed

Palmer, T N

2014-06-28

This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. In this approach, the conventionally hard boundary between the dynamical core and the sub-grid parametrizations is blurred. This approach is motivated by the relatively shallow power-law spectrum for atmospheric energy on scales of hundreds of kilometres and less. It is first argued that, because of this, the closure schemes for weather and climate simulators should be based on stochastic-dynamic systems rather than deterministic formulae. Second, as high-wavenumber elements of the dynamical core will necessarily inherit this stochasticity during time integration, it is argued that the dynamical core will be significantly over-engineered if all computations, regardless of scale, are performed completely deterministically and if all variables are represented with maximum numerical precision (in practice using double-precision floating-point numbers). As the era of exascale computing is approached, an energy- and computationally efficient approach to cloud-resolved weather and climate simulation is described where determinism and numerical precision are focused on the largest scales only.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

PubMed

Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

2012-07-02

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

On the Modeling of Shells in Multibody Dynamics

NASA Technical Reports Server (NTRS)

Bauchau, Olivier A.; Choi, Jou-Young; Bottasso, Carlo L.

2000-01-01

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the, constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.

Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma

NASA Astrophysics Data System (ADS)

Dolgov, S. V.; Smirnov, A. P.; Tyrtyshnikov, E. E.

2014-04-01

We consider numerical modeling of the Farley-Buneman instability in the Earth's ionosphere plasma. The ion behavior is governed by the kinetic Vlasov equation with the BGK collisional term in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed. The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.

Experimental and numerical modeling of rarefied gas flows through orifices and short tubes

NASA Astrophysics Data System (ADS)

Gimelshein, S. F.; Markelov, G. N.; Lilly, T. C.; Selden, N. P.; Ketsdever, A. D.

2005-05-01

Flow through circular orifices with thickness-to-diameter ratios varying from 0.015 to 1.2 is studied experimentally and numerically with kinetic and continuum approaches. Helium and nitrogen gases are used in the range of Reynolds numbers from 0.02 to over 700. Good agreement between experimental and numerical results is observed for mass flow and thrust corrected for the experimental facility background pressure. For thick-to-thin orifice ratios of mass flow and thrust vs pressure, a minimum is established. The thick orifice propulsion efficiency is much higher than that of a thin orifice. The effects of edge roundness and surface specularity on a thick orifice specific impulse were found to be relatively small.

An approach to solving large reliability models

NASA Technical Reports Server (NTRS)

Boyd, Mark A.; Veeraraghavan, Malathi; Dugan, Joanne Bechta; Trivedi, Kishor S.

1988-01-01

This paper describes a unified approach to the problem of solving large realistic reliability models. The methodology integrates behavioral decomposition, state trunction, and efficient sparse matrix-based numerical methods. The use of fault trees, together with ancillary information regarding dependencies to automatically generate the underlying Markov model state space is proposed. The effectiveness of this approach is illustrated by modeling a state-of-the-art flight control system and a multiprocessor system. Nonexponential distributions for times to failure of components are assumed in the latter example. The modeling tool used for most of this analysis is HARP (the Hybrid Automated Reliability Predictor).

Méthode du second membre modifié pour la gestion de rapports de viscosité importants dans le problème de Stokes bifluide

NASA Astrophysics Data System (ADS)

Bui, Thi Thu Cuc; Frey, Pascal; Maury, Bertrand

2008-06-01

In this Note, we present a method to solve numerically the Stokes equation for the incompressible flow between two immiscible fluids presenting very different viscosities. The resolution of the finite element systems of equations is performed using Uzawa's method. The stiffness matrix conditioning problems related to the very important viscosity ratios are circumvented using an new iterative scheme. A numerical example is proposed to show the efficiency of this approach. To cite this article: T.T.C. Bui et al., C. R. Mecanique 336 (2008).

A new operational approach for solving fractional variational problems depending on indefinite integrals

NASA Astrophysics Data System (ADS)

Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

2018-04-01

In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems.

PubMed

Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

2015-11-11

Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.

Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

NASA Technical Reports Server (NTRS)

Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark

2002-01-01

Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

Validation, Optimization and Simulation of a Solar Thermoelectric Generator Model

NASA Astrophysics Data System (ADS)

Madkhali, Hadi Ali; Hamil, Ali; Lee, HoSung

2017-12-01

This study explores thermoelectrics as a viable option for small-scale solar thermal applications. Thermoelectric technology is based on the Seebeck effect, which states that a voltage is induced when a temperature gradient is applied to the junctions of two differing materials. This research proposes to analyze, validate, simulate, and optimize a prototype solar thermoelectric generator (STEG) model in order to increase efficiency. The intent is to further develop STEGs as a viable and productive energy source that limits pollution and reduces the cost of energy production. An empirical study (Kraemer et al. in Nat Mater 10:532, 2011) on the solar thermoelectric generator reported a high efficiency performance of 4.6%. The system had a vacuum glass enclosure, a flat panel (absorber), thermoelectric generator and water circulation for the cold side. The theoretical and numerical approach of this current study validated the experimental results from Kraemer's study to a high degree. The numerical simulation process utilizes a two-stage approach in ANSYS software for Fluent and Thermal-Electric Systems. The solar load model technique uses solar radiation under AM 1.5G conditions in Fluent. This analytical model applies Dr. Ho Sung Lee's theory of optimal design to improve the performance of the STEG system by using dimensionless parameters. Applying this theory, using two cover glasses and radiation shields, the STEG model can achieve a highest efficiency of 7%.

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Multi-scale image segmentation and numerical modeling in carbonate rocks

NASA Astrophysics Data System (ADS)

Alves, G. C.; Vanorio, T.

2016-12-01

Numerical methods based on computational simulations can be an important tool in estimating physical properties of rocks. These can complement experimental results, especially when time constraints and sample availability are a problem. However, computational models created at different scales can yield conflicting results with respect to the physical laboratory. This problem is exacerbated in carbonate rocks due to their heterogeneity at all scales. We developed a multi-scale approach performing segmentation of the rock images and numerical modeling across several scales, accounting for those heterogeneities. As a first step, we measured the porosity and the elastic properties of a group of carbonate samples with varying micrite content. Then, samples were imaged by Scanning Electron Microscope (SEM) as well as optical microscope at different magnifications. We applied three different image segmentation techniques to create numerical models from the SEM images and performed numerical simulations of the elastic wave-equation. Our results show that a multi-scale approach can efficiently account for micro-porosities in tight micrite-supported samples, yielding acoustic velocities comparable to those obtained experimentally. Nevertheless, in high-porosity samples characterized by larger grain/micrite ratio, results show that SEM scale images tend to overestimate velocities, mostly due to their inability to capture macro- and/or intragranular- porosity. This suggests that, for high-porosity carbonate samples, optical microscope images would be more suited for numerical simulations.

GPR detectability of rocks in a Martian-like shallow subsoil: A numerical approach

NASA Astrophysics Data System (ADS)

Valerio, Guido; Galli, Alessandro; Matteo Barone, Pier; Lauro, Sebastian E.; Mattei, Elisabetta; Pettinelli, Elena

2012-03-01

In this work, the ability of Ground Penetrating Radar (GPR) to detect rocks buried in composite soil is studied in connection with the planned ExoMars mission, as GPR will be used during this mission to scan the Martian subsurface to help define feasible sites for shallow drilling. A realistic model of the operating environment is implemented through a full-wave electromagnetic simulator, taking into account the antenna system and the signal features. The flexibility and efficiency of this numerical approach has allowed for the analysis of a great variety of configurations. The regolith is modeled based on data from recent explorations, while various kinds of embedded rocks are considered that have different geometrical and physical characteristics. The simulated results are compared with ad hoc GPR measurements performed on basalts buried in a mixture of glass beads, as an analogue of a dry sandy Martian soil. A very good agreement between theoretical and experimental results is found, thus validating the proposed numerical approach. This research has defined useful and reliable information concerning the prediction of scattering effects from buried objects in the environment where the ExoMars rover will operate.

Analysis of composite plates by using mechanics of structure genome and comparison with ANSYS

NASA Astrophysics Data System (ADS)

Zhao, Banghua

Motivated by a recently discovered concept, Structure Genome (SG) which is defined as the smallest mathematical building block of a structure, a new approach named Mechanics of Structure Genome (MSG) to model and analyze composite plates is introduced. MSG is implemented in a general-purpose code named SwiftComp(TM), which provides the constitutive models needed in structural analysis by homogenization and pointwise local fields by dehomogenization. To improve the user friendliness of SwiftComp(TM), a simple graphic user interface (GUI) based on ANSYS Mechanical APDL platform, called ANSYS-SwiftComp GUI is developed, which provides a convenient way to create some common SG models or arbitrary customized SG models in ANSYS and invoke SwiftComp(TM) to perform homogenization and dehomogenization. The global structural analysis can also be handled in ANSYS after homogenization, which could predict the global behavior and provide needed inputs for dehomogenization. To demonstrate the accuracy and efficiency of the MSG approach, several numerical cases are studied and compared using both MSG and ANSYS. In the ANSYS approach, 3D solid element models (ANSYS 3D approach) are used as reference models and the 2D shell element models created by ANSYS Composite PrepPost (ACP approach) are compared with the MSG approach. The results of the MSG approach agree well with the ANSYS 3D approach while being as efficient as the ACP approach. Therefore, the MSG approach provides an efficient and accurate new way to model composite plates.

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schaerer, Roman Pascal, E-mail: schaerer@mathcces.rwth-aachen.de; Bansal, Pratyuksh; Torrilhon, Manuel

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropymore » distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.« less

Investigation of different simulation approaches on a high-head Francis turbine and comparison with model test data: Francis-99

NASA Astrophysics Data System (ADS)

Mössinger, Peter; Jester-Zürker, Roland; Jung, Alexander

2015-01-01

Numerical investigations of hydraulic turbo machines under steady-state conditions are state of the art in current product development processes. Nevertheless allow increasing computational resources refined discretization methods, more sophisticated turbulence models and therefore better predictions of results as well as the quantification of existing uncertainties. Single stage investigations are done using in-house tools for meshing and set-up procedure. Beside different model domains and a mesh study to reduce mesh dependencies, the variation of several eddy viscosity and Reynolds stress turbulence models are investigated. All obtained results are compared with available model test data. In addition to global values, measured magnitudes in the vaneless space, at runner blade and draft tube positions in term of pressure and velocity are considered. From there it is possible to estimate the influence and relevance of various model domains depending on different operating points and numerical variations. Good agreement can be found for pressure and velocity measurements with all model configurations and, except the BSL-RSM model, all turbulence models. At part load, deviations in hydraulic efficiency are at a large magnitude, whereas at best efficiency and high load operating point efficiencies are close to the measurement. A consideration of the runner side gap geometry as well as a refined mesh is able to improve the results either in relation to hydraulic efficiency or velocity distribution with the drawbacks of less stable numerics and increasing computational time.

Numerical determination of personal aerosol sampler aspiration efficiency.

PubMed

Lo Savio, Simone; Paradisi, Paolo; Tampieri, Francesco; Belosi, Franco; Morigi, Maria Pia; Agostini, Sergio

2003-04-01

In this work the determination of the aspiration efficiency of personal aerosol samplers, commonly used in occupational exposure assessment, is investigated by means of CFD techniques. Specifically, it will be described a code to calculate the particle trajectories in a given flow field. At the present state the code considers only the effects of the mean flow field on the particle motion, whereas the turbulent diffusion effects are neglected. Comparisons with experimental measurements are also given in the framework of a research contract, supported by the European Community, with several experimental contributions from the participants. The main objective of the European research is to develop a new approach to experimentation with airborne particle flows, working on a reduced scale. This methodology has the advantage of allowing real-time aerosol determination and use of small wind tunnels, with a better experimental control. In this article we describe how the methodology has been verified using computational fluid dynamics. Experimental and numerical aspiration efficiencies have been compared and the influence of gravity and turbulence intensity in full and reduced scale has been investigated. The numerical techniques described here are in agreement with previous similar research and allow at least qualitative predictions of aspiration efficiency for real samplers, taking care of orientation from the incoming air flow. The major discrepancies among predicted and experimental results may be a consequence of bounce effects, which are very difficult to eliminate also by greasing the sampler surface.

Hybrid discrete/continuum algorithms for stochastic reaction networks

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; ...

2014-10-22

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less

Observer efficiency in discrimination tasks simulating malignant and benign breast lesions imaged with ultrasound

PubMed Central

Abbey, Craig K.; Zemp, Roger J.; Liu, Jie; Lindfors, Karen K.; Insana, Michael F.

2009-01-01

We investigate and extend the ideal observer methodology developed by Smith and Wagner to detection and discrimination tasks related to breast sonography. We provide a numerical approach for evaluating the ideal observer acting on radio-frequency (RF) frame data, which involves inversion of large nonstationary covariance matrices, and we describe a power-series approach to computing this inverse. Considering a truncated power series suggests that the RF data be Wiener-filtered before forming the final envelope image. We have compared human performance for Wiener-filtered and conventional B-mode envelope images using psychophysical studies for 5 tasks related to breast cancer classification. We find significant improvements in visual detection and discrimination efficiency in four of these five tasks. We also use the Smith-Wagner approach to distinguish between human and processing inefficiencies, and find that generally the principle limitation comes from the information lost in computing the final envelope image. PMID:16468454

Interaction Entropy: A New Paradigm for Highly Efficient and Reliable Computation of Protein-Ligand Binding Free Energy.

PubMed

Duan, Lili; Liu, Xiao; Zhang, John Z H

2016-05-04

Efficient and reliable calculation of protein-ligand binding free energy is a grand challenge in computational biology and is of critical importance in drug design and many other molecular recognition problems. The main challenge lies in the calculation of entropic contribution to protein-ligand binding or interaction systems. In this report, we present a new interaction entropy method which is theoretically rigorous, computationally efficient, and numerically reliable for calculating entropic contribution to free energy in protein-ligand binding and other interaction processes. Drastically different from the widely employed but extremely expensive normal mode method for calculating entropy change in protein-ligand binding, the new method calculates the entropic component (interaction entropy or -TΔS) of the binding free energy directly from molecular dynamics simulation without any extra computational cost. Extensive study of over a dozen randomly selected protein-ligand binding systems demonstrated that this interaction entropy method is both computationally efficient and numerically reliable and is vastly superior to the standard normal mode approach. This interaction entropy paradigm introduces a novel and intuitive conceptual understanding of the entropic effect in protein-ligand binding and other general interaction systems as well as a practical method for highly efficient calculation of this effect.

Modeling and analysis of cascade solar cells

NASA Technical Reports Server (NTRS)

Ho, F. D.

1986-01-01

A brief review is given of the present status of the development of cascade solar cells. It is known that photovoltaic efficiencies can be improved through this development. The designs and calculations of the multijunction cells, however, are quite complicated. The main goal is to find a method which is a compromise between accuracy and simplicity for modeling a cascade solar cell. Three approaches are presently under way, among them (1) equivalent circuit approach, (2) numerical approach, and (3) analytical approach. Here, the first and the second approaches are discussed. The equivalent circuit approach using SPICE (Simulation Program, Integrated Circuit Emphasis) to the cascade cells and the cascade-cell array is highlighted. The methods of extracting parameters for modeling are discussed.

Efficient calculation of the polarizability: a simplified effective-energy technique

NASA Astrophysics Data System (ADS)

Berger, J. A.; Reining, L.; Sottile, F.

2012-09-01

In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 82, 041103(R) (2010)] we introduced the effective-energy technique to calculate in an accurate and numerically efficient manner the GW self-energy as well as the polarizability, which is required to evaluate the screened Coulomb interaction W. In this work we show that the effective-energy technique can be used to further simplify the expression for the polarizability without a significant loss of accuracy. In contrast to standard sum-over-state methods where huge summations over empty states are required, our approach only requires summations over occupied states. The three simplest approximations we obtain for the polarizability are explicit functionals of an independent- or quasi-particle one-body reduced density matrix. We provide evidence of the numerical accuracy of this simplified effective-energy technique as well as an analysis of our method.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

Numerical analysis of biosonar beamforming mechanisms and strategies in bats.

PubMed

Müller, Rolf

2010-09-01

Beamforming is critical to the function of most sonar systems. The conspicuous noseleaf and pinna shapes in bats suggest that beamforming mechanisms based on diffraction of the outgoing and incoming ultrasonic waves play a major role in bat biosonar. Numerical methods can be used to investigate the relationships between baffle geometry, acoustic mechanisms, and resulting beampatterns. Key advantages of numerical approaches are: efficient, high-resolution estimation of beampatterns, spatially dense predictions of near-field amplitudes, and the malleability of the underlying shape representations. A numerical approach that combines near-field predictions based on a finite-element formulation for harmonic solutions to the Helmholtz equation with a free-field projection based on the Kirchhoff integral to obtain estimates of the far-field beampattern is reviewed. This method has been used to predict physical beamforming mechanisms such as frequency-dependent beamforming with half-open resonance cavities in the noseleaf of horseshoe bats and beam narrowing through extension of the pinna aperture with skin folds in false vampire bats. The fine structure of biosonar beampatterns is discussed for the case of the Chinese noctule and methods for assessing the spatial information conveyed by beampatterns are demonstrated for the brown long-eared bat.

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

NASA Astrophysics Data System (ADS)

Mascarenhas, Eduardo; Flayac, Hugo; Savona, Vincenzo

2015-08-01

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Compositional Reservoir Simulation of Highly Heterogeneous and Anisotropic Fractured Media in 2D and 3D Unstructured Gridding

NASA Astrophysics Data System (ADS)

Zidane, A.; Firoozabadi, A.

2017-12-01

We present an efficient and accurate numerical model for multicomponent compressible single-phase flow in 2D and 3D fractured media based on higher-order discretization. The numerical model accounts for heterogeneity and anisotropy in unstructured gridding with low mesh dependency. The efficiency of our model is demonstrated by having comparable CPU time between fractured and unfractured media. The fracture cross-flow equilibrium approach (FCFE) is applied on triangular finite elements (FE) in 2D. This allows simulating fractured reservoirs with all possible orientations of fractures as opposed to rectangular FE. In 3D we apply the FCFE approach on the prism FE. The prism FE with FCFE allows simulating realistic fractured domains compared to hexahedron FE. In addition, when using FCFE on triangular and prism FE there is no limitation on the number of intersecting fractures, whereas in rectangular and hexahedron FE the number is limited to 2 in 2D and 3 in 3D. To generate domains with complicated boundaries, we have developed a computer-aided design (CAD) interface in our model. The advances introduced in this work are demonstrated through various examples.

Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures

DTIC Science & Technology

2017-10-04

Report: Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures The views, opinions and/or findings contained in this...Chapel Hill Title: Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures Report Term: 0-Other Email: dm...algorithms for scientific and geometric computing by exploiting the power and performance efficiency of heterogeneous shared memory architectures . These

Analysis of a highly birefringent asymmetric photonic crystal fibre based on a surface plasmon resonance sensor

NASA Astrophysics Data System (ADS)

Liu, Chao; Wang, Famei; Zheng, Shijie; Sun, Tao; Lv, Jingwei; Liu, Qiang; Yang, Lin; Mu, Haiwei; Chu, Paul K.

2016-07-01

A highly birefringent photonic crystal fibre is proposed and characterized based on a surface plasmon resonance sensor. The birefringence of the sensor is numerically analyzed by the finite-element method. In the numerical simulation, the resonance wavelength can be directly positioned at this birefringence abrupt change point and the depth of the abrupt change of birefringence reflects the intensity of excited surface plasmon. Consequently, the novel approach can accurately locate the resonance peak of the system without analyzing the loss spectrum. Simulated average sensitivity is as high as 1131 nm/RIU, corresponding to a resolution of 1 × 10-4 RIU in this sensor. Therefore, results obtained via the approach not only show polarization independence and less noble metal consumption, but also reveal better performance in terms of accuracy and computation efficiency.

Applying the Network Simulation Method for testing chaos in a resistively and capacitively shunted Josephson junction model

NASA Astrophysics Data System (ADS)

Bellver, Fernando Gimeno; Garratón, Manuel Caravaca; Soto Meca, Antonio; López, Juan Antonio Vera; Guirao, Juan L. G.; Fernández-Martínez, Manuel

In this paper, we explore the chaotic behavior of resistively and capacitively shunted Josephson junctions via the so-called Network Simulation Method. Such a numerical approach establishes a formal equivalence among physical transport processes and electrical networks, and hence, it can be applied to efficiently deal with a wide range of differential systems. The generality underlying that electrical equivalence allows to apply the circuit theory to several scientific and technological problems. In this work, the Fast Fourier Transform has been applied for chaos detection purposes and the calculations have been carried out in PSpice, an electrical circuit software. Overall, it holds that such a numerical approach leads to quickly computationally solve Josephson differential models. An empirical application regarding the study of the Josephson model completes the paper.

Computational methods for yeast prion curing curves.

PubMed

Ridout, Martin S

2008-10-01

If the chemical guanidine hydrochloride is added to a dividing culture of yeast cells in which some of the protein Sup35p is in its prion form, the proportion of cells that carry replicating units of the prion, termed propagons, decreases gradually over time. Stochastic models to describe this process of 'curing' have been developed in earlier work. The present paper investigates the use of numerical methods of Laplace transform inversion to calculate curing curves and contrasts this with an alternative, more direct, approach that involves numerical integration. Transform inversion is found to provide a much more efficient computational approach that allows different models to be investigated with minimal programming effort. The method is used to investigate the robustness of the curing curve to changes in the assumed distribution of cell generation times. Matlab code is available for carrying out the calculations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Altsybeyev, V.V., E-mail: v.altsybeev@spbu.ru; Ponomarev, V.A.

The particle tracking method with a so-called gun iteration for modeling the space charge is discussed in the following paper. We suggest to apply the emission model based on the Gauss's law for the calculation of the space charge limited current density distribution using considered method. Based on the presented emission model we have developed a numerical algorithm for this calculations. This approach allows us to perform accurate and low time consumpting numerical simulations for different vacuum sources with the curved emitting surfaces and also in the presence of additional physical effects such as bipolar flows and backscattered electrons. Themore » results of the simulations of the cylindrical diode and diode with elliptical emitter with the use of axysimmetric coordinates are presented. The high efficiency and accuracy of the suggested approach are confirmed by the obtained results and comparisons with the analytical solutions.« less

Using memory-efficient algorithm for large-scale time-domain modeling of surface plasmon polaritons propagation in organic light emitting diodes

NASA Astrophysics Data System (ADS)

Zakirov, Andrey; Belousov, Sergei; Valuev, Ilya; Levchenko, Vadim; Perepelkina, Anastasia; Zempo, Yasunari

2017-10-01

We demonstrate an efficient approach to numerical modeling of optical properties of large-scale structures with typical dimensions much greater than the wavelength of light. For this purpose, we use the finite-difference time-domain (FDTD) method enhanced with a memory efficient Locally Recursive non-Locally Asynchronous (LRnLA) algorithm called DiamondTorre and implemented for General Purpose Graphical Processing Units (GPGPU) architecture. We apply our approach to simulation of optical properties of organic light emitting diodes (OLEDs), which is an essential step in the process of designing OLEDs with improved efficiency. Specifically, we consider a problem of excitation and propagation of surface plasmon polaritons (SPPs) in a typical OLED, which is a challenging task given that SPP decay length can be about two orders of magnitude greater than the wavelength of excitation. We show that with our approach it is possible to extend the simulated volume size sufficiently so that SPP decay dynamics is accounted for. We further consider an OLED with periodically corrugated metallic cathode and show how the SPP decay length can be greatly reduced due to scattering off the corrugation. Ultimately, we compare the performance of our algorithm to the conventional FDTD and demonstrate that our approach can efficiently be used for large-scale FDTD simulations with the use of only a single GPGPU-powered workstation, which is not practically feasible with the conventional FDTD.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Recursive linearization of multibody dynamics equations of motion

NASA Technical Reports Server (NTRS)

Lin, Tsung-Chieh; Yae, K. Harold

1989-01-01

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Avoiding numerical pitfalls in social force models

NASA Astrophysics Data System (ADS)

Köster, Gerta; Treml, Franz; Gödel, Marion

2013-06-01

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

Bed turbulent kinetic energy boundary conditions for trapping efficiency and spatial distribution of sediments in basins.

PubMed

Isenmann, Gilles; Dufresne, Matthieu; Vazquez, José; Mose, Robert

2017-10-01

The purpose of this study is to develop and validate a numerical tool for evaluating the performance of a settling basin regarding the trapping of suspended matter. The Euler-Lagrange approach was chosen to model the flow and sediment transport. The numerical model developed relies on the open source library OpenFOAM ® , enhanced with new particle/wall interaction conditions to limit sediment deposition in zones with favourable hydrodynamic conditions (shear stress, turbulent kinetic energy). In particular, a new relation is proposed for calculating the turbulent kinetic energy threshold as a function of the properties of each particle (diameter and density). The numerical model is compared to three experimental datasets taken from the literature and collected for scale models of basins. The comparison of the numerical and experimental results permits concluding on the model's capacity to predict the trapping of particles in a settling basin with an absolute error in the region of 5% when the sediment depositions occur over the entire bed. In the case of sediment depositions localised in preferential zones, their distribution is reproduced well by the model and trapping efficiency is evaluated with an absolute error in the region of 10% (excluding cases of particles with very low density).

Optimal Energy Efficiency Fairness of Nodes in Wireless Powered Communication Networks.

PubMed

Zhang, Jing; Zhou, Qingjie; Ng, Derrick Wing Kwan; Jo, Minho

2017-09-15

In wireless powered communication networks (WPCNs), it is essential to research energy efficiency fairness in order to evaluate the balance of nodes for receiving information and harvesting energy. In this paper, we propose an efficient iterative algorithm for optimal energy efficiency proportional fairness in WPCN. The main idea is to use stochastic geometry to derive the mean proportionally fairness utility function with respect to user association probability and receive threshold. Subsequently, we prove that the relaxed proportionally fairness utility function is a concave function for user association probability and receive threshold, respectively. At the same time, a sub-optimal algorithm by exploiting alternating optimization approach is proposed. Through numerical simulations, we demonstrate that our sub-optimal algorithm can obtain a result close to optimal energy efficiency proportional fairness with significant reduction of computational complexity.

Optimal Energy Efficiency Fairness of Nodes in Wireless Powered Communication Networks

PubMed Central

Zhou, Qingjie; Ng, Derrick Wing Kwan; Jo, Minho

2017-01-01

In wireless powered communication networks (WPCNs), it is essential to research energy efficiency fairness in order to evaluate the balance of nodes for receiving information and harvesting energy. In this paper, we propose an efficient iterative algorithm for optimal energy efficiency proportional fairness in WPCN. The main idea is to use stochastic geometry to derive the mean proportionally fairness utility function with respect to user association probability and receive threshold. Subsequently, we prove that the relaxed proportionally fairness utility function is a concave function for user association probability and receive threshold, respectively. At the same time, a sub-optimal algorithm by exploiting alternating optimization approach is proposed. Through numerical simulations, we demonstrate that our sub-optimal algorithm can obtain a result close to optimal energy efficiency proportional fairness with significant reduction of computational complexity. PMID:28914818

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

A Parallel Numerical Algorithm To Solve Linear Systems Of Equations Emerging From 3D Radiative Transfer

NASA Astrophysics Data System (ADS)

Wichert, Viktoria; Arkenberg, Mario; Hauschildt, Peter H.

2016-10-01

Highly resolved state-of-the-art 3D atmosphere simulations will remain computationally extremely expensive for years to come. In addition to the need for more computing power, rethinking coding practices is necessary. We take a dual approach by introducing especially adapted, parallel numerical methods and correspondingly parallelizing critical code passages. In the following, we present our respective work on PHOENIX/3D. With new parallel numerical algorithms, there is a big opportunity for improvement when iteratively solving the system of equations emerging from the operator splitting of the radiative transfer equation J = ΛS. The narrow-banded approximate Λ-operator Λ* , which is used in PHOENIX/3D, occurs in each iteration step. By implementing a numerical algorithm which takes advantage of its characteristic traits, the parallel code's efficiency is further increased and a speed-up in computational time can be achieved.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Machine learning action parameters in lattice quantum chromodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shanahan, Phiala; Trewartha, Daneil; Detmold, William

Numerical lattice quantum chromodynamics studies of the strong interaction underpin theoretical understanding of many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. Finally, the high information contentmore » and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.« less

Machine learning action parameters in lattice quantum chromodynamics

DOE PAGES

Shanahan, Phiala; Trewartha, Daneil; Detmold, William

2018-05-16

Numerical lattice quantum chromodynamics studies of the strong interaction underpin theoretical understanding of many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. Finally, the high information contentmore » and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.« less

A computational approach for hypersonic nonequilibrium radiation utilizing space partition algorithm and Gauss quadrature

NASA Astrophysics Data System (ADS)

Shang, J. S.; Andrienko, D. A.; Huang, P. G.; Surzhikov, S. T.

2014-06-01

An efficient computational capability for nonequilibrium radiation simulation via the ray tracing technique has been accomplished. The radiative rate equation is iteratively coupled with the aerodynamic conservation laws including nonequilibrium chemical and chemical-physical kinetic models. The spectral properties along tracing rays are determined by a space partition algorithm of the nearest neighbor search process, and the numerical accuracy is further enhanced by a local resolution refinement using the Gauss-Lobatto polynomial. The interdisciplinary governing equations are solved by an implicit delta formulation through the diminishing residual approach. The axisymmetric radiating flow fields over the reentry RAM-CII probe have been simulated and verified with flight data and previous solutions by traditional methods. A computational efficiency gain nearly forty times is realized over that of the existing simulation procedures.

Laser-modified Coulomb scattering states of an electron in the parabolic quasi-Sturmian-Floquet approach

NASA Astrophysics Data System (ADS)

Zaytsev, A. S.; Zaytsev, S. A.; Ancarani, L. U.; Kouzakov, K. A.

2018-04-01

Electron scattering states in combined Coulomb and laser fields are investigated with a nonperturbative approach based on the Hermitian Floquet theory. Taking into account the Coulomb-specific asymptotic behavior of the electron wave functions at large distances, a Lippmann-Schwinger-Floquet equation is derived in the Kramers-Henneberger frame. Such a scattering-state equation is solved numerically employing a set of parabolic quasi-Sturmian functions which have the great advantage of possessing, by construction, adequately chosen incoming or outgoing Coulomb asymptotic behaviors. Our quasi-Sturmian-Floquet approach is tested with a calculation of triple differential cross sections for a laser-assisted (e ,2 e ) process on atomic hydrogen within a first-order Born treatment of the projectile-atom interaction. Convergence with respect to the number of Floquet-Fourier expansion terms is numerically demonstrated. The illustration shows that the developed method is very efficient for the computation of light-dressed states of an electron moving in a Coulomb potential in the presence of laser radiation.

Gutzwiller Monte Carlo approach for a critical dissipative spin model

NASA Astrophysics Data System (ADS)

Casteels, Wim; Wilson, Ryan M.; Wouters, Michiel

2018-06-01

We use the Gutzwiller Monte Carlo approach to simulate the dissipative X Y Z model in the vicinity of a dissipative phase transition. This approach captures classical spatial correlations together with the full on-site quantum behavior while neglecting nonlocal quantum effects. By considering finite two-dimensional lattices of various sizes, we identify a ferromagnetic and two paramagnetic phases, in agreement with earlier studies. The greatly reduced numerical complexity of the Gutzwiller Monte Carlo approach facilitates efficient simulation of relatively large lattice sizes. The inclusion of the spatial correlations allows to capture parts of the phase diagram that are completely missed by the widely applied Gutzwiller decoupling of the density matrix.

On some methods for improving time of reachability sets computation for the dynamic system control problem

NASA Astrophysics Data System (ADS)

Zimovets, Artem; Matviychuk, Alexander; Ushakov, Vladimir

2016-12-01

The paper presents two different approaches to reduce the time of computer calculation of reachability sets. First of these two approaches use different data structures for storing the reachability sets in the computer memory for calculation in single-threaded mode. Second approach is based on using parallel algorithms with reference to the data structures from the first approach. Within the framework of this paper parallel algorithm of approximate reachability set calculation on computer with SMP-architecture is proposed. The results of numerical modelling are presented in the form of tables which demonstrate high efficiency of parallel computing technology and also show how computing time depends on the used data structure.

An Efficient Local Correlation Matrix Decomposition Approach for the Localization Implementation of Ensemble-Based Assimilation Methods

NASA Astrophysics Data System (ADS)

Zhang, Hongqin; Tian, Xiangjun

2018-04-01

Ensemble-based data assimilation methods often use the so-called localization scheme to improve the representation of the ensemble background error covariance (Be). Extensive research has been undertaken to reduce the computational cost of these methods by using the localized ensemble samples to localize Be by means of a direct decomposition of the local correlation matrix C. However, the computational costs of the direct decomposition of the local correlation matrix C are still extremely high due to its high dimension. In this paper, we propose an efficient local correlation matrix decomposition approach based on the concept of alternating directions. This approach is intended to avoid direct decomposition of the correlation matrix. Instead, we first decompose the correlation matrix into 1-D correlation matrices in the three coordinate directions, then construct their empirical orthogonal function decomposition at low resolution. This procedure is followed by the 1-D spline interpolation process to transform the above decompositions to the high-resolution grid. Finally, an efficient correlation matrix decomposition is achieved by computing the very similar Kronecker product. We conducted a series of comparison experiments to illustrate the validity and accuracy of the proposed local correlation matrix decomposition approach. The effectiveness of the proposed correlation matrix decomposition approach and its efficient localization implementation of the nonlinear least-squares four-dimensional variational assimilation are further demonstrated by several groups of numerical experiments based on the Advanced Research Weather Research and Forecasting model.

Flexible Environmental Modeling with Python and Open - GIS

NASA Astrophysics Data System (ADS)

Pryet, Alexandre; Atteia, Olivier; Delottier, Hugo; Cousquer, Yohann

2015-04-01

Numerical modeling now represents a prominent task of environmental studies. During the last decades, numerous commercial programs have been made available to environmental modelers. These software applications offer user-friendly graphical user interfaces that allow an efficient management of many case studies. However, they suffer from a lack of flexibility and closed-source policies impede source code reviewing and enhancement for original studies. Advanced modeling studies require flexible tools capable of managing thousands of model runs for parameter optimization, uncertainty and sensitivity analysis. In addition, there is a growing need for the coupling of various numerical models associating, for instance, groundwater flow modeling to multi-species geochemical reactions. Researchers have produced hundreds of open-source powerful command line programs. However, there is a need for a flexible graphical user interface allowing an efficient processing of geospatial data that comes along any environmental study. Here, we present the advantages of using the free and open-source Qgis platform and the Python scripting language for conducting environmental modeling studies. The interactive graphical user interface is first used for the visualization and pre-processing of input geospatial datasets. Python scripting language is then employed for further input data processing, call to one or several models, and post-processing of model outputs. Model results are eventually sent back to the GIS program, processed and visualized. This approach combines the advantages of interactive graphical interfaces and the flexibility of Python scripting language for data processing and model calls. The numerous python modules available facilitate geospatial data processing and numerical analysis of model outputs. Once input data has been prepared with the graphical user interface, models may be run thousands of times from the command line with sequential or parallel calls. We illustrate this approach with several case studies in groundwater hydrology and geochemistry and provide links to several python libraries that facilitate pre- and post-processing operations.

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron

2016-02-01

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.

Control Synthesis of Discrete-Time T-S Fuzzy Systems: Reducing the Conservatism Whilst Alleviating the Computational Burden.

PubMed

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Peng, Chen

2017-09-01

The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi-Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix approach in the literature, we aim to design a more efficient slack variable approach under a general framework of homogenous matrix polynomials. Thanks to the introduction of a new extended representation for homogeneous matrix polynomials, related matrices with the same coefficient are collected together into one sole set and thus those redundant terms of the augmented multi-indexed matrix approach can be removed, i.e., the computational burden can be alleviated in this paper. More importantly, due to the fact that more useful information is involved into control design, the conservatism of the proposed approach as well is less than the counterpart of the augmented multi-indexed matrix approach. Finally, numerical experiments are given to show the effectiveness of the proposed approach.

Efficient integration method for fictitious domain approaches

NASA Astrophysics Data System (ADS)

Duczek, Sascha; Gabbert, Ulrich

2015-10-01

In the current article, we present an efficient and accurate numerical method for the integration of the system matrices in fictitious domain approaches such as the finite cell method (FCM). In the framework of the FCM, the physical domain is embedded in a geometrically larger domain of simple shape which is discretized using a regular Cartesian grid of cells. Therefore, a spacetree-based adaptive quadrature technique is normally deployed to resolve the geometry of the structure. Depending on the complexity of the structure under investigation this method accounts for most of the computational effort. To reduce the computational costs for computing the system matrices an efficient quadrature scheme based on the divergence theorem (Gauß-Ostrogradsky theorem) is proposed. Using this theorem the dimension of the integral is reduced by one, i.e. instead of solving the integral for the whole domain only its contour needs to be considered. In the current paper, we present the general principles of the integration method and its implementation. The results to several two-dimensional benchmark problems highlight its properties. The efficiency of the proposed method is compared to conventional spacetree-based integration techniques.

Theory and implementation of H-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

NASA Astrophysics Data System (ADS)

Chaillat, Stéphanie; Desiderio, Luca; Ciarlet, Patrick

2017-12-01

In this work, we study the accuracy and efficiency of hierarchical matrix (H-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard H-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. H2-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard H-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the H-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method.

Accounting for care: exploring tensions and contradictions.

PubMed

Choiniere, Jacqueline A

2011-01-01

Within the context of neoliberal restructuring, accountability is primarily linked to efficiency, determined through standardized, numerically based technologies and focused on lengths of stay, utilization indicators, and the like. Disappearing from view in this approach is what is actually happening at the point of care for registered nurses. Grounded in semistructured interviews, this article casts a critical light on the tensions and contradictions experienced by nurses, arguing that instead of a more accountable, effective, or efficient system, this path is jeopardizing nurses' ability to provide needed care within healthy, supportive work environments, setting into motion a fundamental transformation of nursing practice.

Impact of the shape of the implantable ports on their efficiency of flow (injection and flushing)

PubMed Central

Guiffant, Gérard; Flaud, Patrice; Durussel, Jean Jacques; Merckx, Jacques

2014-01-01

Now widely used, totally implantable venous access devices allow mid- and long-term, frequent, repeated, or continuous injection of therapeutic products by vascular, cavitary, or perineural access. The effective flushing of these devices is a key factor that ensures their long-lasting use. We present experimental results and a numerical simulation to demonstrate that the implementation of rounded edge wall cavities improves flushing efficiency. We use the same approaches to suggest that the deposit amount may be reduced by the use of rounded edge wall cavities. PMID:25258561

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn; Lin, Guang, E-mail: guanglin@purdue.edu

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Towards lightweight and flexible high performance nanocrystalline silicon solar cells through light trapping and transport layers

NASA Astrophysics Data System (ADS)

Gray, Zachary R.

This thesis investigates ways to enhance the efficiency of thin film solar cells through the application of both novel nano-element array light trapping architectures and nickel oxide hole transport/electron blocking layers. Experimental results independently demonstrate a 22% enhancement in short circuit current density (JSC) resulting from a nano-element array light trapping architecture and a ˜23% enhancement in fill factor (FF) and ˜16% enhancement in open circuit voltage (VOC) resulting from a nickel oxide transport layer. In each case, the overall efficiency of the device employing the light trapping or transport layer was superior to that of the corresponding control device. Since the efficiency of a solar cell scales with the product of JSC, FF, and VOC, it follows that the results of this thesis suggest high performance thin film solar cells can be realized in the event light trapping architectures and transport layers can be simultaneously optimized. The realizations of these performance enhancements stem from extensive process optimization for numerous light trapping and transport layer fabrication approaches. These approaches were guided by numerical modeling techniques which will also be discussed. Key developments in this thesis include (1) the fabrication of nano-element topographies conducive to light trapping using various fabrication approaches, (2) the deposition of defect free nc-Si:H onto structured topographies by switching from SiH4 to SiF 4 PECVD gas chemistry, and (3) the development of the atomic layer deposition (ALD) growth conditions for NiO. Keywords: light trapping, nano-element array, hole transport layer, electron blocking layer, nickel oxide, nanocrystalline silicon, aluminum doped zinc oxide, atomic layer deposition, plasma enhanced chemical vapor deposition, electron beam lithography, ANSYS HFSS.

An adiabatic linearized path integral approach for quantum time-correlation functions II: a cumulant expansion method for improving convergence.

PubMed

Causo, Maria Serena; Ciccotti, Giovanni; Bonella, Sara; Vuilleumier, Rodolphe

2006-08-17

Linearized mixed quantum-classical simulations are a promising approach for calculating time-correlation functions. At the moment, however, they suffer from some numerical problems that may compromise their efficiency and reliability in applications to realistic condensed-phase systems. In this paper, we present a method that improves upon the convergence properties of the standard algorithm for linearized calculations by implementing a cumulant expansion of the relevant averages. The effectiveness of the new approach is tested by applying it to the challenging computation of the diffusion of an excess electron in a metal-molten salt solution.

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

Lattice dynamics calculations based on density-functional perturbation theory in real space

NASA Astrophysics Data System (ADS)

Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias

2017-06-01

A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

Shock capturing finite difference algorithms for supersonic flow past fighter and missile type configurations

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.

Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

NASA Astrophysics Data System (ADS)

Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang

2004-05-01

We propose a simple, fast sweeping method based on the Lax-Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton-Jacobi equations in any number of spatial dimensions. By using the Lax-Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss-Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss-Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min-max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton-Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

NASA Astrophysics Data System (ADS)

Roubinet, D.; Linde, N.; Jougnot, D.; Irving, J.

2016-05-01

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

Numerical calculation of the Fresnel transform.

PubMed

Kelly, Damien P

2014-04-01

In this paper, we address the problem of calculating Fresnel diffraction integrals using a finite number of uniformly spaced samples. General and simple sampling rules of thumb are derived that allow the user to calculate the distribution for any propagation distance. It is shown how these rules can be extended to fast-Fourier-transform-based algorithms to increase calculation efficiency. A comparison with other theoretical approaches is made.

SIM_EXPLORE: Software for Directed Exploration of Complex Systems

NASA Technical Reports Server (NTRS)

Burl, Michael; Wang, Esther; Enke, Brian; Merline, William J.

2013-01-01

Physics-based numerical simulation codes are widely used in science and engineering to model complex systems that would be infeasible to study otherwise. While such codes may provide the highest- fidelity representation of system behavior, they are often so slow to run that insight into the system is limited. Trying to understand the effects of inputs on outputs by conducting an exhaustive grid-based sweep over the input parameter space is simply too time-consuming. An alternative approach called "directed exploration" has been developed to harvest information from numerical simulators more efficiently. The basic idea is to employ active learning and supervised machine learning to choose cleverly at each step which simulation trials to run next based on the results of previous trials. SIM_EXPLORE is a new computer program that uses directed exploration to explore efficiently complex systems represented by numerical simulations. The software sequentially identifies and runs simulation trials that it believes will be most informative given the results of previous trials. The results of new trials are incorporated into the software's model of the system behavior. The updated model is then used to pick the next round of new trials. This process, implemented as a closed-loop system wrapped around existing simulation code, provides a means to improve the speed and efficiency with which a set of simulations can yield scientifically useful results. The software focuses on the case in which the feedback from the simulation trials is binary-valued, i.e., the learner is only informed of the success or failure of the simulation trial to produce a desired output. The software offers a number of choices for the supervised learning algorithm (the method used to model the system behavior given the results so far) and a number of choices for the active learning strategy (the method used to choose which new simulation trials to run given the current behavior model). The software also makes use of the LEGION distributed computing framework to leverage the power of a set of compute nodes. The approach has been demonstrated on a planetary science application in which numerical simulations are used to study the formation of asteroid families.

LOCAL ORTHOGONAL CUTTING METHOD FOR COMPUTING MEDIAL CURVES AND ITS BIOMEDICAL APPLICATIONS

PubMed Central

Einstein, Daniel R.; Dyedov, Vladimir

2010-01-01

Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, both in terms of theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method called local orthogonal cutting (LOC) for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature (ICC), and integrated stability and consistency tests. These concepts lend themselves to robust numerical techniques and result in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods. PMID:20628546

Co-Optimization of Fuels & Engines for Tomorrow's Energy-Efficient Vehicles

DOE Office of Scientific and Technical Information (OSTI.GOV)

2016-03-01

A new U.S. Department of Energy (DOE) initiative is accelerating the introduction of affordable, scalable, and sustainable biofuels and high-efficiency, low-emission vehicle engines. The simultaneous fuels and vehicles research and development (R&D) is designed to deliver maximum energy savings, emissions reduction, and on-road vehicle performance. The initiative's integrated approach combines the previously independent areas of biofuels and combustion R&D, bringing together two DOE Office of Energy Efficiency & Renewable Energy research offices, nine national laboratories, and numerous industry and academic partners to more rapidly identify commercially viable solutions. This multi-year project will provide industry with the scientific underpinnings required tomore » move new biofuels and advanced engine systems to market faster while identifying and addressing barriers to their commercialization. This project's ambitious, first-of-its-kind approach simultaneously tackles fuel and engine innovation to co-optimize performance of both elements and provide dramatic and rapid cuts in fuel use and emissions.« less

Efficient simulation of press hardening process through integrated structural and CFD analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palaniswamy, Hariharasudhan; Mondalek, Pamela; Wronski, Maciek

Press hardened steel parts are being increasingly used in automotive structures for their higher strength to meet safety standards while reducing vehicle weight to improve fuel consumption. However, manufacturing of sheet metal parts by press hardening process to achieve desired properties is extremely challenging as it involves complex interaction of plastic deformation, metallurgical change, thermal distribution, and fluid flow. Numerical simulation is critical for successful design of the process and to understand the interaction among the numerous process parameters to control the press hardening process in order to consistently achieve desired part properties. Until now there has been no integratedmore » commercial software solution that can efficiently model the complete process from forming of the blank, heat transfer between the blank and tool, microstructure evolution in the blank, heat loss from tool to the fluid that flows through water channels in the tools. In this study, a numerical solution based on Altair HyperWorks® product suite involving RADIOSS®, a non-linear finite element based structural analysis solver and AcuSolve®, an incompressible fluid flow solver based on Galerkin Least Square Finite Element Method have been utilized to develop an efficient solution for complete press hardening process design and analysis. RADIOSS is used to handle the plastic deformation, heat transfer between the blank and tool, and microstructure evolution in the blank during cooling. While AcuSolve is used to efficiently model heat loss from tool to the fluid that flows through water channels in the tools. The approach is demonstrated through some case studies.« less

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits. Thesis

NASA Technical Reports Server (NTRS)

Oh, K. S.; Schutt-Aine, J.

1995-01-01

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Electromagnetic properties of metal-dielectric media and their applications

NASA Astrophysics Data System (ADS)

Animilli, Shravan Rakesh

The main objective of this dissertation is to investigate nano-structured random composite materials, which exhibit anomalous phenomena, such as the extraordinary enhancements of linear and non-linear optical processes due to excitation of collective electronic states, surface plasmons (SP). The main goal is to develop a time and memory efficient novel numerical method to study the properties of these random media in three dimensions (3D) by utilization of multi core processing and packages such as MPI for parallel execution. The developed numerical studies are then utilized to provide a comprehensive characterization and optimization of a surface plasmon enhanced solar cell (SPESC) and to serve as a test bed for enhanced bio and chemical sensing. In this context, this thesis work develops an efficient and exact numerical algorithm here referred to as Block Elimination Method (BE) which provides the unique capability of modeling extremely large scale composite materials (with up to 1 million strongly interacting metal or dielectric particles). This capability is crucial in order to study the electromagnetic response of large scale inhomogeneous (fractal) films and bulk composites at critical concentrations (percolation). The developed numerical method is used to accurately estimate parameters that describe the composite materials, including the effective conductivity and correlation length scaling exponents, as well as density of states and localization length exponents at the band center. This works reveals, for a first time, a unique de-localization mechanism that plays an important role in the excitation of charge-density waves, i.e. surface plasmons (SP), in metal-dielectric composites. It also shows that in 3D metal-dielectric percolation systems the local fields distribution function for frequencies close to the single particle plasmon resonance is log-normal which is a signature of a metal-dielectric phase transition manifested in the optical response of the composites. Based on the obtained numerical data a scaling theory for the higher order electric field moments is developed. A distinct evidence of singularities in the surface plasmon density of states and localization length is obtained, correlating with results previously obtained for two dimensional systems. This leads to the main finding of this work; i.e., the delocalization of surface plasmon states in percolating metal-dielectric composite materials is universally present regardless of the dimensionality of the problem. This dissertation also proposes a new approach toward developing highly efficient inorganic/organic solar cell, by presenting a method for enhancement in the optical absorption and overall cell efficiency. Specifically, the approach improves the operation characteristics of inorganic semiconductor (e.g. Si and a-Si) and organic (P3HT:PCBM) thin film solar cells by integrating a thin, inhomogeneous, metal-dielectric composite (MDC) electrode at the interface between the transparent electrode and active layer. Through numerical simulations, we show that under solar illumination, surface plasmons are excited within the fractal MDC electrode across an extremely broad range of optical frequencies, trapping the incoming light and ensuring an optimal absorption into the active layer of the solar cells. An analytical model is developed to study the I-V characteristics of the cells, providing a pathway toward achieving optimal efficiency and better understanding of the behavior of charge carriers. Using this model, it is shown that including gold MDC electrodes can lead to an enhancement in solar cell power conversion efficiency up to 33% higher compared to the benchmark device.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Local phase method for designing and optimizing metasurface devices.

PubMed

Hsu, Liyi; Dupré, Matthieu; Ndao, Abdoulaye; Yellowhair, Julius; Kanté, Boubacar

2017-10-16

Metasurfaces have attracted significant attention due to their novel designs for flat optics. However, the approach usually used to engineer metasurface devices assumes that neighboring elements are identical, by extracting the phase information from simulations with periodic boundaries, or that near-field coupling between particles is negligible, by extracting the phase from single particle simulations. This is not the case most of the time and the approach thus prevents the optimization of devices that operate away from their optimum. Here, we propose a versatile numerical method to obtain the phase of each element within the metasurface (meta-atoms) while accounting for near-field coupling. Quantifying the phase error of each element of the metasurfaces with the proposed local phase method paves the way to the design of highly efficient metasurface devices including, but not limited to, deflectors, high numerical aperture metasurface concentrators, lenses, cloaks, and modulators.

Comparison of methods for developing the dynamics of rigid-body systems

NASA Technical Reports Server (NTRS)

Ju, M. S.; Mansour, J. M.

1989-01-01

Several approaches for developing the equations of motion for a three-degree-of-freedom PUMA robot were compared on the basis of computational efficiency (i.e., the number of additions, subtractions, multiplications, and divisions). Of particular interest was the investigation of the use of computer algebra as a tool for developing the equations of motion. Three approaches were implemented algebraically: Lagrange's method, Kane's method, and Wittenburg's method. Each formulation was developed in absolute and relative coordinates. These six cases were compared to each other and to a recursive numerical formulation. The results showed that all of the formulations implemented algebraically required fewer calculations than the recursive numerical algorithm. The algebraic formulations required fewer calculations in absolute coordinates than in relative coordinates. Each of the algebraic formulations could be simplified, using patterns from Kane's method, to yield the same number of calculations in a given coordinate system.

A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance

NASA Astrophysics Data System (ADS)

Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide

2016-12-01

We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations. The proposed method is tested on three application problems of interest in mathematical finance, namely the calculation of the survival probability of an indebted firm, the pricing of a single-knock-out put option and the pricing of a double-knock-out put option. The results obtained reveal that the novel approach is extremely accurate and fast, and performs significantly better than the finite difference method.

A computational and cellular solids approach to the stiffness-based design of bone scaffolds.

PubMed

Norato, J A; Wagoner Johnson, A J

2011-09-01

We derive a cellular solids approach to the design of bone scaffolds for stiffness and pore size. Specifically, we focus on scaffolds made of stacked, alternating, orthogonal layers of hydroxyapatite rods, such as those obtained via micro-robotic deposition, and aim to determine the rod diameter, spacing and overlap required to obtain specified elastic moduli and pore size. To validate and calibrate the cellular solids model, we employ a finite element model and determine the effective scaffold moduli via numerical homogenization. In order to perform an efficient, automated execution of the numerical studies, we employ a geometry projection method so that analyses corresponding to different scaffold dimensions can be performed on a fixed, non-conforming mesh. Based on the developed model, we provide design charts to aid in the selection of rod diameter, spacing and overlap to be used in the robotic deposition to attain desired elastic moduli and pore size.

Variational Approach to Enhanced Sampling and Free Energy Calculations

NASA Astrophysics Data System (ADS)

Valsson, Omar; Parrinello, Michele

2014-08-01

The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.

Application of Gauss's law space-charge limited emission model in iterative particle tracking method

NASA Astrophysics Data System (ADS)

Altsybeyev, V. V.; Ponomarev, V. A.

2016-11-01

The particle tracking method with a so-called gun iteration for modeling the space charge is discussed in the following paper. We suggest to apply the emission model based on the Gauss's law for the calculation of the space charge limited current density distribution using considered method. Based on the presented emission model we have developed a numerical algorithm for this calculations. This approach allows us to perform accurate and low time consumpting numerical simulations for different vacuum sources with the curved emitting surfaces and also in the presence of additional physical effects such as bipolar flows and backscattered electrons. The results of the simulations of the cylindrical diode and diode with elliptical emitter with the use of axysimmetric coordinates are presented. The high efficiency and accuracy of the suggested approach are confirmed by the obtained results and comparisons with the analytical solutions.

Full-degrees-of-freedom frequency based substructuring

NASA Astrophysics Data System (ADS)

Drozg, Armin; Čepon, Gregor; Boltežar, Miha

2018-01-01

Dividing the whole system into multiple subsystems and a separate dynamic analysis is common practice in the field of structural dynamics. The substructuring process improves the computational efficiency and enables an effective realization of the local optimization, modal updating and sensitivity analyses. This paper focuses on frequency-based substructuring methods using experimentally obtained data. An efficient substructuring process has already been demonstrated using numerically obtained frequency-response functions (FRFs). However, the experimental process suffers from several difficulties, among which, many of them are related to the rotational degrees of freedom. Thus, several attempts have been made to measure, expand or combine numerical correction methods in order to obtain a complete response model. The proposed methods have numerous limitations and are not yet generally applicable. Therefore, in this paper an alternative approach based on experimentally obtained data only, is proposed. The force-excited part of the FRF matrix is measured with piezoelectric translational and rotational direct accelerometers. The incomplete moment-excited part of the FRF matrix is expanded, based on the modal model. The proposed procedure is integrated in a Lagrange Multiplier Frequency Based Substructuring method and demonstrated on a simple beam structure, where the connection coordinates are mainly associated with the rotational degrees of freedom.

MCore: A High-Order Finite-Volume Dynamical Core for Atmospheric General Circulation Models

NASA Astrophysics Data System (ADS)

Ullrich, P.; Jablonowski, C.

2011-12-01

The desire for increasingly accurate predictions of the atmosphere has driven numerical models to smaller and smaller resolutions, while simultaneously exponentially driving up the cost of existing numerical models. Even with the modern rapid advancement of computational performance, it is estimated that it will take more than twenty years before existing models approach the scales needed to resolve atmospheric convection. However, smarter numerical methods may allow us to glimpse the types of results we would expect from these fine-scale simulations while only requiring a fraction of the computational cost. The next generation of atmospheric models will likely need to rely on both high-order accuracy and adaptive mesh refinement in order to properly capture features of interest. We present our ongoing research on developing a set of ``smart'' numerical methods for simulating the global non-hydrostatic fluid equations which govern atmospheric motions. We have harnessed a high-order finite-volume based approach in developing an atmospheric dynamical core on the cubed-sphere. This type of method is desirable for applications involving adaptive grids, since it has been shown that spuriously reflected wave modes are intrinsically damped out under this approach. The model further makes use of an implicit-explicit Runge-Kutta-Rosenbrock (IMEX-RKR) time integrator for accurate and efficient coupling of the horizontal and vertical model components. We survey the algorithmic development of the model and present results from idealized dynamical core test cases, as well as give a glimpse at future work with our model.

Model Evaluation To Measuring Efficiencies of ICT Development In Indonesia Region Using DEA

NASA Astrophysics Data System (ADS)

Efendi, Syahril; Fadly Syahputra, M.; Anggia Muchtar, M.

2018-01-01

ICT Pura or digital city is a program designed by the Indonesian government with the main objective is to determine the level of readiness of each district and city in each province in the era of digital economy. It is necessarily to evaluate whether a city or a region that was successfully managing ICT better than other city and significantly contributes to the communities and living systems. Data envelopment analysis (DEA) is a well known technique to estimate efficiency and returns to scale through the construction of a best practice frontier, based on non-parametric mathematical programming approach. This paper addresses DEA BCC method to get index of efficiencies for all region in Indonesia covered by ICT Pura. Numerical result is given.

A finite element approach to self-consistent field theory calculations of multiblock polymers

NASA Astrophysics Data System (ADS)

Ackerman, David M.; Delaney, Kris; Fredrickson, Glenn H.; Ganapathysubramanian, Baskar

2017-02-01

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.

Using auxiliary information to improve wildlife disease surveillance when infected animals are not detected: a Bayesian approach

USGS Publications Warehouse

Heisey, Dennis M.; Jennelle, Christopher S.; Russell, Robin E.; Walsh, Daniel P.

2014-01-01

There are numerous situations in which it is important to determine whether a particular disease of interest is present in a free-ranging wildlife population. However adequate disease surveillance can be labor-intensive and expensive and thus there is substantial motivation to conduct it as efficiently as possible. Surveillance is often based on the assumption of a simple random sample, but this can almost always be improved upon if there is auxiliary information available about disease risk factors. We present a Bayesian approach to disease surveillance when auxiliary risk information is available which will usually allow for substantial improvements over simple random sampling. Others have employed risk weights in surveillance, but this can result in overly optimistic statements regarding freedom from disease due to not accounting for the uncertainty in the auxiliary information; our approach remedies this. We compare our Bayesian approach to a published example of risk weights applied to chronic wasting disease in deer in Colorado, and we also present calculations to examine when uncertainty in the auxiliary information has a serious impact on the risk weights approach. Our approach allows “apples-to-apples” comparisons of surveillance efficiencies between units where heterogeneous samples were collected

A finite element approach to self-consistent field theory calculations of multiblock polymers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ackerman, David M.; Delaney, Kris; Fredrickson, Glenn H.

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibriummore » polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.« less

Rice growing farmers efficiency measurement using a slack based interval DEA model with undesirable outputs

NASA Astrophysics Data System (ADS)

Khan, Sahubar Ali Mohd. Nadhar; Ramli, Razamin; Baten, M. D. Azizul

2017-11-01

In recent years eco-efficiency which considers the effect of production process on environment in determining the efficiency of firms have gained traction and a lot of attention. Rice farming is one of such production processes which typically produces two types of outputs which are economic desirable as well as environmentally undesirable. In efficiency analysis, these undesirable outputs cannot be ignored and need to be included in the model to obtain the actual estimation of firm's efficiency. There are numerous approaches that have been used in data envelopment analysis (DEA) literature to account for undesirable outputs of which directional distance function (DDF) approach is the most widely used as it allows for simultaneous increase in desirable outputs and reduction of undesirable outputs. Additionally, slack based DDF DEA approaches considers the output shortfalls and input excess in determining efficiency. In situations when data uncertainty is present, the deterministic DEA model is not suitable to be used as the effects of uncertain data will not be considered. In this case, it has been found that interval data approach is suitable to account for data uncertainty as it is much simpler to model and need less information regarding the underlying data distribution and membership function. The proposed model uses an enhanced DEA model which is based on DDF approach and incorporates slack based measure to determine efficiency in the presence of undesirable factors and data uncertainty. Interval data approach was used to estimate the values of inputs, undesirable outputs and desirable outputs. Two separate slack based interval DEA models were constructed for optimistic and pessimistic scenarios. The developed model was used to determine rice farmers efficiency from Kepala Batas, Kedah. The obtained results were later compared to the results obtained using a deterministic DDF DEA model. The study found that 15 out of 30 farmers are efficient in all cases. It is also found that the average efficiency values of all farmers for deterministic case is always lower than the optimistic scenario and higher than pessimistic scenario. The results confirm with the hypothesis since farmers who operates in optimistic scenario are in best production situation compared to pessimistic scenario in which they operate in worst production situation. The results show that the proposed model can be applied when data uncertainty is present in the production environment.

A time-domain finite element boundary integral approach for elastic wave scattering

NASA Astrophysics Data System (ADS)

Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.

2018-04-01

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Bessel smoothing filter for spectral-element mesh

NASA Astrophysics Data System (ADS)

Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.

2017-06-01

Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the efficiency and flexibility of the approach proposed.

Decoupled CFD-based optimization of efficiency and cavitation performance of a double-suction pump

NASA Astrophysics Data System (ADS)

Škerlavaj, A.; Morgut, M.; Jošt, D.; Nobile, E.

2017-04-01

In this study the impeller geometry of a double-suction pump ensuring the best performances in terms of hydraulic efficiency and reluctance of cavitation is determined using an optimization strategy, which was driven by means of the modeFRONTIER optimization platform. The different impeller shapes (designs) are modified according to the optimization parameters and tested with a computational fluid dynamics (CFD) software, namely ANSYS CFX. The simulations are performed using a decoupled approach, where only the impeller domain region is numerically investigated for computational convenience. The flow losses in the volute are estimated on the base of the velocity distribution at the impeller outlet. The best designs are then validated considering the computationally more expensive full geometry CFD model. The overall results show that the proposed approach is suitable for quick impeller shape optimization.

A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities

NASA Astrophysics Data System (ADS)

Hajarolasvadi, Setare; Elbanna, Ahmed E.

2017-11-01

The finite difference (FD) and the spectral boundary integral (SBI) methods have been used extensively to model spontaneously-propagating shear cracks in a variety of engineering and geophysical applications. In this paper, we propose a new modelling approach in which these two methods are combined through consistent exchange of boundary tractions and displacements. Benefiting from the flexibility of FD and the efficiency of SBI methods, the proposed hybrid scheme will solve a wide range of problems in a computationally efficient way. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low-velocity layer and the other in which off-fault plasticity is permitted. We discuss possible potential uses of the hybrid scheme in earthquake cycle simulations as well as an exact absorbing boundary condition.

Viscoelastic damped response of cross-ply laminated shallow spherical shells subjected to various impulsive loads

NASA Astrophysics Data System (ADS)

Şahan, Mehmet Fatih

2017-11-01

In this paper, the viscoelastic damped response of cross-ply laminated shallow spherical shells is investigated numerically in a transformed Laplace space. In the proposed approach, the governing differential equations of cross-ply laminated shallow spherical shell are derived using the dynamic version of the principle of virtual displacements. Following this, the Laplace transform is employed in the transient analysis of viscoelastic laminated shell problem. Also, damping can be incorporated with ease in the transformed domain. The transformed time-independent equations in spatial coordinate are solved numerically by Gauss elimination. Numerical inverse transformation of the results into the real domain are operated by the modified Durbin transform method. Verification of the presented method is carried out by comparing the results with those obtained by the Newmark method and ANSYS finite element software. Furthermore, the developed solution approach is applied to problems with several impulsive loads. The novelty of the present study lies in the fact that a combination of the Navier method and Laplace transform is employed in the analysis of cross-ply laminated shallow spherical viscoelastic shells. The numerical sample results have proved that the presented method constitutes a highly accurate and efficient solution, which can be easily applied to the laminated viscoelastic shell problems.

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Lam, P.; Fertis, D.; Zeid, I.

1982-01-01

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

NASA Astrophysics Data System (ADS)

Yokota, Rio; Barba, L. A.; Narumi, Tetsu; Yasuoka, Kenji

2013-03-01

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on GPU hardware using single precision. The simulations use a vortex particle method to solve the Navier-Stokes equations, with a highly parallel fast multipole method (FMM) as numerical engine, and match the current record in mesh size for this application, a cube of 40963 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the FFT algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the FMM-based vortex method achieving 74% parallel efficiency on 4096 processes (one GPU per MPI process, 3 GPUs per node of the TSUBAME-2.0 system). The FFT-based spectral method is able to achieve just 14% parallel efficiency on the same number of MPI processes (using only CPU cores), due to the all-to-all communication pattern of the FFT algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

Mean-Field Description of Ionic Size Effects with Non-Uniform Ionic Sizes: A Numerical Approach

PubMed Central

Zhou, Shenggao; Wang, Zhongming; Li, Bo

2013-01-01

Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, i.e., there is no explicit, Boltzmann type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such non-uniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with non-uniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson–Boltzmann theory, or the generalized Poisson–Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed. PMID:21929014

Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Mitchell, Travis; Leonardi, Christopher; Bolster, Diogo

2017-11-01

Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013), 10.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, Nai-Yuan; Zavala, Victor M.

We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection viamore » symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.« less

Extended Importance Sampling for Reliability Analysis under Evidence Theory

NASA Astrophysics Data System (ADS)

Yuan, X. K.; Chen, B.; Zhang, B. Q.

2018-05-01

In early engineering practice, the lack of data and information makes uncertainty difficult to deal with. However, evidence theory has been proposed to handle uncertainty with limited information as an alternative way to traditional probability theory. In this contribution, a simulation-based approach, called ‘Extended importance sampling’, is proposed based on evidence theory to handle problems with epistemic uncertainty. The proposed approach stems from the traditional importance sampling for reliability analysis under probability theory, and is developed to handle the problem with epistemic uncertainty. It first introduces a nominal instrumental probability density function (PDF) for every epistemic uncertainty variable, and thus an ‘equivalent’ reliability problem under probability theory is obtained. Then the samples of these variables are generated in a way of importance sampling. Based on these samples, the plausibility and belief (upper and lower bounds of probability) can be estimated. It is more efficient than direct Monte Carlo simulation. Numerical and engineering examples are given to illustrate the efficiency and feasible of the proposed approach.

Game theoretic sensor management for target tracking

NASA Astrophysics Data System (ADS)

Shen, Dan; Chen, Genshe; Blasch, Erik; Pham, Khanh; Douville, Philip; Yang, Chun; Kadar, Ivan

2010-04-01

This paper develops and evaluates a game-theoretic approach to distributed sensor-network management for target tracking via sensor-based negotiation. We present a distributed sensor-based negotiation game model for sensor management for multi-sensor multi-target tacking situations. In our negotiation framework, each negotiation agent represents a sensor and each sensor maximizes their utility using a game approach. The greediness of each sensor is limited by the fact that the sensor-to-target assignment efficiency will decrease if too many sensor resources are assigned to a same target. It is similar to the market concept in real world, such as agreements between buyers and sellers in an auction market. Sensors are willing to switch targets so that they can obtain their highest utility and the most efficient way of applying their resources. Our sub-game perfect equilibrium-based negotiation strategies dynamically and distributedly assign sensors to targets. Numerical simulations are performed to demonstrate our sensor-based negotiation approach for distributed sensor management.

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

NASA Technical Reports Server (NTRS)

Nark, Douglas M.; Watson, Willie R.; Mani, Ramani

2007-01-01

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Systematic Comparison of Reverse Phase and Hydrophilic Interaction Liquid Chromatography Platforms for the Analysis of N-linked Glycans

PubMed Central

Walker, S. Hunter; Carlisle, Brandon C.; Muddiman, David C.

2013-01-01

Due to the hydrophilic nature of glycans, reverse phase chromatography has not been widely used as a glycomic separation technique coupled to mass spectrometry. Other approaches such as hydrophilic interaction chromatography and porous graphitized carbon chromatography are often employed, though these strategies frequently suffer from decreased chromatographic resolution, long equilibration times, indefinite retention, and column bleed. Herein, it is shown that through an efficient hydrazone formation derivatization of N-linked glycans (∼4 hr of additional sample preparation time which is carried out in parallel), numerous experimental and practical advantages are gained when analyzing the glycans by online reverse phase chromatography. These benefits include an increased number of glycans detected, increased peak capacity of the separation, and the ability to analyze glycans on the identical liquid chromatography-mass spectrometry platform commonly used for proteomic analyses. The data presented show that separation of derivatized N-linked glycans by reverse phase chromatography significantly out-performs traditional separation of native or derivatized glycans by hydrophilic interaction chromatography. Furthermore, the movement to a more ubiquitous separation technique will afford numerous research groups the opportunity to analyze both proteomic and glycomic samples on the same platform with minimal time and physical change between experiments, increasing the efficiency of ‘multi-omic’ biological approaches. PMID:22954204

An adjoint method of sensitivity analysis for residual vibrations of structures subject to impacts

NASA Astrophysics Data System (ADS)

Yan, Kun; Cheng, Gengdong

2018-03-01

For structures subject to impact loads, the residual vibration reduction is more and more important as the machines become faster and lighter. An efficient sensitivity analysis of residual vibration with respect to structural or operational parameters is indispensable for using a gradient based optimization algorithm, which reduces the residual vibration in either active or passive way. In this paper, an integrated quadratic performance index is used as the measure of the residual vibration, since it globally measures the residual vibration response and its calculation can be simplified greatly with Lyapunov equation. Several sensitivity analysis approaches for performance index were developed based on the assumption that the initial excitations of residual vibration were given and independent of structural design. Since the resulting excitations by the impact load often depend on structural design, this paper aims to propose a new efficient sensitivity analysis method for residual vibration of structures subject to impacts to consider the dependence. The new method is developed by combining two existing methods and using adjoint variable approach. Three numerical examples are carried out and demonstrate the accuracy of the proposed method. The numerical results show that the dependence of initial excitations on structural design variables may strongly affects the accuracy of sensitivities.

Automatic red eye correction and its quality metric

NASA Astrophysics Data System (ADS)

Safonov, Ilia V.; Rychagov, Michael N.; Kang, KiMin; Kim, Sang Ho

2008-01-01

The red eye artifacts are troublesome defect of amateur photos. Correction of red eyes during printing without user intervention and making photos more pleasant for an observer are important tasks. The novel efficient technique of automatic correction of red eyes aimed for photo printers is proposed. This algorithm is independent from face orientation and capable to detect paired red eyes as well as single red eyes. The approach is based on application of 3D tables with typicalness levels for red eyes and human skin tones and directional edge detection filters for processing of redness image. Machine learning is applied for feature selection. For classification of red eye regions a cascade of classifiers including Gentle AdaBoost committee from Classification and Regression Trees (CART) is applied. Retouching stage includes desaturation, darkening and blending with initial image. Several versions of approach implementation using trade-off between detection and correction quality, processing time, memory volume are possible. The numeric quality criterion of automatic red eye correction is proposed. This quality metric is constructed by applying Analytic Hierarchy Process (AHP) for consumer opinions about correction outcomes. Proposed numeric metric helped to choose algorithm parameters via optimization procedure. Experimental results demonstrate high accuracy and efficiency of the proposed algorithm in comparison with existing solutions.

Evaluation of Optimal Formulas for Gravitational Tensors up to Gravitational Curvatures of a Tesseroid

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-01-01

The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss-Legendre Quadrature (GLQ) and Newton-Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell's thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC formulas can avoid the polar singularity problem.

Complete synthetic seismograms based on a spherical self-gravitating Earth model with an atmosphere-ocean-mantle-core structure

NASA Astrophysics Data System (ADS)

Wang, Rongjiang; Heimann, Sebastian; Zhang, Yong; Wang, Hansheng; Dahm, Torsten

2017-04-01

A hybrid method is proposed to calculate complete synthetic seismograms based on a spherically symmetric and self-gravitating Earth with a multi-layered structure of atmosphere, ocean, mantle, liquid core and solid core. For large wavelengths, a numerical scheme is used to solve the geodynamic boundary-value problem without any approximation on the deformation and gravity coupling. With the decreasing wavelength, the gravity effect on the deformation becomes negligible and the analytical propagator scheme can be used. Many useful approaches are used to overcome the numerical problems that may arise in both analytical and numerical schemes. Some of these approaches have been established in the seismological community and the others are developed for the first time. Based on the stable and efficient hybrid algorithm, an all-in-one code QSSP is implemented to cover the complete spectrum of seismological interests. The performance of the code is demonstrated by various tests including the curvature effect on teleseismic body and surface waves, the appearance of multiple reflected, teleseismic core phases, the gravity effect on long period surface waves and free oscillations, the simulation of near-field displacement seismograms with the static offset, the coupling of tsunami and infrasound waves, and free oscillations of the solid Earth, the atmosphere and the ocean. QSSP is open source software that can be used as a stand-alone FORTRAN code or may be applied in combination with a Python toolbox to calculate and handle Green's function databases for efficient coding of source inversion problems.

Complete synthetic seismograms based on a spherical self-gravitating Earth model with an atmosphere-ocean-mantle-core structure

NASA Astrophysics Data System (ADS)

Wang, Rongjiang; Heimann, Sebastian; Zhang, Yong; Wang, Hansheng; Dahm, Torsten

2017-09-01

A hybrid method is proposed to calculate complete synthetic seismograms based on a spherically symmetric and self-gravitating Earth with a multilayered structure of atmosphere, ocean, mantle, liquid core and solid core. For large wavelengths, a numerical scheme is used to solve the geodynamic boundary-value problem without any approximation on the deformation and gravity coupling. With decreasing wavelength, the gravity effect on the deformation becomes negligible and the analytical propagator scheme can be used. Many useful approaches are used to overcome the numerical problems that may arise in both analytical and numerical schemes. Some of these approaches have been established in the seismological community and the others are developed for the first time. Based on the stable and efficient hybrid algorithm, an all-in-one code QSSP is implemented to cover the complete spectrum of seismological interests. The performance of the code is demonstrated by various tests including the curvature effect on teleseismic body and surface waves, the appearance of multiple reflected, teleseismic core phases, the gravity effect on long period surface waves and free oscillations, the simulation of near-field displacement seismograms with the static offset, the coupling of tsunami and infrasound waves, and free oscillations of the solid Earth, the atmosphere and the ocean. QSSP is open source software that can be used as a stand-alone FORTRAN code or may be applied in combination with a Python toolbox to calculate and handle Green's function databases for efficient coding of source inversion problems.

Sound Power Estimation for Beam and Plate Structures Using Polyvinylidene Fluoride Films as Sensors

PubMed Central

Mao, Qibo; Zhong, Haibing

2017-01-01

The theory for calculation and/or measurement of sound power based on the classical velocity-based radiation mode (V-mode) approach is well established for planar structures. However, the current V-mode theory is limited in scope in that it can only be applied to conventional motion sensors (i.e., accelerometers). In this study, in order to estimate the sound power of vibrating beam and plate structure by using polyvinylidene fluoride (PVDF) films as sensors, a PVDF-based radiation mode (C-mode) approach concept is introduced to determine the sound power radiation from the output signals of PVDF films of the vibrating structure. The proposed method is a hybrid of vibration measurement and numerical calculation of C-modes. The proposed C-mode approach has the following advantages: (1) compared to conventional motion sensors, the PVDF films are lightweight, flexible, and low-cost; (2) there is no need for special measuring environments, since the proposed method does not require the measurement of sound fields; (3) In low frequency range (typically with dimensionless frequency kl < 4), the radiation efficiencies of the C-modes fall off very rapidly with increasing mode order, furthermore, the shapes of the C-modes remain almost unchanged, which means that the computation load can be significantly reduced due to the fact only the first few dominant C-modes are involved in the low frequency range. Numerical simulations and experimental investigations were carried out to verify the accuracy and efficiency of the proposed method. PMID:28509870

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

Simplex-based optimization of numerical and categorical inputs in early bioprocess development: Case studies in HT chromatography.

PubMed

Konstantinidis, Spyridon; Titchener-Hooker, Nigel; Velayudhan, Ajoy

2017-08-01

Bioprocess development studies often involve the investigation of numerical and categorical inputs via the adoption of Design of Experiments (DoE) techniques. An attractive alternative is the deployment of a grid compatible Simplex variant which has been shown to yield optima rapidly and consistently. In this work, the method is combined with dummy variables and it is deployed in three case studies wherein spaces are comprised of both categorical and numerical inputs, a situation intractable by traditional Simplex methods. The first study employs in silico data and lays out the dummy variable methodology. The latter two employ experimental data from chromatography based studies performed with the filter-plate and miniature column High Throughput (HT) techniques. The solute of interest in the former case study was a monoclonal antibody whereas the latter dealt with the separation of a binary system of model proteins. The implemented approach prevented the stranding of the Simplex method at local optima, due to the arbitrary handling of the categorical inputs, and allowed for the concurrent optimization of numerical and categorical, multilevel and/or dichotomous, inputs. The deployment of the Simplex method, combined with dummy variables, was therefore entirely successful in identifying and characterizing global optima in all three case studies. The Simplex-based method was further shown to be of equivalent efficiency to a DoE-based approach, represented here by D-Optimal designs. Such an approach failed, however, to both capture trends and identify optima, and led to poor operating conditions. It is suggested that the Simplex-variant is suited to development activities involving numerical and categorical inputs in early bioprocess development. © 2017 The Authors. Biotechnology Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Assessment of the performance of numerical modeling in reproducing a replenishment of sediments in a water-worked channel

NASA Astrophysics Data System (ADS)

Juez, C.; Battisacco, E.; Schleiss, A. J.; Franca, M. J.

2016-06-01

The artificial replenishment of sediment is used as a method to re-establish sediment continuity downstream of a dam. However, the impact of this technique on the hydraulics conditions, and resulting bed morphology, is yet to be understood. Several numerical tools have been developed during last years for modeling sediment transport and morphology evolution which can be used for this application. These models range from 1D to 3D approaches: the first being over simplistic for the simulation of such a complex geometry; the latter requires often a prohibitive computational effort. However, 2D models are computationally efficient and in these cases may already provide sufficiently accurate predictions of the morphology evolution caused by the sediment replenishment in a river. Here, the 2D shallow water equations in combination with the Exner equation are solved by means of a weak-coupled strategy. The classical friction approach considered for reproducing the bed channel roughness has been modified to take into account the morphological effect of replenishment which provokes a channel bed fining. Computational outcomes are compared with four sets of experimental data obtained from several replenishment configurations studied in the laboratory. The experiments differ in terms of placement volume and configuration. A set of analysis parameters is proposed for the experimental-numerical comparison, with particular attention to the spreading, covered surface and travel distance of placed replenishment grains. The numerical tool is reliable in reproducing the overall tendency shown by the experimental data. The effect of fining roughness is better reproduced with the approach herein proposed. However, it is also highlighted that the sediment clusters found in the experiment are not well numerically reproduced in the regions of the channel with a limited number of sediment grains.

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics.

PubMed

Lin, Yen Ting; Chylek, Lily A; Lemons, Nathan W; Hlavacek, William S

2018-06-21

The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.

An adjoint-based framework for maximizing mixing in binary fluids

NASA Astrophysics Data System (ADS)

Eggl, Maximilian; Schmid, Peter

2017-11-01

Mixing in the inertial, but laminar parameter regime is a common application in a wide range of industries. Enhancing the efficiency of mixing processes thus has a fundamental effect on product quality, material homogeneity and, last but not least, production costs. In this project, we address mixing efficiency in the above mentioned regime (Reynolds number Re = 1000 , Peclet number Pe = 1000) by developing and demonstrating an algorithm based on nonlinear adjoint looping that minimizes the variance of a passive scalar field which models our binary Newtonian fluids. The numerical method is based on the FLUSI code (Engels et al. 2016), a Fourier pseudo-spectral code, which we modified and augmented by scalar transport and adjoint equations. Mixing is accomplished by moving stirrers which are numerically modeled using a penalization approach. In our two-dimensional simulations we consider rotating circular and elliptic stirrers and extract optimal mixing strategies from the iterative scheme. The case of optimizing shape and rotational speed of the stirrers will be demonstrated.

Formation Flying Design and Applications in Weak Stability Boundary Regions

NASA Technical Reports Server (NTRS)

Folta, David

2003-01-01

Weak Stability regions serve as superior locations for interferometric scientific investigations. These regions are often selected to minimize environmental disturbances and maximize observing efficiency. Design of formations in these regions are becoming ever more challenging as more complex missions are envisioned. The development of algorithms to enable the capability for formation design must be further enabled to incorporate better understanding of WSB solution space. This development will improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple formation missions in WSB regions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes both algorithm and software development. The Constellation-X, Maxim, and Stellar Imager missions are examples of the use of improved numerical methods for attaining constrained formation geometries and controlling their dynamical evolution. This paper presents a survey of formation missions in the WSB regions and a brief description of the formation design using numerical and dynamical techniques.

Formation flying design and applications in weak stability boundary regions.

PubMed

Folta, David

2004-05-01

Weak stability regions serve as superior locations for interferomertric scientific investigations. These regions are often selected to minimize environmental disturbances and maximize observation efficiency. Designs of formations in these regions are becoming ever more challenging as more complex missions are envisioned. The development of algorithms to enable the capability for formation design must be further enabled to incorporate better understanding of weak stability boundary solution space. This development will improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple formation missions in weak stability boundary regions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes both algorithm and software development. The Constellation-X, Maxim, and Stellar Imager missions are examples of the use of improved numeric methods to attain constrained formation geometries and control their dynamical evolution. This paper presents a survey of formation missions in the weak stability boundary regions and a brief description of formation design using numerical and dynamical techniques.

A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots

NASA Technical Reports Server (NTRS)

Yang, S. L.; Cline, M. C.; Chen, R.; Chang, Y. L.

1993-01-01

A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots.

Efficient implicit LES method for the simulation of turbulent cavitating flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Egerer, Christian P., E-mail: christian.egerer@aer.mw.tum.de; Schmidt, Steffen J.; Hickel, Stefan

2016-07-01

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flowmore » field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.« less

Caustic Singularities Of High-Gain, Dual-Shaped Reflectors

NASA Technical Reports Server (NTRS)

Galindo, Victor; Veruttipong, Thavath W.; Imbriale, William A.; Rengarajan, Sambiam

1991-01-01

Report presents study of some sources of error in analysis, by geometric theory of diffraction (GTD), of performance of high-gain, dual-shaped antenna reflector. Study probes into underlying analytic causes of singularity, with view toward devising and testing practical methods to avoid problems caused by singularity. Hybrid physical optics (PO) approach used to study near-field spillover or noise-temperature characteristics of high-gain relector antenna efficiently and accurately. Report illustrates this approach and underlying principles by presenting numerical results, for both offset and symmetrical reflector systems, computed by GTD, PO, and PO/GO methods.

Practical adaptive quantum tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Ferrie, Christopher; Flammia, Steven T.

2017-11-01

We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques. We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements. http://cgranade.com complete data and source code for this work are available online [1], and can be previewed at https://goo.gl/koiWxR.

Analysis of SET pulses propagation probabilities in sequential circuits

NASA Astrophysics Data System (ADS)

Cai, Shuo; Yu, Fei; Yang, Yiqun

2018-05-01

As the feature size of CMOS transistors scales down, single event transient (SET) has been an important consideration in designing logic circuits. Many researches have been done in analyzing the impact of SET. However, it is difficult to consider numerous factors. We present a new approach for analyzing the SET pulses propagation probabilities (SPPs). It considers all masking effects and uses SET pulses propagation probabilities matrices (SPPMs) to represent the SPPs in current cycle. Based on the matrix union operations, the SPPs in consecutive cycles can be calculated. Experimental results show that our approach is practicable and efficient.

Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo

DOE PAGES

White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; ...

2015-07-07

Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less

A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2003-01-01

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.

Fiber optic light collection system for scanning-tunneling-microscope-induced light emission.

PubMed

Watkins, Neil J; Long, James P; Kafafi, Zakya H; Mäkinen, Antti J

2007-05-01

We report a compact light collection scheme suitable for retrofitting a scanning tunneling microscope (STM) for STM-induced light emission experiments. The approach uses a pair of optical fibers with large core diameters and high numerical apertures to maximize light collection efficiency and to moderate the mechanical precision required for alignment. Bench tests indicate that efficiency reduction is almost entirely due to reflective losses at the fiber ends, while losses due to fiber misalignment have virtually been eliminated. Photon-map imaging with nanometer features is demonstrated on a stepped Au(111) surface with signal rates exceeding 10(4) counts/s.

Acoustic radiation efficiency of a periodically corrugated rigid piston

NASA Astrophysics Data System (ADS)

Estrada, Héctor; Uris, Antonio; Meseguer, Francisco

2012-09-01

The radiation of sound by a periodically corrugated rigid piston is explored using theoretical and numerical approaches and compared with the radiation of flat rigid piston. The depth and the period of the corrugation are considered to be comparable with the wavelength in the surrounding fluid. Radiation enhancement is predicted due to cavity resonances and coherent diffraction. In addition, broad regions of low radiation efficiency are observed. Both effects could have an impact in acoustic transducers technology, either to increase the piston radiated power or to create a source of evanescent acoustic waves. The possibilities offered by this strategy in the nonlinear acoustic regime are also briefly discussed.

Systems identification technology development for large space systems

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1982-01-01

A methodology for synthesizinng systems identification, both parameter and state, estimation and related control schemes for flexible aerospace structures is developed with emphasis on the Maypole hoop column antenna as a real world application. Modeling studies of the Maypole cable hoop membrane type antenna are conducted using a transfer matrix numerical analysis approach. This methodology was chosen as particularly well suited for handling a large number of antenna configurations of a generic type. A dedicated transfer matrix analysis, both by virtue of its specialization and the inherently easy compartmentalization of the formulation and numerical procedures, is significantly more efficient not only in computer time required but, more importantly, in the time needed to review and interpret the results.

Comparative experimental and numerical studies of usual insulation materials and PCMs in buildings at Casablanca

NASA Astrophysics Data System (ADS)

Mourid, Amina; El Alami, Mustapha

2018-05-01

In this paper, we present a comparative thermal study of the usual insulation materials used in the building as well as the innovate one like phase change materials (PCMs). Both experimental study and numerical approach were applied in this work for summer season. In the experimental study the PCM was installed on the outer surface on the ceiling of one of two full-scale rooms located at FSAC, Casablanca. A simulation model was performed with TRNSYS’17 software. We have established as a criterion of comparison the internal temperatures. An economic study also has been carried out. Based on this latter, that the PCM is most efficient.

Parallel solution of high-order numerical schemes for solving incompressible flows

NASA Technical Reports Server (NTRS)

Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.

1993-01-01

A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.

An Enriched Shell Element for Delamination Simulation in Composite Laminates

NASA Technical Reports Server (NTRS)

McElroy, Mark

2015-01-01

A formulation is presented for an enriched shell finite element capable of delamination simulation in composite laminates. The element uses an adaptive splitting approach for damage characterization that allows for straightforward low-fidelity model creation and a numerically efficient solution. The Floating Node Method is used in conjunction with the Virtual Crack Closure Technique to predict delamination growth and represent it discretely at an arbitrary ply interface. The enriched element is verified for Mode I delamination simulation using numerical benchmark data. After determining important mesh configuration guidelines for the vicinity of the delamination front in the model, a good correlation was found between the enriched shell element model results and the benchmark data set.

Gimbal-Angle Vectors of the Nonredundant CMG Cluster

NASA Astrophysics Data System (ADS)

Lee, Donghun; Bang, Hyochoong

2018-05-01

This paper deals with the method using the preferred gimbal angles of a control moment gyro (CMG) cluster for controlling spacecraft attitude. To apply the method to the nonredundant CMG cluster, analytical gimbal-angle solutions for the zero angular momentum state are derived, and the gimbal-angle vectors for the nonzero angular momentum states are studied by a numerical method. It will be shown that the number of the gimbal-angle vectors is determined from the given skew angle and the angular momentum state of the CMG cluster. Through numerical examples, it is shown that the method using the preferred gimbal-angle is an efficient approach to avoid internal singularities for the nonredundant CMG cluster.

Rapid assessment of nonlinear optical propagation effects in dielectrics

PubMed Central

Hoyo, J. del; de la Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process. PMID:25564243

A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

DOE PAGES

Cheung, James; Frischknecht, Amalie L.; Perego, Mauro; ...

2017-07-20

Here, we develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independentlymore » on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.« less

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

NASA Astrophysics Data System (ADS)

Cheung, James; Frischknecht, Amalie L.; Perego, Mauro; Bochev, Pavel

2017-11-01

We develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson-Nernst-Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independently on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheung, James; Frischknecht, Amalie L.; Perego, Mauro

Here, we develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independentlymore » on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.« less

Rapid assessment of nonlinear optical propagation effects in dielectrics.

PubMed

del Hoyo, J; de la Cruz, A Ruiz; Grace, E; Ferrer, A; Siegel, J; Pasquazi, A; Assanto, G; Solis, J

2015-01-07

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Rapid assessment of nonlinear optical propagation effects in dielectrics

NASA Astrophysics Data System (ADS)

Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Design of experiments applications in bioprocessing: concepts and approach.

PubMed

Kumar, Vijesh; Bhalla, Akriti; Rathore, Anurag S

2014-01-01

Most biotechnology unit operations are complex in nature with numerous process variables, feed material attributes, and raw material attributes that can have significant impact on the performance of the process. Design of experiments (DOE)-based approach offers a solution to this conundrum and allows for an efficient estimation of the main effects and the interactions with minimal number of experiments. Numerous publications illustrate application of DOE towards development of different bioprocessing unit operations. However, a systematic approach for evaluation of the different DOE designs and for choosing the optimal design for a given application has not been published yet. Through this work we have compared the I-optimal and D-optimal designs to the commonly used central composite and Box-Behnken designs for bioprocess applications. A systematic methodology is proposed for construction of the model and for precise prediction of the responses for the three case studies involving some of the commonly used unit operations in downstream processing. Use of Akaike information criterion for model selection has been examined and found to be suitable for the applications under consideration. © 2013 American Institute of Chemical Engineers.

Electro-optic response in thin smectic C* film with chevron structures

NASA Astrophysics Data System (ADS)

Kudreyko, Aleksey A.; Migranov, Nail G.; Migranova, Dana N.

2016-12-01

The effects in electrostatic models of chevron surface-stabilized ferroelectric liquid crystals are investigated through numerical modeling. To study smectic C* director distribution within the cell, we consider two nonlinear approaches: the chevron interface does not interplay with the electric field; the electric field interplays with the chevron interface. The obtained results of the director field distribution are compared with the earlier linearized studies. We find that whether or not the electric field interplays with the chevron interface, the electro-optic response requires a generalized approach for its description. The threshold electric field, which is necessary for switching between two stable director states in the chevron cell is evaluated. This study suggests that, in many cases of practical interest, electro-optic response to the electric field and the threshold electric field can be precisely estimated. We argue that, beside being numerically efficient, our approach provides a convenient and a novel standpoint for looking at the electro-optic response problem. Project supported by the Russian Foundation for Basic Research (RFBR) (Grant Nos. 16-32-00043 and 14-02-97026).

Numerical Analysis of Dusty-Gas Flows

NASA Astrophysics Data System (ADS)

Saito, T.

2002-02-01

This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.

Algorithmic design of a noise-resistant and efficient closed-loop deep brain stimulation system: A computational approach.

PubMed

Karamintziou, Sofia D; Custódio, Ana Luísa; Piallat, Brigitte; Polosan, Mircea; Chabardès, Stéphan; Stathis, Pantelis G; Tagaris, George A; Sakas, Damianos E; Polychronaki, Georgia E; Tsirogiannis, George L; David, Olivier; Nikita, Konstantina S

2017-01-01

Advances in the field of closed-loop neuromodulation call for analysis and modeling approaches capable of confronting challenges related to the complex neuronal response to stimulation and the presence of strong internal and measurement noise in neural recordings. Here we elaborate on the algorithmic aspects of a noise-resistant closed-loop subthalamic nucleus deep brain stimulation system for advanced Parkinson's disease and treatment-refractory obsessive-compulsive disorder, ensuring remarkable performance in terms of both efficiency and selectivity of stimulation, as well as in terms of computational speed. First, we propose an efficient method drawn from dynamical systems theory, for the reliable assessment of significant nonlinear coupling between beta and high-frequency subthalamic neuronal activity, as a biomarker for feedback control. Further, we present a model-based strategy through which optimal parameters of stimulation for minimum energy desynchronizing control of neuronal activity are being identified. The strategy integrates stochastic modeling and derivative-free optimization of neural dynamics based on quadratic modeling. On the basis of numerical simulations, we demonstrate the potential of the presented modeling approach to identify, at a relatively low computational cost, stimulation settings potentially associated with a significantly higher degree of efficiency and selectivity compared with stimulation settings determined post-operatively. Our data reinforce the hypothesis that model-based control strategies are crucial for the design of novel stimulation protocols at the backstage of clinical applications.

Army Reserve Comprehensive Water Efficiency Assessments

DOE Office of Scientific and Technical Information (OSTI.GOV)

McMordie Stoughton, Kate; Kearney, Jaime

The Army Reserve has partnered with the Pacific Northwest National Laboratory (PNNL) to develop comprehensive water assessments for numerous Army Reserve Centers in all five regions including the Pacific islands and Puerto Rico, and at Fort Buchanan and Fort Hunter Liggett. The objective of these assessments is to quantify water use at the site, and identify innovative water efficiency projects that can be implemented to help reduce water demand and increase efficiency. Several of these assessments have focused on a strategic plan for achieving net zero water to help meet the Army’s Net Zero Directive . The Army Reserve hasmore » also leveraged this approach as part of the energy conservation investment program (ECIP), energy savings performance contracts (ESPCs), and utility energy service contracts (UESCs). This article documents the process involved.« less

Thermodynamic analysis of engineering solutions aimed at raising the efficiency of integrated gasification combined cycle

NASA Astrophysics Data System (ADS)

Gordeev, S. I.; Bogatova, T. F.; Ryzhkov, A. F.

2017-11-01

Raising the efficiency and environmental friendliness of electric power generation from coal is the aim of numerous research groups today. The traditional approach based on the steam power cycle has reached its efficiency limit, prompted by materials development and maneuverability performance. The rival approach based on the combined cycle is also drawing nearer to its efficiency limit. However, there is a reserve for efficiency increase of the integrated gasification combined cycle, which has the energy efficiency at the level of modern steam-turbine power units. The limit of increase in efficiency is the efficiency of NGCC. One of the main problems of the IGCC is higher costs of receiving and preparing fuel gas for GTU. It would be reasonable to decrease the necessary amount of fuel gas in the power unit to minimize the costs. The effect can be reached by raising of the heat value of fuel gas, its heat content and the heat content of cycle air. On the example of the process flowsheet of the IGCC with a power of 500 MW, running on Kuznetsk bituminous coal, by means of software Thermoflex, the influence of the developed technical solutions on the efficiency of the power plant is considered. It is received that rise in steam-air blast temperature to 900°C leads to an increase in conversion efficiency up to 84.2%. An increase in temperature levels of fuel gas clean-up to 900°C leads to an increase in the IGCC efficiency gross/net by 3.42%. Cycle air heating reduces the need for fuel gas by 40% and raises the IGCC efficiency gross/net by 0.85-1.22%. The offered solutions for IGCC allow to exceed net efficiency of analogous plants by 1.8-2.3%.

An Analysis of Polynomial Chaos Approximations for Modeling Single-Fluid-Phase Flow in Porous Medium Systems

PubMed Central

Rupert, C.P.; Miller, C.T.

2008-01-01

We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method. PMID:18836519

Incorporating extrinsic noise into the stochastic simulation of biochemical reactions: A comparison of approaches

NASA Astrophysics Data System (ADS)

Thanh, Vo Hong; Marchetti, Luca; Reali, Federico; Priami, Corrado

2018-02-01

The stochastic simulation algorithm (SSA) has been widely used for simulating biochemical reaction networks. SSA is able to capture the inherently intrinsic noise of the biological system, which is due to the discreteness of species population and to the randomness of their reciprocal interactions. However, SSA does not consider other sources of heterogeneity in biochemical reaction systems, which are referred to as extrinsic noise. Here, we extend two simulation approaches, namely, the integration-based method and the rejection-based method, to take extrinsic noise into account by allowing the reaction propensities to vary in time and state dependent manner. For both methods, new efficient implementations are introduced and their efficiency and applicability to biological models are investigated. Our numerical results suggest that the rejection-based method performs better than the integration-based method when the extrinsic noise is considered.

An Effective Evolutionary Approach for Bicriteria Shortest Path Routing Problems

NASA Astrophysics Data System (ADS)

Lin, Lin; Gen, Mitsuo

Routing problem is one of the important research issues in communication network fields. In this paper, we consider a bicriteria shortest path routing (bSPR) model dedicated to calculating nondominated paths for (1) the minimum total cost and (2) the minimum transmission delay. To solve this bSPR problem, we propose a new multiobjective genetic algorithm (moGA): (1) an efficient chromosome representation using the priority-based encoding method; (2) a new operator of GA parameters auto-tuning, which is adaptively regulation of exploration and exploitation based on the change of the average fitness of parents and offspring which is occurred at each generation; and (3) an interactive adaptive-weight fitness assignment mechanism is implemented that assigns weights to each objective and combines the weighted objectives into a single objective function. Numerical experiments with various scales of network design problems show the effectiveness and the efficiency of our approach by comparing with the recent researches.

Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alam, Aftab; Khan, S. N.; Wilson, Brian G.

2011-07-06

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in ab initio electronic-structure calculations. We combine a weighted Voronoi tessellation with isoparametric integration via Gauss-Legendre quadratures to provide rapidly convergent VP integrals for a variety of integrands, including those with a Coulomb singularity. We showcase the capability of our approach by first applying it to an analytic charge-density model achieving machine-precision accuracy with expected convergence properties in milliseconds. For contrast, we compare our results to those using shape-functions and show our approach is greater than 10 5 times faster and 10more » 7 times more accurate. Furthermore, a weighted Voronoi tessellation also allows for a physics-based partitioning of space that guarantees convex, space-filling VP while reflecting accurate atomic size and site charges, as we show within KKR methods applied to Fe-Pd alloys.« less

Aerodynamic design and optimization in one shot

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Kuruvila, G.; Salas, M. D.

1992-01-01

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Towards a suite of test cases and a pycomodo library to assess and improve numerical methods in ocean models

NASA Astrophysics Data System (ADS)

Garnier, Valérie; Honnorat, Marc; Benshila, Rachid; Boutet, Martial; Cambon, Gildas; Chanut, Jérome; Couvelard, Xavier; Debreu, Laurent; Ducousso, Nicolas; Duhaut, Thomas; Dumas, Franck; Flavoni, Simona; Gouillon, Flavien; Lathuilière, Cyril; Le Boyer, Arnaud; Le Sommer, Julien; Lyard, Florent; Marsaleix, Patrick; Marchesiello, Patrick; Soufflet, Yves

2016-04-01

The COMODO group (http://www.comodo-ocean.fr) gathers developers of global and limited-area ocean models (NEMO, ROMS_AGRIF, S, MARS, HYCOM, S-TUGO) with the aim to address well-identified numerical issues. In order to evaluate existing models, to improve numerical approaches and methods or concept (such as effective resolution) to assess the behavior of numerical model in complex hydrodynamical regimes and to propose guidelines for the development of future ocean models, a benchmark suite that covers both idealized test cases dedicated to targeted properties of numerical schemes and more complex test case allowing the evaluation of the kernel coherence is proposed. The benchmark suite is built to study separately, then together, the main components of an ocean model : the continuity and momentum equations, the advection-diffusion of the tracers, the vertical coordinate design and the time stepping algorithms. The test cases are chosen for their simplicity of implementation (analytic initial conditions), for their capacity to focus on a (few) scheme or part of the kernel, for the availability of analytical solutions or accurate diagnoses and lastly to simulate a key oceanic processus in a controlled environment. Idealized test cases allow to verify properties of numerical schemes advection-diffusion of tracers, - upwelling, - lock exchange, - baroclinic vortex, - adiabatic motion along bathymetry, and to put into light numerical issues that remain undetected in realistic configurations - trajectory of barotropic vortex, - interaction current - topography. When complexity in the simulated dynamics grows up, - internal wave, - unstable baroclinic jet, the sharing of the same experimental designs by different existing models is useful to get a measure of the model sensitivity to numerical choices (Soufflet et al., 2016). Lastly, test cases help in understanding the submesoscale influence on the dynamics (Couvelard et al., 2015). Such a benchmark suite is an interesting bed to continue research in numerical approaches as well as an efficient tool to maintain any oceanic code and assure the users a stamped model in a certain range of hydrodynamical regimes. Thanks to a common netCDF format, this suite is completed with a python library that encompasses all the tools and metrics used to assess the efficiency of the numerical methods. References - Couvelard X., F. Dumas, V. Garnier, A.L. Ponte, C. Talandier, A.M. Treguier (2015). Mixed layer formation and restratification in presence of mesoscale and submesoscale turbulence. Ocean Modelling, Vol 96-2, p 243-253. doi:10.1016/j.ocemod.2015.10.004. - Soufflet Y., P. Marchesiello, F. Lemarié, J. Jouanno, X. Capet, L. Debreu , R. Benshila (2016). On effective resolution in ocean models. Ocean Modelling, in press. doi:10.1016/j.ocemod.2015.12.004

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Hybrid ODE/SSA methods and the cell cycle model

NASA Astrophysics Data System (ADS)

Wang, S.; Chen, M.; Cao, Y.

2017-07-01

Stochastic effect in cellular systems has been an important topic in systems biology. Stochastic modeling and simulation methods are important tools to study stochastic effect. Given the low efficiency of stochastic simulation algorithms, the hybrid method, which combines an ordinary differential equation (ODE) system with a stochastic chemically reacting system, shows its unique advantages in the modeling and simulation of biochemical systems. The efficiency of hybrid method is usually limited by reactions in the stochastic subsystem, which are modeled and simulated using Gillespie's framework and frequently interrupt the integration of the ODE subsystem. In this paper we develop an efficient implementation approach for the hybrid method coupled with traditional ODE solvers. We also compare the efficiency of hybrid methods with three widely used ODE solvers RADAU5, DASSL, and DLSODAR. Numerical experiments with three biochemical models are presented. A detailed discussion is presented for the performances of three ODE solvers.

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

NASA Astrophysics Data System (ADS)

Sewerin, Fabian; Rigopoulos, Stelios

2017-10-01

Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicates the computational efficiency of the numerical solution scheme.

A convex penalty for switching control of partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Ford, Neville J.; Connolly, Joseph A.

2009-07-01

We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.

On computations of the integrated space shuttle flowfield using overset grids

NASA Technical Reports Server (NTRS)

Chiu, I-T.; Pletcher, R. H.; Steger, J. L.

1990-01-01

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield.

The application of quaternions and other spatial representations to the reconstruction of re-entry vehicle motion.

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Sapio, Vincent

2010-09-01

The analysis of spacecraft kinematics and dynamics requires an efficient scheme for spatial representation. While the representation of displacement in three dimensional Euclidean space is straightforward, orientation in three dimensions poses particular challenges. The unit quaternion provides an approach that mitigates many of the problems intrinsic in other representation approaches, including the ill-conditioning that arises from computing many successive rotations. This report focuses on the computational utility of unit quaternions and their application to the reconstruction of re-entry vehicle (RV) motion history from sensor data. To this end they will be used in conjunction with other kinematic and data processingmore » techniques. We will present a numerical implementation for the reconstruction of RV motion solely from gyroscope and accelerometer data. This will make use of unit quaternions due to their numerical efficacy in dealing with the composition of many incremental rotations over a time series. In addition to signal processing and data conditioning procedures, algorithms for numerical quaternion-based integration of gyroscope data will be addressed, as well as accelerometer triangulation and integration to yield RV trajectory. Actual processed flight data will be presented to demonstrate the implementation of these methods.« less

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Hierarchical Boltzmann simulations and model error estimation

NASA Astrophysics Data System (ADS)

Torrilhon, Manuel; Sarna, Neeraj

2017-08-01

A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

A coupled approach for the three-dimensional simulation of pipe leakage in variably saturated soil

NASA Astrophysics Data System (ADS)

Peche, Aaron; Graf, Thomas; Fuchs, Lothar; Neuweiler, Insa

2017-12-01

In urban water pipe networks, pipe leakage may lead to subsurface contamination or to reduced waste water treatment efficiency. The quantification of pipe leakage is challenging due to inaccessibility and unknown hydraulic properties of the soil. A novel physically-based model for three-dimensional numerical simulation of pipe leakage in variably saturated soil is presented. We describe the newly implemented coupling between the pipe flow simulator HYSTEM-EXTRAN and the groundwater flow simulator OpenGeoSys and its validation. We further describe a novel upscaling of leakage using transfer functions derived from numerical simulations. This upscaling enables the simulation of numerous pipe defects with the benefit of reduced computation times. Finally, we investigate the response of leakage to different time-dependent pipe flow events and conclude that larger pipe flow volume and duration lead to larger leakage while the peak position in time has a small effect on leakage.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Coupling Hydraulic Fracturing Propagation and Gas Well Performance for Simulation of Production in Unconventional Shale Gas Reservoirs

NASA Astrophysics Data System (ADS)

Wang, C.; Winterfeld, P. H.; Wu, Y. S.; Wang, Y.; Chen, D.; Yin, C.; Pan, Z.

2014-12-01

Hydraulic fracturing combined with horizontal drilling has made it possible to economically produce natural gas from unconventional shale gas reservoirs. An efficient methodology for evaluating hydraulic fracturing operation parameters, such as fluid and proppant properties, injection rates, and wellhead pressure, is essential for the evaluation and efficient design of these processes. Traditional numerical evaluation and optimization approaches are usually based on simulated fracture properties such as the fracture area. In our opinion, a methodology based on simulated production data is better, because production is the goal of hydraulic fracturing and we can calibrate this approach with production data that is already known. This numerical methodology requires a fully-coupled hydraulic fracture propagation and multi-phase flow model. In this paper, we present a general fully-coupled numerical framework to simulate hydraulic fracturing and post-fracture gas well performance. This three-dimensional, multi-phase simulator focuses on: (1) fracture width increase and fracture propagation that occurs as slurry is injected into the fracture, (2) erosion caused by fracture fluids and leakoff, (3) proppant subsidence and flowback, and (4) multi-phase fluid flow through various-scaled anisotropic natural and man-made fractures. Mathematical and numerical details on how to fully couple the fracture propagation and fluid flow parts are discussed. Hydraulic fracturing and production operation parameters, and properties of the reservoir, fluids, and proppants, are taken into account. The well may be horizontal, vertical, or deviated, as well as open-hole or cemented. The simulator is verified based on benchmarks from the literature and we show its application by simulating fracture network (hydraulic and natural fractures) propagation and production data history matching of a field in China. We also conduct a series of real-data modeling studies with different combinations of hydraulic fracturing parameters and present the methodology to design these operations with feedback of simulated production data. The unified model aids in the optimization of hydraulic fracturing design, operations, and production.

CSR Fields: Direct Numerical Solution of the Maxwell___s Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novokhatski, A.; /SLAC

2011-06-22

We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particlemore » accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in [1]. Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in [2]. We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields [3].« less

Electrochemotherapy of Spinal Metastases Using Transpedicular Approach—A Numerical Feasibility Study

PubMed Central

Cindrič, Helena; Tedesco, Giuseppe; Cadossi, Matteo; Gasbarrini, Alessandro; Miklavčič, Damijan

2018-01-01

Vertebral column is the most frequent site for bone metastases. It has been demonstrated in previous studies that bone metastases can be efficiently treated by electrochemotherapy. We developed a novel approach to treat spinal metastases, that is, transpedicular approach that combines electrochemotherapy with already established technologies for insertion of fixation screws in spinal surgery. In the transpedicular approach, needle electrodes are inserted into the vertebral body through pedicles and placed around the tumor. The main goal of our study was to numerically investigate the feasibility of the proposed treatment approach. Three clinical cases were used in this study—1 with a tumor completely contained within the vertebral body and 2 with tumors spread also to the pedicles and spinal canal. Anatomically accurate numerical models were built for all 3 cases, and numerical computations of electric field distribution in tumor and surrounding tissue were performed to determine the treatment outcome. Complete coverage of tumor volume with sufficiently high electric field is a prerequisite for successful electrochemotherapy. Close to 100% tumor coverage was obtained in all 3 cases studied. Two cases exhibited tumor coverage of >99%, while the coverage in the third case was 98.88%. Tumor tissue that remained untreated was positioned on the margin of the tumor volume. We also evaluated hypothetical damage to spinal cord and nerves. Only 1 case, which featured a tumor grown into the spinal canal, exhibited potential risk of neural damage. Our study shows that the proposed transpedicular approach to treat spinal metastases is feasible and safe if the majority of tumor volume is contained within the vertebral body. In cases where the spinal cord and nerves are contained within the margin of the tumor volume, a successful and safe treatment is still possible, but special attention needs to be given to evaluation of potential neural damage. PMID:29759043

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

Modal, ray, and beam techniques for analyzing the EM scattering by open-ended waveguide cavities

NASA Technical Reports Server (NTRS)

Pathak, Prabhakar H.; Burkholder, Robert J.

1989-01-01

The problem of high-frequency electromagnetic (EM) scattering by open-ended waveguide cavities with an interior termination is analyzed via three different approaches. When cavities can be adequately modeled by joining together piecewise separable waveguide sections, a hybrid combination of asymptotic high-frequency and modal techniques is employed. In the case of more arbitrarily shaped waveguide cavities for which modes cannot even be defined in the conventional sense, the geometrical optics ray approach proves to be highly useful. However, at sufficiently high frequencies, both of these approaches tend to become inefficient. Hence, a paraxial Gaussian batch technique, which retains much of the simplicity of the ray approximation but is potentially more efficient, is investigated. Typical numerical results based on the different approaches are discussed.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Limit analysis of hollow spheres or spheroids with Hill orthotropic matrix

NASA Astrophysics Data System (ADS)

Pastor, Franck; Pastor, Joseph; Kondo, Djimedo

2012-03-01

Recent theoretical studies of the literature are concerned by the hollow sphere or spheroid (confocal) problems with orthotropic Hill type matrix. They have been developed in the framework of the limit analysis kinematical approach by using very simple trial velocity fields. The present Note provides, through numerical upper and lower bounds, a rigorous assessment of the approximate criteria derived in these theoretical works. To this end, existing static 3D codes for a von Mises matrix have been easily extended to the orthotropic case. Conversely, instead of the non-obvious extension of the existing kinematic codes, a new original mixed approach has been elaborated on the basis of the plane strain structure formulation earlier developed by F. Pastor (2007). Indeed, such a formulation does not need the expressions of the unit dissipated powers. Interestingly, it delivers a numerical code better conditioned and notably more rapid than the previous one, while preserving the rigorous upper bound character of the corresponding numerical results. The efficiency of the whole approach is first demonstrated through comparisons of the results to the analytical upper bounds of Benzerga and Besson (2001) or Monchiet et al. (2008) in the case of spherical voids in the Hill matrix. Moreover, we provide upper and lower bounds results for the hollow spheroid with the Hill matrix which are compared to those of Monchiet et al. (2008).

Experimental and numerical study of two dimensional heat and mass transfer in unsaturated soil with and application to soil thermal energy storage (SBTES) systems

NASA Astrophysics Data System (ADS)

Moradi, A.; Smits, K. M.

2014-12-01

A promising energy storage option to compensate for daily and seasonal energy offsets is to inject and store heat generated from renewable energy sources (e.g. solar energy) in the ground, oftentimes referred to as soil borehole thermal energy storage (SBTES). Nonetheless in SBTES modeling efforts, it is widely recognized that the movement of water vapor is closely coupled to thermal processes. However, their mutual interactions are rarely considered in most soil water modeling efforts or in practical applications. The validation of numerical models that are designed to capture these processes is difficult due to the scarcity of experimental data, limiting the testing and refinement of heat and water transfer theories. A common assumption in most SBTES modeling approaches is to consider the soil as a purely conductive medium with constant hydraulic and thermal properties. However, this simplified approach can be improved upon by better understanding the coupled processes at play. Consequently, developing new modeling techniques along with suitable experimental tools to add more complexity in coupled processes has critical importance in obtaining necessary knowledge in efficient design and implementation of SBTES systems. The goal of this work is to better understand heat and mass transfer processes for SBTES. In this study, we implemented a fully coupled numerical model that solves for heat, liquid water and water vapor flux and allows for non-equilibrium liquid/gas phase change. This model was then used to investigate the influence of different hydraulic and thermal parameterizations on SBTES system efficiency. A two dimensional tank apparatus was used with a series of soil moisture, temperature and soil thermal properties sensors. Four experiments were performed with different test soils. Experimental results provide evidences of thermally induced moisture flow that was also confirmed by numerical results. Numerical results showed that for the test conditions applied here, moisture flow is more influenced by thermal gradients rather than hydraulic gradients. The results also demonstrate that convective fluxes are higher compared to conductive fluxes indicating that moisture flow has more contribution to the overall heat flux than conductive fluxes.

Numerical Simulation of Transitional, Hypersonic Flows using a Hybrid Particle-Continuum Method

NASA Astrophysics Data System (ADS)

Verhoff, Ashley Marie

Analysis of hypersonic flows requires consideration of multiscale phenomena due to the range of flight regimes encountered, from rarefied conditions in the upper atmosphere to fully continuum flow at low altitudes. At transitional Knudsen numbers there are likely to be localized regions of strong thermodynamic nonequilibrium effects that invalidate the continuum assumptions of the Navier-Stokes equations. Accurate simulation of these regions, which include shock waves, boundary and shear layers, and low-density wakes, requires a kinetic theory-based approach where no prior assumptions are made regarding the molecular distribution function. Because of the nature of these types of flows, there is much to be gained in terms of both numerical efficiency and physical accuracy by developing hybrid particle-continuum simulation approaches. The focus of the present research effort is the continued development of the Modular Particle-Continuum (MPC) method, where the Navier-Stokes equations are solved numerically using computational fluid dynamics (CFD) techniques in regions of the flow field where continuum assumptions are valid, and the direct simulation Monte Carlo (DSMC) method is used where strong thermodynamic nonequilibrium effects are present. Numerical solutions of transitional, hypersonic flows are thus obtained with increased physical accuracy relative to CFD alone, and improved numerical efficiency is achieved in comparison to DSMC alone because this more computationally expensive method is restricted to those regions of the flow field where it is necessary to maintain physical accuracy. In this dissertation, a comprehensive assessment of the physical accuracy of the MPC method is performed, leading to the implementation of a non-vacuum supersonic outflow boundary condition in particle domains, and more consistent initialization of DSMC simulator particles along hybrid interfaces. The relative errors between MPC and full DSMC results are greatly reduced as a direct result of these improvements. Next, a new parameter for detecting rotational nonequilibrium effects is proposed and shown to offer advantages over other continuum breakdown parameters, achieving further accuracy gains. Lastly, the capabilities of the MPC method are extended to accommodate multiple chemical species in rotational nonequilibrium, each of which is allowed to equilibrate independently, enabling application of the MPC method to more realistic atmospheric flows.

Manifold regularized matrix completion for multi-label learning with ADMM.

PubMed

Liu, Bin; Li, Yingming; Xu, Zenglin

2018-05-01

Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach. Copyright © 2018 Elsevier Ltd. All rights reserved.

Efficient 3D multi-region prostate MRI segmentation using dual optimization.

PubMed

Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron

2013-01-01

Efficient and accurate extraction of the prostate, in particular its clinically meaningful sub-regions from 3D MR images, is of great interest in image-guided prostate interventions and diagnosis of prostate cancer. In this work, we propose a novel multi-region segmentation approach to simultaneously locating the boundaries of the prostate and its two major sub-regions: the central gland and the peripheral zone. The proposed method utilizes the prior knowledge of the spatial region consistency and employs a customized prostate appearance model to simultaneously segment multiple clinically meaningful regions. We solve the resulted challenging combinatorial optimization problem by means of convex relaxation, for which we introduce a novel spatially continuous flow-maximization model and demonstrate its duality to the investigated convex relaxed optimization problem with the region consistency constraint. Moreover, the proposed continuous max-flow model naturally leads to a new and efficient continuous max-flow based algorithm, which enjoys great advantages in numerics and can be readily implemented on GPUs. Experiments using 15 T2-weighted 3D prostate MR images, by inter- and intra-operator variability, demonstrate the promising performance of the proposed approach.

Real-time probabilistic covariance tracking with efficient model update.

PubMed

Wu, Yi; Cheng, Jian; Wang, Jinqiao; Lu, Hanqing; Wang, Jun; Ling, Haibin; Blasch, Erik; Bai, Li

2012-05-01

The recently proposed covariance region descriptor has been proven robust and versatile for a modest computational cost. The covariance matrix enables efficient fusion of different types of features, where the spatial and statistical properties, as well as their correlation, are characterized. The similarity between two covariance descriptors is measured on Riemannian manifolds. Based on the same metric but with a probabilistic framework, we propose a novel tracking approach on Riemannian manifolds with a novel incremental covariance tensor learning (ICTL). To address the appearance variations, ICTL incrementally learns a low-dimensional covariance tensor representation and efficiently adapts online to appearance changes of the target with only O(1) computational complexity, resulting in a real-time performance. The covariance-based representation and the ICTL are then combined with the particle filter framework to allow better handling of background clutter, as well as the temporary occlusions. We test the proposed probabilistic ICTL tracker on numerous benchmark sequences involving different types of challenges including occlusions and variations in illumination, scale, and pose. The proposed approach demonstrates excellent real-time performance, both qualitatively and quantitatively, in comparison with several previously proposed trackers.

Efficient Spatio-Temporal Local Binary Patterns for Spontaneous Facial Micro-Expression Recognition

PubMed Central

Wang, Yandan; See, John; Phan, Raphael C.-W.; Oh, Yee-Hui

2015-01-01

Micro-expression recognition is still in the preliminary stage, owing much to the numerous difficulties faced in the development of datasets. Since micro-expression is an important affective clue for clinical diagnosis and deceit analysis, much effort has gone into the creation of these datasets for research purposes. There are currently two publicly available spontaneous micro-expression datasets—SMIC and CASME II, both with baseline results released using the widely used dynamic texture descriptor LBP-TOP for feature extraction. Although LBP-TOP is popular and widely used, it is still not compact enough. In this paper, we draw further inspiration from the concept of LBP-TOP that considers three orthogonal planes by proposing two efficient approaches for feature extraction. The compact robust form described by the proposed LBP-Six Intersection Points (SIP) and a super-compact LBP-Three Mean Orthogonal Planes (MOP) not only preserves the essential patterns, but also reduces the redundancy that affects the discriminality of the encoded features. Through a comprehensive set of experiments, we demonstrate the strengths of our approaches in terms of recognition accuracy and efficiency. PMID:25993498

Nested sparse grid collocation method with delay and transformation for subsurface flow and transport problems

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

In numerical modeling of subsurface flow and transport problems, formation properties may not be deterministically characterized, which leads to uncertainty in simulation results. In this study, we propose a sparse grid collocation method, which adopts nested quadrature rules with delay and transformation to quantify the uncertainty of model solutions. We show that the nested Kronrod-Patterson-Hermite quadrature is more efficient than the unnested Gauss-Hermite quadrature. We compare the convergence rates of various quadrature rules including the domain truncation and domain mapping approaches. To further improve accuracy and efficiency, we present a delayed process in selecting quadrature nodes and a transformed process for approximating unsmooth or discontinuous solutions. The proposed method is tested by an analytical function and in one-dimensional single-phase and two-phase flow problems with different spatial variances and correlation lengths. An additional example is given to demonstrate its applicability to three-dimensional black-oil models. It is found from these examples that the proposed method provides a promising approach for obtaining satisfactory estimation of the solution statistics and is much more efficient than the Monte-Carlo simulations.

Efficient numerical evaluation of Feynman integrals

NASA Astrophysics Data System (ADS)

Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran

2016-03-01

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

Large Eddy Simulations of Colorless Distributed Combustion Systems

NASA Astrophysics Data System (ADS)

Abdulrahman, Husam F.; Jaberi, Farhad; Gupta, Ashwani

2014-11-01

Development of efficient and low-emission colorless distributed combustion (CDC) systems for gas turbine applications require careful examination of the role of various flow and combustion parameters. Numerical simulations of CDC in a laboratory-scale combustor have been conducted to carefully examine the effects of these parameters on the CDC. The computational model is based on a hybrid modeling approach combining large eddy simulation (LES) with the filtered mass density function (FMDF) equations, solved with high order numerical methods and complex chemical kinetics. The simulated combustor operates based on the principle of high temperature air combustion (HiTAC) and has shown to significantly reduce the NOx, and CO emissions while improving the reaction pattern factor and stability without using any flame stabilizer and with low pressure drop and noise. The focus of the current work is to investigate the mixing of air and hydrocarbon fuels and the non-premixed and premixed reactions within the combustor by the LES/FMDF with the reduced chemical kinetic mechanisms for the same flow conditions and configurations investigated experimentally. The main goal is to develop better CDC with higher mixing and efficiency, ultra-low emission levels and optimum residence time. The computational results establish the consistency and the reliability of LES/FMDF and its Lagrangian-Eulerian numerical methodology.

Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tavakoli, Rouhollah, E-mail: rtavakoli@sharif.ir

An unconditionally energy stable time stepping scheme is introduced to solve Cahn–Morral-like equations in the present study. It is constructed based on the combination of David Eyre's time stepping scheme and Schur complement approach. Although the presented method is general and independent of the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi-component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments demonstrate themore » success and performance of the presented method. According to the numerical results, the method is convergent and energy stable, independent of the choice of time stepsize. Its MATLAB implementation is included in the appendix for the numerical evaluation of algorithm and reproduction of the presented results. -- Highlights: •Extension of Eyre's convex–concave splitting scheme to multiphase systems. •Efficient solution of spinodal decomposition in multi-component systems. •Efficient solution of least perimeter periodic space partitioning problem. •Developing a penalization strategy to avoid trivial solutions. •Presentation of MATLAB implementation of the introduced algorithm.« less

A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

Towards a Highly Efficient Meshfree Simulation of Non-Newtonian Free Surface Ice Flow: Application to the Haut Glacier d'Arolla

NASA Astrophysics Data System (ADS)

Shcherbakov, V.; Ahlkrona, J.

2016-12-01

In this work we develop a highly efficient meshfree approach to ice sheet modeling. Traditionally mesh based methods such as finite element methods are employed to simulate glacier and ice sheet dynamics. These methods are mature and well developed. However, despite of numerous advantages these methods suffer from some drawbacks such as necessity to remesh the computational domain every time it changes its shape, which significantly complicates the implementation on moving domains, or a costly assembly procedure for nonlinear problems. We introduce a novel meshfree approach that frees us from all these issues. The approach is built upon a radial basis function (RBF) method that, thanks to its meshfree nature, allows for an efficient handling of moving margins and free ice surface. RBF methods are also accurate and easy to implement. Since the formulation is stated in strong form it allows for a substantial reduction of the computational cost associated with the linear system assembly inside the nonlinear solver. We implement a global RBF method that defines an approximation on the entire computational domain. This method exhibits high accuracy properties. However, it suffers from a disadvantage that the coefficient matrix is dense, and therefore the computational efficiency decreases. In order to overcome this issue we also implement a localized RBF method that rests upon a partition of unity approach to subdivide the domain into several smaller subdomains. The radial basis function partition of unity method (RBF-PUM) inherits high approximation characteristics form the global RBF method while resulting in a sparse system of equations, which essentially increases the computational efficiency. To demonstrate the usefulness of the RBF methods we model the velocity field of ice flow in the Haut Glacier d'Arolla. We assume that the flow is governed by the nonlinear Blatter-Pattyn equations. We test the methods for different basal conditions and for a free moving surface. Both RBF methods are compared with a classical finite element method in terms of accuracy and efficiency. We find that the RBF methods are more efficient than the finite element method and well suited for ice dynamics modeling, especially the partition of unity approach.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Yukun; Solid-State Lighting Engineering Research Center, Xi'an Jiaotong University, Xi'an, Shaanxi 710049; Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ

Size-tunable bimetallic bowtie nanoantennas have been utilized to suppress the efficiency roll-off characteristics in organic light-emitting diodes (OLEDs) using both the numerical and experimental approaches. The resonant range can be widened by the strong dual-atomic couplings in bimetallic bowtie nanoantennas. Compared with the green OLED with conventional bowtie nanoantennas at a high current density of 800 mA/cm{sup 2}, the measured efficiency roll-off ratio of the OLED with size-modulated bowtie nanoantennas is decreased from 53.2% to 41.8%, and the measured current efficiency is enhanced by 29.9%. When the size-modulated bowtie nanoantennas are utilized in blue phosphorescent OLEDs, the experimental roll-off ratio ismore » suppressed from 43.6% to 25.9% at 250 mA/cm{sup 2}, and the measured current efficiency is also enhanced significantly. It is proposed that the efficiency roll-off suppression is mainly related to the enhanced localized surface plasmon effect, which leads to a shorter radiative lifetime.« less

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Concise expression of a classical radiation spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, C.

1993-06-01

In this paper we present a concise expression of the classical electromagnetic radiation spectrum of a moving charge. It is shown to be equivalent to the often used and much more complicated form derived from the Lienard-Wiechert potentials when the observation distance [ital R] satisfies the condition [ital R][much gt][gamma][lambda]. The expression reveals a relationship between the radiation spectrum and the motion of the radiation source. It also forms the basis of an efficient computing approach, which is of practical value in numerical calculations of the spectral output of accelerated charges. The advantages of this approach for analytical and numericalmore » applications are discussed and the bending-magnet synchrotron radiation spectrum is calculated according to the approach.« less

Modelization of highly nonlinear waves in coastal regions

NASA Astrophysics Data System (ADS)

Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

2015-04-01

The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.

Bayesian cloud detection for MERIS, AATSR, and their combination

NASA Astrophysics Data System (ADS)

Hollstein, A.; Fischer, J.; Carbajal Henken, C.; Preusker, R.

2014-11-01

A broad range of different of Bayesian cloud detection schemes is applied to measurements from the Medium Resolution Imaging Spectrometer (MERIS), the Advanced Along-Track Scanning Radiometer (AATSR), and their combination. The cloud masks were designed to be numerically efficient and suited for the processing of large amounts of data. Results from the classical and naive approach to Bayesian cloud masking are discussed for MERIS and AATSR as well as for their combination. A sensitivity study on the resolution of multidimensional histograms, which were post-processed by Gaussian smoothing, shows how theoretically insufficient amounts of truth data can be used to set up accurate classical Bayesian cloud masks. Sets of exploited features from single and derived channels are numerically optimized and results for naive and classical Bayesian cloud masks are presented. The application of the Bayesian approach is discussed in terms of reproducing existing algorithms, enhancing existing algorithms, increasing the robustness of existing algorithms, and on setting up new classification schemes based on manually classified scenes.

Bayesian cloud detection for MERIS, AATSR, and their combination

NASA Astrophysics Data System (ADS)

Hollstein, A.; Fischer, J.; Carbajal Henken, C.; Preusker, R.

2015-04-01

A broad range of different of Bayesian cloud detection schemes is applied to measurements from the Medium Resolution Imaging Spectrometer (MERIS), the Advanced Along-Track Scanning Radiometer (AATSR), and their combination. The cloud detection schemes were designed to be numerically efficient and suited for the processing of large numbers of data. Results from the classical and naive approach to Bayesian cloud masking are discussed for MERIS and AATSR as well as for their combination. A sensitivity study on the resolution of multidimensional histograms, which were post-processed by Gaussian smoothing, shows how theoretically insufficient numbers of truth data can be used to set up accurate classical Bayesian cloud masks. Sets of exploited features from single and derived channels are numerically optimized and results for naive and classical Bayesian cloud masks are presented. The application of the Bayesian approach is discussed in terms of reproducing existing algorithms, enhancing existing algorithms, increasing the robustness of existing algorithms, and on setting up new classification schemes based on manually classified scenes.

A mixed-mode traffic assignment model with new time-flow impedance function

NASA Astrophysics Data System (ADS)

Lin, Gui-Hua; Hu, Yu; Zou, Yuan-Yang

2018-01-01

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.

Inlet Flow Control and Prediction Technologies for Embedded Propulsion Systems

NASA Technical Reports Server (NTRS)

McMillan, Michelle L.; Gissen, Abe; Vukasinovic, Bojan; Lakebrink, Matthew T.; Glezer, Ari; Mani, Mori; Mace, James

2010-01-01

Fail-safe inlet flow control may enable high-speed cruise efficiency, low noise signature, and reduced fuel-burn goals for hybrid wing-body aircraft. The objectives of this program are to develop flow control and prediction methodologies for boundary-layer ingesting (BLI) inlets used in these aircraft. This report covers the second of a three year program. The approach integrates experiments and numerical simulations. Both passive and active flow-control devices were tested in a small-scale wind tunnel. Hybrid actuation approaches, combining a passive microvane and active synthetic jet, were tested in various geometric arrangements. Detailed flow measurements were taken to provide insight into the flow physics. Results of the numerical simulations were correlated against experimental data. The sensitivity of results to grid resolution and turbulence models was examined. Aerodynamic benefits from microvanes and microramps were assessed when installed in an offset BLI inlet. Benefits were quantified in terms of recovery and distortion changes. Microvanes were more effective than microramps at improving recovery and distortion.

3D prostate TRUS segmentation using globally optimized volume-preserving prior.

PubMed

Qiu, Wu; Rajchl, Martin; Guo, Fumin; Sun, Yue; Ukwatta, Eranga; Fenster, Aaron; Yuan, Jing

2014-01-01

An efficient and accurate segmentation of 3D transrectal ultrasound (TRUS) images plays an important role in the planning and treatment of the practical 3D TRUS guided prostate biopsy. However, a meaningful segmentation of 3D TRUS images tends to suffer from US speckles, shadowing and missing edges etc, which make it a challenging task to delineate the correct prostate boundaries. In this paper, we propose a novel convex optimization based approach to extracting the prostate surface from the given 3D TRUS image, while preserving a new global volume-size prior. We, especially, study the proposed combinatorial optimization problem by convex relaxation and introduce its dual continuous max-flow formulation with the new bounded flow conservation constraint, which results in an efficient numerical solver implemented on GPUs. Experimental results using 12 patient 3D TRUS images show that the proposed approach while preserving the volume-size prior yielded a mean DSC of 89.5% +/- 2.4%, a MAD of 1.4 +/- 0.6 mm, a MAXD of 5.2 +/- 3.2 mm, and a VD of 7.5% +/- 6.2% in - 1 minute, deomonstrating the advantages of both accuracy and efficiency. In addition, the low standard deviation of the segmentation accuracy shows a good reliability of the proposed approach.

A framework for scalable parameter estimation of gene circuit models using structural information.

PubMed

Kuwahara, Hiroyuki; Fan, Ming; Wang, Suojin; Gao, Xin

2013-07-01

Systematic and scalable parameter estimation is a key to construct complex gene regulatory models and to ultimately facilitate an integrative systems biology approach to quantitatively understand the molecular mechanisms underpinning gene regulation. Here, we report a novel framework for efficient and scalable parameter estimation that focuses specifically on modeling of gene circuits. Exploiting the structure commonly found in gene circuit models, this framework decomposes a system of coupled rate equations into individual ones and efficiently integrates them separately to reconstruct the mean time evolution of the gene products. The accuracy of the parameter estimates is refined by iteratively increasing the accuracy of numerical integration using the model structure. As a case study, we applied our framework to four gene circuit models with complex dynamics based on three synthetic datasets and one time series microarray data set. We compared our framework to three state-of-the-art parameter estimation methods and found that our approach consistently generated higher quality parameter solutions efficiently. Although many general-purpose parameter estimation methods have been applied for modeling of gene circuits, our results suggest that the use of more tailored approaches to use domain-specific information may be a key to reverse engineering of complex biological systems. http://sfb.kaust.edu.sa/Pages/Software.aspx. Supplementary data are available at Bioinformatics online.

Voltage Control of Antiferromagnetic Phases at Near-Terahertz Frequencies

NASA Astrophysics Data System (ADS)

Barra, Anthony; Domann, John; Kim, Ki Wook; Carman, Greg

2018-03-01

A method to control antiferromagnetism using voltage-induced strain is proposed and theoretically examined. Voltage-induced magnetoelastic anisotropy is shown to provide sufficient torque to switch an antiferromagnetic domain 90° either from out of plane to in plane or between in-plane axes. Numerical results indicate that strain-mediated antiferromagnetic switching can occur in an 80-nm nanopatterned disk at frequencies approaching 1 THz but that the switching speed heavily depends on the system's mechanical design. Furthermore, the energy cost to induce magnetic switching is only 450 aJ, indicating that magnetoelastic control of antiferromagnetism is substantially more energy efficient than other approaches.

ADRC for spacecraft attitude and position synchronization in libration point orbits

NASA Astrophysics Data System (ADS)

Gao, Chen; Yuan, Jianping; Zhao, Yakun

2018-04-01

This paper addresses the problem of spacecraft attitude and position synchronization in libration point orbits between a leader and a follower. Using dual quaternion, the dimensionless relative coupled dynamical model is derived considering computation efficiency and accuracy. Then a model-independent dimensionless cascade pose-feedback active disturbance rejection controller is designed to spacecraft attitude and position tracking control problems considering parameter uncertainties and external disturbances. Numerical simulations for the final approach phase in spacecraft rendezvous and docking and formation flying are done, and the results show high-precision tracking errors and satisfactory convergent rates under bounded control torque and force which validate the proposed approach.

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Kai; Song, Linze; Shi, Qiang, E-mail: qshi@iccas.ac.cn

Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performedmore » to demonstrate the efficiency of the new method.« less

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Adaptive Load-Balancing Algorithms using Symmetric Broadcast Networks

NASA Technical Reports Server (NTRS)

Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Biegel, Bryan A. (Technical Monitor)

2002-01-01

In a distributed computing environment, it is important to ensure that the processor workloads are adequately balanced, Among numerous load-balancing algorithms, a unique approach due to Das and Prasad defines a symmetric broadcast network (SBN) that provides a robust communication pattern among the processors in a topology-independent manner. In this paper, we propose and analyze three efficient SBN-based dynamic load-balancing algorithms, and implement them on an SGI Origin2000. A thorough experimental study with Poisson distributed synthetic loads demonstrates that our algorithms are effective in balancing system load. By optimizing completion time and idle time, the proposed algorithms are shown to compare favorably with several existing approaches.

Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective.

PubMed

Sharma, Sanjiv; Coetzee, Etienne B; Lowenberg, Mark H; Neild, Simon A; Krauskopf, Bernd

2015-09-28

Bifurcation analysis is a powerful method for studying the steady-state nonlinear dynamics of systems. Software tools exist for the numerical continuation of steady-state solutions as parameters of the system are varied. These tools make it possible to generate 'maps of solutions' in an efficient way that provide valuable insight into the overall dynamic behaviour of a system and potentially to influence the design process. While this approach has been employed in the military aircraft control community to understand the effectiveness of controllers, the use of bifurcation analysis in the wider aircraft industry is yet limited. This paper reports progress on how bifurcation analysis can play a role as part of the design process for passenger aircraft. © 2015 The Author(s).

Consistent Chemical Mechanism from Collaborative Data Processing

DOE PAGES

Slavinskaya, Nadezda; Starcke, Jan-Hendrik; Abbasi, Mehdi; ...

2016-04-01

Numerical tool of Process Informatics Model (PrIMe) is mathematically rigorous and numerically efficient approach for analysis and optimization of chemical systems. It handles heterogeneous data and is scalable to a large number of parameters. The Boundto-Bound Data Collaboration module of the automated data-centric infrastructure of PrIMe was used for the systematic uncertainty and data consistency analyses of the H 2/CO reaction model (73/17) and 94 experimental targets (ignition delay times). The empirical rule for evaluation of the shock tube experimental data is proposed. The initial results demonstrate clear benefits of the PrIMe methods for an evaluation of the kinetic datamore » quality and data consistency and for developing predictive kinetic models.« less

Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set

NASA Astrophysics Data System (ADS)

Pemmaraju, C. D.; Vila, F. D.; Kas, J. J.; Sato, S. A.; Rehr, J. J.; Yabana, K.; Prendergast, David

2018-05-01

The interaction of laser fields with solid-state systems can be modeled efficiently within the velocity-gauge formalism of real-time time dependent density functional theory (RT-TDDFT). In this article, we discuss the implementation of the velocity-gauge RT-TDDFT equations for electron dynamics within a linear combination of atomic orbitals (LCAO) basis set framework. Numerical results obtained from our LCAO implementation, for the electronic response of periodic systems to both weak and intense laser fields, are compared to those obtained from established real-space grid and Full-Potential Linearized Augmented Planewave approaches. Potential applications of the LCAO based scheme in the context of extreme ultra-violet and soft X-ray spectroscopies involving core-electronic excitations are discussed.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

Multiphoton ionization of many-electron atoms and highly-charged ions in intense laser fields: a relativistic time-dependent density functional theory approach

NASA Astrophysics Data System (ADS)

Tumakov, Dmitry A.; Telnov, Dmitry A.; Maltsev, Ilia A.; Plunien, Günter; Shabaev, Vladimir M.

2017-10-01

We develop an efficient numerical implementation of the relativistic time-dependent density functional theory (RTDDFT) to study multielectron highly-charged ions subject to intense linearly-polarized laser fields. The interaction with the electromagnetic field is described within the electric dipole approximation. The resulting time-dependent relativistic Kohn-Sham (RKS) equations possess an axial symmetry and are solved accurately and efficiently with the help of the time-dependent generalized pseudospectral method. As a case study, we calculate multiphoton ionization probabilities of the neutral argon atom and argon-like xenon ion. Relativistic effects are assessed by comparison of our present results with existing non-relativistic data.

CFD studies on biomass thermochemical conversion.

PubMed

Wang, Yiqun; Yan, Lifeng

2008-06-01

Thermochemical conversion of biomass offers an efficient and economically process to provide gaseous, liquid and solid fuels and prepare chemicals derived from biomass. Computational fluid dynamic (CFD) modeling applications on biomass thermochemical processes help to optimize the design and operation of thermochemical reactors. Recent progression in numerical techniques and computing efficacy has advanced CFD as a widely used approach to provide efficient design solutions in industry. This paper introduces the fundamentals involved in developing a CFD solution. Mathematical equations governing the fluid flow, heat and mass transfer and chemical reactions in thermochemical systems are described and sub-models for individual processes are presented. It provides a review of various applications of CFD in the biomass thermochemical process field.

Statistical mechanics of the mixed majority minority game with random external information

NASA Astrophysics Data System (ADS)

DeMartino, A.; Giardina, I.; Mosetti, G.

2003-08-01

We study the asymptotic macroscopic properties of the mixed majority-minority game, modelling a population in which two types of heterogeneous adaptive agents, namely 'fundamentalists' driven by differentiation and 'trend-followers' driven by imitation, interact. The presence of a fraction f of trend-followers is shown to induce (a) a significant loss of informational efficiency with respect to a pure minority game (in particular, an efficient, unpredictable phase exists only for f < 1/2), and (b) a catastrophic increase of global fluctuations for f > 1/2. We solve the model by means of an approximate static (replica) theory and by a direct dynamical (generating functional) technique. The two approaches coincide and match numerical results convincingly.

CFD Studies on Biomass Thermochemical Conversion

PubMed Central

Wang, Yiqun; Yan, Lifeng

2008-01-01

Thermochemical conversion of biomass offers an efficient and economically process to provide gaseous, liquid and solid fuels and prepare chemicals derived from biomass. Computational fluid dynamic (CFD) modeling applications on biomass thermochemical processes help to optimize the design and operation of thermochemical reactors. Recent progression in numerical techniques and computing efficacy has advanced CFD as a widely used approach to provide efficient design solutions in industry. This paper introduces the fundamentals involved in developing a CFD solution. Mathematical equations governing the fluid flow, heat and mass transfer and chemical reactions in thermochemical systems are described and sub-models for individual processes are presented. It provides a review of various applications of CFD in the biomass thermochemical process field. PMID:19325848

Developmental trajectories of children's symbolic numerical magnitude processing skills and associated cognitive competencies.

PubMed

Vanbinst, Kiran; Ceulemans, Eva; Peters, Lien; Ghesquière, Pol; De Smedt, Bert

2018-02-01

Although symbolic numerical magnitude processing skills are key for learning arithmetic, their developmental trajectories remain unknown. Therefore, we delineated during the first 3years of primary education (5-8years of age) groups with distinguishable developmental trajectories of symbolic numerical magnitude processing skills using a model-based clustering approach. Three clusters were identified and were labeled as inaccurate, accurate but slow, and accurate and fast. The clusters did not differ in age, sex, socioeconomic status, or IQ. We also tested whether these clusters differed in domain-specific (nonsymbolic magnitude processing and digit identification) and domain-general (visuospatial short-term memory, verbal working memory, and processing speed) cognitive competencies that might contribute to children's ability to (efficiently) process the numerical meaning of Arabic numerical symbols. We observed minor differences between clusters in these cognitive competencies except for verbal working memory for which no differences were observed. Follow-up analyses further revealed that the above-mentioned cognitive competencies did not merely account for the cluster differences in children's development of symbolic numerical magnitude processing skills, suggesting that other factors account for these individual differences. On the other hand, the three trajectories of symbolic numerical magnitude processing revealed remarkable and stable differences in children's arithmetic fact retrieval, which stresses the importance of symbolic numerical magnitude processing for learning arithmetic. Copyright © 2017 Elsevier Inc. All rights reserved.

Large-eddy simulation of wind turbine wake interactions on locally refined Cartesian grids

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2014-11-01

Performing high-fidelity numerical simulations of turbulent flow in wind farms remains a challenging issue mainly because of the large computational resources required to accurately simulate the turbine wakes and turbine/turbine interactions. The discretization of the governing equations on structured grids for mesoscale calculations may not be the most efficient approach for resolving the large disparity of spatial scales. A 3D Cartesian grid refinement method enabling the efficient coupling of the Actuator Line Model (ALM) with locally refined unstructured Cartesian grids adapted to accurately resolve tip vortices and multi-turbine interactions, is presented. Second order schemes are employed for the discretization of the incompressible Navier-Stokes equations in a hybrid staggered/non-staggered formulation coupled with a fractional step method that ensures the satisfaction of local mass conservation to machine zero. The current approach enables multi-resolution LES of turbulent flow in multi-turbine wind farms. The numerical simulations are in good agreement with experimental measurements and are able to resolve the rich dynamics of turbine wakes on grids containing only a small fraction of the grid nodes that would be required in simulations without local mesh refinement. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the National Science Foundation under Award number NSF PFI:BIC 1318201.

Modelling biochemical reaction systems by stochastic differential equations with reflection.

PubMed

Niu, Yuanling; Burrage, Kevin; Chen, Luonan

2016-05-07

In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

NASA Astrophysics Data System (ADS)

Karwas, Alex

Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach is capable of accurately simulating sailcraft motion. Sailcraft and spacecraft simulations are compared to flight data and to other numerical solution techniques. The new formulation shows an increase in accuracy over a widely used trajectory propagation technique. Simulations for two-dimensional, three-dimensional, and variable attitude trajectories are presented to show the multiple capabilities of the new technique. An element of optimal control is also part of the new technique. An additional equation is added to the sailcraft equations of motion that maximizes thrust in a specific direction. A technical description and results of an example optimization problem are presented. The spacecraft attitude dynamics equations take the simulation a step further by providing control torques using the angular rate and acceleration outputs of the numerical formulation.

Sensitivity Analysis and Optimization of Enclosure Radiation with Applications to Crystal Growth

NASA Technical Reports Server (NTRS)

Tiller, Michael M.

1995-01-01

In engineering, simulation software is often used as a convenient means for carrying out experiments to evaluate physical systems. The benefit of using simulations as 'numerical' experiments is that the experimental conditions can be easily modified and repeated at much lower cost than the comparable physical experiment. The goal of these experiments is to 'improve' the process or result of the experiment. In most cases, the computational experiments employ the same trial and error approach as their physical counterparts. When using this approach for complex systems, the cause and effect relationship of the system may never be fully understood and efficient strategies for improvement never utilized. However, it is possible when running simulations to accurately and efficiently determine the sensitivity of the system results with respect to simulation to accurately and efficiently determine the sensitivity of the system results with respect to simulation parameters (e.g., initial conditions, boundary conditions, and material properties) by manipulating the underlying computations. This results in a better understanding of the system dynamics and gives us efficient means to improve processing conditions. We begin by discussing the steps involved in performing simulations. Then we consider how sensitivity information about simulation results can be obtained and ways this information may be used to improve the process or result of the experiment. Next, we discuss optimization and the efficient algorithms which use sensitivity information. We draw on all this information to propose a generalized approach for integrating simulation and optimization, with an emphasis on software programming issues. After discussing our approach to simulation and optimization we consider an application involving crystal growth. This application is interesting because it includes radiative heat transfer. We discuss the computation of radiative new factors and the impact this mode of heat transfer has on our approach. Finally, we will demonstrate the results of our optimization.

Work Optimization Predicts Accretionary Faulting: An Integration of Physical and Numerical Experiments

NASA Astrophysics Data System (ADS)

McBeck, Jessica A.; Cooke, Michele L.; Herbert, Justin W.; Maillot, Bertrand; Souloumiac, Pauline

2017-09-01

We employ work optimization to predict the geometry of frontal thrusts at two stages of an evolving physical accretion experiment. Faults that produce the largest gains in efficiency, or change in external work per new fault area, ΔWext/ΔA, are considered most likely to develop. The predicted thrust geometry matches within 1 mm of the observed position and within a few degrees of the observed fault dip, for both the first forethrust and backthrust when the observed forethrust is active. The positions of the second backthrust and forethrust that produce >90% of the maximum ΔWext/ΔA also overlap the observed thrusts. The work optimal fault dips are within a few degrees of the fault dips that maximize the average Coulomb stress. Slip gradients along the detachment produce local elevated shear stresses and high strain energy density regions that promote thrust initiation near the detachment. The mechanical efficiency (Wext) of the system decreases at each of the two simulated stages of faulting and resembles the evolution of experimental force. The higher ΔWext/ΔA due to the development of the first pair relative to the second pair indicates that the development of new thrusts may lead to diminishing efficiency gains as the wedge evolves. The numerical estimates of work consumed by fault propagation overlap the range calculated from experimental force data and crustal faults. The integration of numerical and physical experiments provides a powerful approach that demonstrates the utility of work optimization to predict the development of faults.

Brownian dynamics of confined rigid bodies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar, E-mail: donev@courant.nyu.edu

2015-10-14

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the othermore » based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.« less

Mid-infrared supercontinuum generation in fluoride fiber amplifiers: current status and future perspectives

NASA Astrophysics Data System (ADS)

Gauthier, Jean-Christophe; Robichaud, Louis-Rafaël; Fortin, Vincent; Vallée, Réal; Bernier, Martin

2018-06-01

The quest for a compact and efficient broadband laser source able to probe the numerous fundamental molecular absorption lines in the mid-infrared (3-8 µm) for various applications has been going on for more than a decade. While robust commercial fiber-based supercontinuum (SC) systems have started to appear on the market, they still exhibit poor energy conversion into the mid-infrared (typically under 30%) and are generally not producing wavelengths exceeding 4.7 µm. Here, we present an overview of the results obtained from a novel approach to SC generation based on spectral broadening inside of an erbium-doped fluoride fiber amplifier seeded directly at 2.8 µm, allowing mid-infrared conversion efficiencies reaching up to 95% and spectral coverage approaching the transparency limit of ZrF4 (4.2 µm) and InF3 (5.5 µm) fibers. The general concept of the approach and the physical mechanisms involved are presented alongside the various configurations of the system to adjust the output characteristics in terms of spectral coverage and output power for different applications.

Deformation in Micro Roll Forming of Bipolar Plate

NASA Astrophysics Data System (ADS)

Zhang, P.; Pereira, M.; Rolfe, B.; Daniel, W.; Weiss, M.

2017-09-01

Micro roll forming is a new processing technology to produce bipolar plates for Proton Exchange Membrane Fuel Cells (PEMFC) from thin stainless steel foil. To gain a better understanding of the deformation of the material in this process, numerical studies are necessary before experimental implementation. In general, solid elements with several layers through the material thickness are required to analyse material thinning in processes where the deformation mode is that of bending combined with tension, but this results in high computational costs. This pure solid element approach is especially time-consuming when analysing roll forming processes which generally involves feeding a long strip through a number of successive roll stands. In an attempt to develop a more efficient modelling approach without sacrificing accuracy, two solutions are numerically analysed with ABAQUS/Explicit in this paper. In the first, a small patch of solid elements over the strip width and in the centre of the “pre-cut” sheet is coupled with shell elements while in the second approach pure shell elements are used to discretize the full sheet. In the first approach, the shell element enables accounting for the effect of material being held in the roll stands on material flow while solid elements can be applied to analyse material thinning in a small discrete area of the sheet. Experimental micro roll forming trials are performed to prove that the coupling of solid and shell elements can give acceptable model accuracy while using shell elements alone is shown to result in major deviations between numerical and experimental results.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

An interior penalty stabilised incompressible discontinuous Galerkin-Fourier solver for implicit large eddy simulations

NASA Astrophysics Data System (ADS)

Ferrer, Esteban

2017-11-01

We present an implicit Large Eddy Simulation (iLES) h / p high order (≥2) unstructured Discontinuous Galerkin-Fourier solver with sliding meshes. The solver extends the laminar version of Ferrer and Willden, 2012 [34], to enable the simulation of turbulent flows at moderately high Reynolds numbers in the incompressible regime. This solver allows accurate flow solutions of the laminar and turbulent 3D incompressible Navier-Stokes equations on moving and static regions coupled through a high order sliding interface. The spatial discretisation is provided by the Symmetric Interior Penalty Discontinuous Galerkin (IP-DG) method in the x-y plane coupled with a purely spectral method that uses Fourier series and allows efficient computation of spanwise periodic three-dimensional flows. Since high order methods (e.g. discontinuous Galerkin and Fourier) are unable to provide enough numerical dissipation to enable under-resolved high Reynolds computations (i.e. as necessary in the iLES approach), we adapt the laminar version of the solver to increase (controllably) the dissipation and enhance the stability in under-resolved simulations. The novel stabilisation relies on increasing the penalty parameter included in the DG interior penalty (IP) formulation. The latter penalty term is included when discretising the linear viscous terms in the incompressible Navier-Stokes equations. These viscous penalty fluxes substitute the stabilising effect of non-linear fluxes, which has been the main trend in implicit LES discontinuous Galerkin approaches. The IP-DG penalty term provides energy dissipation, which is controlled by the numerical jumps at element interfaces (e.g. large in under-resolved regions) such as to stabilise under-resolved high Reynolds number flows. This dissipative term has minimal impact in well resolved regions and its implicit treatment does not restrict the use of large time steps, thus providing an efficient stabilization mechanism for iLES. The IP-DG stabilisation is complemented with a Spectral Vanishing Viscosity (SVV) method, in the z-direction, to enhance stability in the continuous Fourier space. The coupling between the numerical viscosity in the DG plane and the SVV damping, provides an efficient approach to stabilise high order methods at moderately high Reynolds numbers. We validate the formulation for three turbulent flow cases: a circular cylinder at Re = 3900, a static and pitch oscillating NACA 0012 airfoil at Re = 10000 and finally a rotating vertical-axis turbine at Re = 40000, with Reynolds based on the circular diameter, airfoil chord and turbine diameter, respectively. All our results compare favourably with published direct numerical simulations, large eddy simulations or experimental data. We conclude that the DG-Fourier high order solver, with IP-SVV stabilisation, proves to be a valuable tool to predict turbulent flows and associated statistics for both static and rotating machinery.

A flowgraph model for bladder carcinoma

PubMed Central

2014-01-01

Background Superficial bladder cancer has been the subject of numerous studies for many years, but the evolution of the disease still remains not well understood. After the tumor has been surgically removed, it may reappear at a similar level of malignancy or progress to a higher level. The process may be reasonably modeled by means of a Markov process. However, in order to more completely model the evolution of the disease, this approach is insufficient. The semi-Markov framework allows a more realistic approach, but calculations become frequently intractable. In this context, flowgraph models provide an efficient approach to successfully manage the evolution of superficial bladder carcinoma. Our aim is to test this methodology in this particular case. Results We have built a successful model for a simple but representative case. Conclusion The flowgraph approach is suitable for modeling of superficial bladder cancer. PMID:25080066

A probabilistic bridge safety evaluation against floods.

PubMed

Liao, Kuo-Wei; Muto, Yasunori; Chen, Wei-Lun; Wu, Bang-Ho

2016-01-01

To further capture the influences of uncertain factors on river bridge safety evaluation, a probabilistic approach is adopted. Because this is a systematic and nonlinear problem, MPP-based reliability analyses are not suitable. A sampling approach such as a Monte Carlo simulation (MCS) or importance sampling is often adopted. To enhance the efficiency of the sampling approach, this study utilizes Bayesian least squares support vector machines to construct a response surface followed by an MCS, providing a more precise safety index. Although there are several factors impacting the flood-resistant reliability of a bridge, previous experiences and studies show that the reliability of the bridge itself plays a key role. Thus, the goal of this study is to analyze the system reliability of a selected bridge that includes five limit states. The random variables considered here include the water surface elevation, water velocity, local scour depth, soil property and wind load. Because the first three variables are deeply affected by river hydraulics, a probabilistic HEC-RAS-based simulation is performed to capture the uncertainties in those random variables. The accuracy and variation of our solutions are confirmed by a direct MCS to ensure the applicability of the proposed approach. The results of a numerical example indicate that the proposed approach can efficiently provide an accurate bridge safety evaluation and maintain satisfactory variation.

Algorithmic design of a noise-resistant and efficient closed-loop deep brain stimulation system: A computational approach

PubMed Central

Karamintziou, Sofia D.; Custódio, Ana Luísa; Piallat, Brigitte; Polosan, Mircea; Chabardès, Stéphan; Stathis, Pantelis G.; Tagaris, George A.; Sakas, Damianos E.; Polychronaki, Georgia E.; Tsirogiannis, George L.; David, Olivier; Nikita, Konstantina S.

2017-01-01

Advances in the field of closed-loop neuromodulation call for analysis and modeling approaches capable of confronting challenges related to the complex neuronal response to stimulation and the presence of strong internal and measurement noise in neural recordings. Here we elaborate on the algorithmic aspects of a noise-resistant closed-loop subthalamic nucleus deep brain stimulation system for advanced Parkinson’s disease and treatment-refractory obsessive-compulsive disorder, ensuring remarkable performance in terms of both efficiency and selectivity of stimulation, as well as in terms of computational speed. First, we propose an efficient method drawn from dynamical systems theory, for the reliable assessment of significant nonlinear coupling between beta and high-frequency subthalamic neuronal activity, as a biomarker for feedback control. Further, we present a model-based strategy through which optimal parameters of stimulation for minimum energy desynchronizing control of neuronal activity are being identified. The strategy integrates stochastic modeling and derivative-free optimization of neural dynamics based on quadratic modeling. On the basis of numerical simulations, we demonstrate the potential of the presented modeling approach to identify, at a relatively low computational cost, stimulation settings potentially associated with a significantly higher degree of efficiency and selectivity compared with stimulation settings determined post-operatively. Our data reinforce the hypothesis that model-based control strategies are crucial for the design of novel stimulation protocols at the backstage of clinical applications. PMID:28222198

CORDIC-based digital signal processing (DSP) element for adaptive signal processing

NASA Astrophysics Data System (ADS)

Bolstad, Gregory D.; Neeld, Kenneth B.

1995-04-01

The High Performance Adaptive Weight Computation (HAWC) processing element is a CORDIC based application specific DSP element that, when connected in a linear array, can perform extremely high throughput (100s of GFLOPS) matrix arithmetic operations on linear systems of equations in real time. In particular, it very efficiently performs the numerically intense computation of optimal least squares solutions for large, over-determined linear systems. Most techniques for computing solutions to these types of problems have used either a hard-wired, non-programmable systolic array approach, or more commonly, programmable DSP or microprocessor approaches. The custom logic methods can be efficient, but are generally inflexible. Approaches using multiple programmable generic DSP devices are very flexible, but suffer from poor efficiency and high computation latencies, primarily due to the large number of DSP devices that must be utilized to achieve the necessary arithmetic throughput. The HAWC processor is implemented as a highly optimized systolic array, yet retains some of the flexibility of a programmable data-flow system, allowing efficient implementation of algorithm variations. This provides flexible matrix processing capabilities that are one to three orders of magnitude less expensive and more dense than the current state of the art, and more importantly, allows a realizable solution to matrix processing problems that were previously considered impractical to physically implement. HAWC has direct applications in RADAR, SONAR, communications, and image processing, as well as in many other types of systems.

On the electromagnetic scattering from infinite rectangular conducting grids

NASA Technical Reports Server (NTRS)

Christodoulou, C.

1985-01-01

The study and development of two numerical techniques for the analysis of electromagnetic scattering from a rectangular wire mesh are described. Both techniques follow from one basic formulation and they are both solved in the spectral domain. These techniques were developed as a result of an investigation towards more efficient numerical computation for mesh scattering. These techniques are efficient for the following reasons: (a1) make use of the Fast Fourier Transform; (b2) they avoid any convolution problems by converting integrodifferential equations into algebraic equations; and (c3) they do not require inversions of any matrices. The first method, the SIT or Spectral Iteration Technique, is applied for regions where the spacing between wires is not less than two wavelengths. The second method, the SDCG or Spectral Domain Conjugate Gradient approach, can be used for any spacing between adjacent wires. A study of electromagnetic wave properties, such as reflection coefficient, induced currents and aperture fields, as functions of frequency, angle of incidence, polarization and thickness of wires is presented. Examples and comparisons or results with other methods are also included to support the validity of the new algorithms.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

Numerical and experimental investigations of human swimming motions

PubMed Central

Takagi, Hideki; Nakashima, Motomu; Sato, Yohei; Matsuuchi, Kazuo; Sanders, Ross H.

2016-01-01

ABSTRACT This paper reviews unsteady flow conditions in human swimming and identifies the limitations and future potential of the current methods of analysing unsteady flow. The capability of computational fluid dynamics (CFD) has been extended from approaches assuming steady-state conditions to consideration of unsteady/transient conditions associated with the body motion of a swimmer. However, to predict hydrodynamic forces and the swimmer’s potential speeds accurately, more robust and efficient numerical methods are necessary, coupled with validation procedures, requiring detailed experimental data reflecting local flow. Experimental data obtained by particle image velocimetry (PIV) in this area are limited, because at present observations are restricted to a two-dimensional 1.0 m2 area, though this could be improved if the output range of the associated laser sheet increased. Simulations of human swimming are expected to improve competitive swimming, and our review has identified two important advances relating to understanding the flow conditions affecting performance in front crawl swimming: one is a mechanism for generating unsteady fluid forces, and the other is a theory relating to increased speed and efficiency. PMID:26699925

Numerical and experimental investigations of human swimming motions.

PubMed

Takagi, Hideki; Nakashima, Motomu; Sato, Yohei; Matsuuchi, Kazuo; Sanders, Ross H

2016-08-01

This paper reviews unsteady flow conditions in human swimming and identifies the limitations and future potential of the current methods of analysing unsteady flow. The capability of computational fluid dynamics (CFD) has been extended from approaches assuming steady-state conditions to consideration of unsteady/transient conditions associated with the body motion of a swimmer. However, to predict hydrodynamic forces and the swimmer's potential speeds accurately, more robust and efficient numerical methods are necessary, coupled with validation procedures, requiring detailed experimental data reflecting local flow. Experimental data obtained by particle image velocimetry (PIV) in this area are limited, because at present observations are restricted to a two-dimensional 1.0 m(2) area, though this could be improved if the output range of the associated laser sheet increased. Simulations of human swimming are expected to improve competitive swimming, and our review has identified two important advances relating to understanding the flow conditions affecting performance in front crawl swimming: one is a mechanism for generating unsteady fluid forces, and the other is a theory relating to increased speed and efficiency.

Efficient sensitivity analysis method for chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Liao, Haitao

2016-05-01

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.

Spherical Harmonic-based Random Fields Based on Real Particle 3D Data: Improved Numerical Algorithm and Quantitative Comparison to Real Particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

X Liu; E Garboczi; m Grigoriu

Many parameters affect the cyclone efficiency, and these parameters can have different effects in different flow regimes. Therefore the maximum-efficiency cyclone length is a function of the specific geometry and operating conditions in use. In this study, we obtained a relationship describing the minimum particle diameter or maximum cyclone efficiency by using a theoretical approach based on cyclone geometry and fluid properties. We have compared the empirical predictions with corresponding literature data and observed good agreement. The results address the importance of fluid properties. Inlet and vortex finder cross-sections, cone-apex diameter, inlet Reynolds number and surface roughness are found tomore » be the other important parameters affecting cyclone height. The surface friction coefficient, on the other hand, is difficult to employ in the calculations.We developed a theoretical approach to find the maximum-efficiency heights for cyclones with tangential inlet and we suggested a relation for this height as a function of cyclone geometry and operating parameters. In order to generalize use of the relation, two dimensionless parameters, namely for geometric and operational variables, we defined and results were presented in graphical form such that one can calculate and enter the values of these dimensionless parameters and then can find the maximum efficiency height of his own specific cyclone.« less

Numerical Simulation of Aerogasdynamics Processes in A Longwall Panel for Estimation of Spontaneous Combustion Hazards

NASA Astrophysics Data System (ADS)

Meshkov, Sergey; Sidorenko, Andrey

2017-11-01

The relevance of a solution of the problem of endogenous fire safety in seams liable to self-ignition is shown. The possibilities of numerical methods of researches of gasdynamic processes are considered. The analysis of methodical approaches with the purpose to create models and carry out numerical researches of aerogasdynamic processes in longwall panels of gas mines is made. Parameters of the gob for longwall mining are considered. The significant influence of geological and mining conditions of conducting mining operations on distribution of air streams on longwall panels and effective management of gas emission is shown. The aerogasdynamic model of longwall panels for further research of influence of parameters of ventilation and properties of gob is presented. The results of numerical researches including distribution of air streams, fields of concentration of methane and oxygen at application of various schemes of airing for conditions of perspective mines of the Pechora basin and Kuzbass are given. Recommendations for increase of efficiency of the coal seams mining liable to selfignition are made. The directions of further researches are defined.

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

NASA Technical Reports Server (NTRS)

Lee, Seongkyu; Brentner, Kenneth S.; Farassat, F.; Morris, Philip J.

2008-01-01

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.

Parametric effect on the mixing of the combination of a hydrogen porthole with an air porthole in transverse gaseous injection flow fields

NASA Astrophysics Data System (ADS)

Li, Lang-quan; Huang, Wei; Yan, Li; Li, Shi-bin

2017-10-01

The dual transverse injection system with a front hydrogen porthole and a rear air porthole arranged in tandem is proposed, and this is a realistic approach for mixing enhancement and penetration improvement of transverse injection in a scramjet combustor. The influence of this dual transverse injection system on mixing characteristics has been evaluated numerically based on grid independency analysis and code validation. The numerical approach employed in the current study has been validated against the available experimental data in the open literature, and the predicted wall static pressure distributions show reasonable agreement with the experimental data for the cases with different jet-to-crossflow pressure ratios. The obtained results predicted by the three-dimensional Reynolds-average Navier - Stokes (RANS) equations coupled with the two equation k-ω shear stress transport (SST) turbulence model show that the air pothole has an great impact on penetration depth and mixing efficiency, and the effect of air jet on flow field varies with different values of the aspect ratio. The air porthole with larger aspect ratio can increase the fuel penetration depth. However, when the aspect ratio is relatively small, the fuel penetration depth decreases, and even smaller than that of the single injection system. At the same time, the air pothole has a highly remarkable improvement on mixing efficiency, especially in the near field. The smaller the aspect ratio of the air porthole is, the higher the mixing efficiency in the near field is. This is due to its larger circulation in the near field. The dual injection system owns more losses of stagnation pressure than the single injection system.

Reliability based design optimization: Formulations and methodologies

NASA Astrophysics Data System (ADS)

Agarwal, Harish

Modern products ranging from simple components to complex systems should be designed to be optimal and reliable. The challenge of modern engineering is to ensure that manufacturing costs are reduced and design cycle times are minimized while achieving requirements for performance and reliability. If the market for the product is competitive, improved quality and reliability can generate very strong competitive advantages. Simulation based design plays an important role in designing almost any kind of automotive, aerospace, and consumer products under these competitive conditions. Single discipline simulations used for analysis are being coupled together to create complex coupled simulation tools. This investigation focuses on the development of efficient and robust methodologies for reliability based design optimization in a simulation based design environment. Original contributions of this research are the development of a novel efficient and robust unilevel methodology for reliability based design optimization, the development of an innovative decoupled reliability based design optimization methodology, the application of homotopy techniques in unilevel reliability based design optimization methodology, and the development of a new framework for reliability based design optimization under epistemic uncertainty. The unilevel methodology for reliability based design optimization is shown to be mathematically equivalent to the traditional nested formulation. Numerical test problems show that the unilevel methodology can reduce computational cost by at least 50% as compared to the nested approach. The decoupled reliability based design optimization methodology is an approximate technique to obtain consistent reliable designs at lesser computational expense. Test problems show that the methodology is computationally efficient compared to the nested approach. A framework for performing reliability based design optimization under epistemic uncertainty is also developed. A trust region managed sequential approximate optimization methodology is employed for this purpose. Results from numerical test studies indicate that the methodology can be used for performing design optimization under severe uncertainty.

2.5-D frequency-domain viscoelastic wave modelling using finite-element method

NASA Astrophysics Data System (ADS)

Zhao, Jian-guo; Huang, Xing-xing; Liu, Wei-fang; Zhao, Wei-jun; Song, Jian-yong; Xiong, Bin; Wang, Shang-xu

2017-10-01

2-D seismic modelling has notable dynamic information discrepancies with field data because of the implicit line-source assumption, whereas 3-D modelling suffers from a huge computational burden. The 2.5-D approach is able to overcome both of the aforementioned limitations. In general, the earth model is treated as an elastic material, but the real media is viscous. In this study, we develop an accurate and efficient frequency-domain finite-element method (FEM) for modelling 2.5-D viscoelastic wave propagation. To perform the 2.5-D approach, we assume that the 2-D viscoelastic media are based on the Kelvin-Voigt rheological model and a 3-D point source. The viscoelastic wave equation is temporally and spatially Fourier transformed into the frequency-wavenumber domain. Then, we systematically derive the weak form and its spatial discretization of 2.5-D viscoelastic wave equations in the frequency-wavenumber domain through the Galerkin weighted residual method for FEM. Fixing a frequency, the 2-D problem for each wavenumber is solved by FEM. Subsequently, a composite Simpson formula is adopted to estimate the inverse Fourier integration to obtain the 3-D wavefield. We implement the stiffness reduction method (SRM) to suppress artificial boundary reflections. The results show that this absorbing boundary condition is valid and efficient in the frequency-wavenumber domain. Finally, three numerical models, an unbounded homogeneous medium, a half-space layered medium and an undulating topography medium, are established. Numerical results validate the accuracy and stability of 2.5-D solutions and present the adaptability of finite-element method to complicated geographic conditions. The proposed 2.5-D modelling strategy has the potential to address modelling studies on wave propagation in real earth media in an accurate and efficient way.

Multiyear Program Plan for the High Temperature Materials Laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arvid E. Pasto

2000-03-17

Recently, the U.S. Department of Energy's (DOE) Office of Heavy Vehicle Technologies (OHVT) prepared a Technology Roadmap describing the challenges facing development of higher fuel efficiency, less polluting sport utility vehicles, vans, and commercial trucks. Based on this roadmap, a multiyear program plan (MYPP) was also developed, in which approaches to solving the numerous challenges are enumerated. Additional planning has been performed by DOE and national laboratory staff, on approaches to solving the numerous challenges faced by heavy vehicle system improvements. Workshops and planning documents have been developed concerning advanced aerodynamics, frictional and other parasitic losses, and thermal management. Similarly,more » the Heavy Vehicle Propulsion Materials Program has developed its own multiyear program plan. The High Temperature Materials Laboratory, a major user facility sponsored by OHVT, has now developed its program plan, described herein. Information was gathered via participation in the development of OHVT's overall Technology Roadmap and MYPP, through personal contacts within the materials-user community, and from attendance at conferences and expositions. Major materials issues for the heavy vehicle industry currently center on trying to increase efficiency of (diesel) engines while at the same time reducing emissions (particularly NO{sub x} and particulates). These requirements dictate the use of increasingly stronger, higher-temperature capable and more corrosion-resistant materials of construction, as well as advanced catalysts, particulate traps, and other pollution-control devices. Exhaust gas recirculation (EGR) is a technique which will certainly be applied to diesel engines in the near future, and its use represents a formidable challenge, as will be described later. Energy-efficient, low cost materials processing methods and surface treatments to improve wear, fracture, and corrosion resistance are also required.« less

Selecting optimal monitoring site locations for peak ambient particulate material concentrations using the MM5-CAMx4 numerical modelling system.

PubMed

Sturman, Andrew; Titov, Mikhail; Zawar-Reza, Peyman

2011-01-15

Installation of temporary or long term monitoring sites is expensive, so it is important to rationally identify potential locations that will achieve the requirements of regional air quality management strategies. A simple, but effective, numerical approach to selecting ambient particulate matter (PM) monitoring site locations has therefore been developed using the MM5-CAMx4 air pollution dispersion modelling system. A new method, 'site efficiency,' was developed to assess the ability of any monitoring site to provide peak ambient air pollution concentrations that are representative of the urban area. 'Site efficiency' varies from 0 to 100%, with the latter representing the most representative site location for monitoring peak PM concentrations. Four heavy pollution episodes in Christchurch (New Zealand) during winter 2005, representing 4 different aerosol dispersion patterns, were used to develop and test this site assessment technique. Evaluation of the efficiency of monitoring sites was undertaken for night and morning aerosol peaks for 4 different particulate material (PM) spatial patterns. The results demonstrate that the existing long term monitoring site at Coles Place is quite well located, with a site efficiency value of 57.8%. A temporary ambient PM monitoring site (operating during winter 2006) showed a lower ability to capture night and morning peak aerosol concentrations. Evaluation of multiple site locations used during an extensive field campaign in Christchurch (New Zealand) in 2000 indicated that the maximum efficiency achieved by any site in the city would be 60-65%, while the efficiency of a virtual background site is calculated to be about 7%. This method of assessing the appropriateness of any potential monitoring site can be used to optimize monitoring site locations for any air pollution measurement programme. Copyright © 2010 Elsevier B.V. All rights reserved.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems.

PubMed

Ravishankar, Saiprasad; Nadakuditi, Raj Rao; Fessler, Jeffrey A

2017-12-01

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

PubMed Central

Ravishankar, Saiprasad; Nadakuditi, Raj Rao; Fessler, Jeffrey A.

2017-01-01

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction. PMID:29376111

Fluidization of spherocylindrical particles

NASA Astrophysics Data System (ADS)

Mahajan, Vinay V.; Nijssen, Tim M. J.; Fitzgerald, Barry W.; Hofman, Jeroen; Kuipers, Hans; Padding, Johan T.

2017-06-01

Multiphase (gas-solid) flows are encountered in numerous industrial applications such as pharmaceutical, food, agricultural processing and energy generation. A coupled computational fluid dynamics (CFD) and discrete element method (DEM) approach is a popular way to study such flows at a particle scale. However, most of these studies deal with spherical particles while in reality, the particles are rarely spherical. The particle shape can have significant effect on hydrodynamics in a fluidized bed. Moreover, most studies in literature use inaccurate drag laws because accurate laws are not readily available. The drag force acting on a non-spherical particle can vary considerably with particle shape, orientation with the flow, Reynolds number and packing fraction. In this work, the CFD-DEM approach is extended to model a laboratory scale fluidized bed of spherocylinder (rod-like) particles. These rod-like particles can be classified as Geldart D particles and have an aspect ratio of 4. Experiments are performed to study the particle flow behavior in a quasi-2D fluidized bed. Numerically obtained results for pressure drop and bed height are compared with experiments. The capability of CFD-DEM approach to efficiently describe the global bed dynamics for fluidized bed of rod-like particles is demonstrated.

Temperature distribution of a simplified rotor due to a uniform heat source

NASA Astrophysics Data System (ADS)

Welzenbach, Sarah; Fischer, Tim; Meier, Felix; Werner, Ewald; kyzy, Sonun Ulan; Munz, Oliver

2018-03-01

In gas turbines, high combustion efficiency as well as operational safety are required. Thus, labyrinth seal systems with honeycomb liners are commonly used. In the case of rubbing events in the seal system, the components can be damaged due to cyclic thermal and mechanical loads. Temperature differences occurring at labyrinth seal fins during rubbing events can be determined by considering a single heat source acting periodically on the surface of a rotating cylinder. Existing literature analysing the temperature distribution on rotating cylindrical bodies due to a stationary heat source is reviewed. The temperature distribution on the circumference of a simplified labyrinth seal fin is calculated using an available and easy to implement analytical approach. A finite element model of the simplified labyrinth seal fin is created and the numerical results are compared to the analytical results. The temperature distributions calculated by the analytical and the numerical approaches coincide for low sliding velocities, while there are discrepancies of the calculated maximum temperatures for higher sliding velocities. The use of the analytical approach allows the conservative estimation of the maximum temperatures arising in labyrinth seal fins during rubbing events. At the same time, high calculation costs can be avoided.

Computational unsteady aerodynamics for lifting surfaces

NASA Technical Reports Server (NTRS)

Edwards, John W.

1988-01-01

Two dimensional problems are solved using numerical techniques. Navier-Stokes equations are studied both in the vorticity-stream function formulation which appears to be the optimal choice for two dimensional problems, using a storage approach, and in the velocity pressure formulation which minimizes the number of unknowns in three dimensional problems. Analysis shows that compact centered conservative second order schemes for the vorticity equation are the most robust for high Reynolds number flows. Serious difficulties remain in the choice of turbulent models, to keep reasonable CPU efficiency.

Theory of many-body radiative heat transfer without the constraint of reciprocity

NASA Astrophysics Data System (ADS)

Zhu, Linxiao; Guo, Yu; Fan, Shanhui

2018-03-01

Using a self-consistent scattered field approach based on fluctuational electrodynamics, we develop compact formulas for radiative heat transfer in many-body systems without the constraint of reciprocity. The formulas allow for efficient numerical calculation for a system consisting of a large number of bodies, and are in principle exact. As a demonstration, for a nonreciprocal many-body system, we investigate persistent heat current at thermal equilibrium and directional heat transfer when the system is away from thermal equilibrium.

On a numerical solving of random generated hexamatrix games

NASA Astrophysics Data System (ADS)

Orlov, Andrei; Strekalovskiy, Alexander

2016-10-01

In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem of finding a Nash equilibrium in the game and a special mathematical optimization problem, and, on the other hand, on the usage of Global Search Theory for solving the latter problem. The efficiency of this approach is demonstrated by the results of computational testing.

Development of numerical methods for overset grids with applications for the integrated Space Shuttle vehicle

NASA Technical Reports Server (NTRS)

Chan, William M.

1995-01-01

Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation.

Engineering topological edge states in two dimensional magnetic photonic crystal

NASA Astrophysics Data System (ADS)

Yang, Bing; Wu, Tong; Zhang, Xiangdong

2017-01-01

Based on a perturbative approach, we propose a simple and efficient method to engineer the topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the field-energy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states "designable."

Structural Analysis Computer Programs for Rigid Multicomponent Pavement Structures with Discontinuities--WESLIQID and WESLAYER. Report 1. Program Development and Numerical Presentations.

DTIC Science & Technology

1981-05-01

represented as a Winkler foundation. The program can treat any number of slabs connected by steel bars or other load trans- fer devices at the joints...dimensional finite element method. The inherent flexibility of such an approach permits the analysis of a rigid pavement with steel bars and stabilized...layers and provides an efficient tool for analyzing stress conditions at the joint. Unfor- tunately, such a procedure would require a tremendously

The Fukushima releases: an inverse modelling approach to assess the source term by using gamma dose rate observations

NASA Astrophysics Data System (ADS)

Saunier, Olivier; Mathieu, Anne; Didier, Damien; Tombette, Marilyne; Quélo, Denis; Winiarek, Victor; Bocquet, Marc

2013-04-01

The Chernobyl nuclear accident and more recently the Fukushima accident highlighted that the largest source of error on consequences assessment is the source term estimation including the time evolution of the release rate and its distribution between radioisotopes. Inverse modelling methods have proved to be efficient to assess the source term due to accidental situation (Gudiksen, 1989, Krysta and Bocquet, 2007, Stohl et al 2011, Winiarek et al 2012). These methods combine environmental measurements and atmospheric dispersion models. They have been recently applied to the Fukushima accident. Most existing approaches are designed to use air sampling measurements (Winiarek et al, 2012) and some of them use also deposition measurements (Stohl et al, 2012, Winiarek et al, 2013). During the Fukushima accident, such measurements are far less numerous and not as well distributed within Japan than the dose rate measurements. To efficiently document the evolution of the contamination, gamma dose rate measurements were numerous, well distributed within Japan and they offered a high temporal frequency. However, dose rate data are not as easy to use as air sampling measurements and until now they were not used in inverse modelling approach. Indeed, dose rate data results from all the gamma emitters present in the ground and in the atmosphere in the vicinity of the receptor. They do not allow one to determine the isotopic composition or to distinguish the plume contribution from wet deposition. The presented approach proposes a way to use dose rate measurement in inverse modeling approach without the need of a-priori information on emissions. The method proved to be efficient and reliable when applied on the Fukushima accident. The emissions for the 8 main isotopes Xe-133, Cs-134, Cs-136, Cs-137, Ba-137m, I-131, I-132 and Te-132 have been assessed. The Daiichi power plant events (such as ventings, explosions…) known to have caused atmospheric releases are well identified in the retrieved source term, except for unit 3 explosion where no measurement was available. The comparisons between the simulations of atmospheric dispersion and deposition of the retrieved source term show a good agreement with environmental observations. Moreover, an important outcome of this study is that the method proved to be perfectly suited to crisis management and should contribute to improve our response in case of a nuclear accident.

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Fast Numerical Simulation of Focused Ultrasound Treatments During Respiratory Motion With Discontinuous Motion Boundaries.

PubMed

Schwenke, Michael; Georgii, Joachim; Preusser, Tobias

2017-07-01

Focused ultrasound (FUS) is rapidly gaining clinical acceptance for several target tissues in the human body. Yet, treating liver targets is not clinically applied due to a high complexity of the procedure (noninvasiveness, target motion, complex anatomy, blood cooling effects, shielding by ribs, and limited image-based monitoring). To reduce the complexity, numerical FUS simulations can be utilized for both treatment planning and execution. These use-cases demand highly accurate and computationally efficient simulations. We propose a numerical method for the simulation of abdominal FUS treatments during respiratory motion of the organs and target. Especially, a novel approach is proposed to simulate the heating during motion by solving Pennes' bioheat equation in a computational reference space, i.e., the equation is mathematically transformed to the reference. The approach allows for motion discontinuities, e.g., the sliding of the liver along the abdominal wall. Implementing the solver completely on the graphics processing unit and combining it with an atlas-based ultrasound simulation approach yields a simulation performance faster than real time (less than 50-s computing time for 100 s of treatment time) on a modern off-the-shelf laptop. The simulation method is incorporated into a treatment planning demonstration application that allows to simulate real patient cases including respiratory motion. The high performance of the presented simulation method opens the door to clinical applications. The methods bear the potential to enable the application of FUS for moving organs.

Complementary Approaches to Existing Target Based Drug Discovery for Identifying Novel Drug Targets.

PubMed

Vasaikar, Suhas; Bhatia, Pooja; Bhatia, Partap G; Chu Yaiw, Koon

2016-11-21

In the past decade, it was observed that the relationship between the emerging New Molecular Entities and the quantum of R&D investment has not been favorable. There might be numerous reasons but few studies stress the introduction of target based drug discovery approach as one of the factors. Although a number of drugs have been developed with an emphasis on a single protein target, yet identification of valid target is complex. The approach focuses on an in vitro single target, which overlooks the complexity of cell and makes process of validation drug targets uncertain. Thus, it is imperative to search for alternatives rather than looking at success stories of target-based drug discovery. It would be beneficial if the drugs were developed to target multiple components. New approaches like reverse engineering and translational research need to take into account both system and target-based approach. This review evaluates the strengths and limitations of known drug discovery approaches and proposes alternative approaches for increasing efficiency against treatment.

Numerical Modelling of Tsunami Generated by Deformable Submarine Slides: Parameterisation of Slide Dynamics for Coupling to Tsunami Propagation Model

NASA Astrophysics Data System (ADS)

Smith, R. C.; Collins, G. S.; Hill, J.; Piggott, M. D.; Mouradian, S. L.

2015-12-01

Numerical modelling informs risk assessment of tsunami generated by submarine slides; however, for large-scale slides modelling can be complex and computationally challenging. Many previous numerical studies have approximated slides as rigid blocks that moved according to prescribed motion. However, wave characteristics are strongly dependent on the motion of the slide and previous work has recommended that more accurate representation of slide dynamics is needed. We have used the finite-element, adaptive-mesh CFD model Fluidity, to perform multi-material simulations of deformable submarine slide-generated waves at real world scales for a 2D scenario in the Gulf of Mexico. Our high-resolution approach represents slide dynamics with good accuracy, compared to other numerical simulations of this scenario, but precludes tracking of wave propagation over large distances. To enable efficient modelling of further propagation of the waves, we investigate an approach to extract information about the slide evolution from our multi-material simulations in order to drive a single-layer wave propagation model, also using Fluidity, which is much less computationally expensive. The extracted submarine slide geometry and position as a function of time are parameterised using simple polynomial functions. The polynomial functions are used to inform a prescribed velocity boundary condition in a single-layer simulation, mimicking the effect the submarine slide motion has on the water column. The approach is verified by successful comparison of wave generation in the single-layer model with that recorded in the multi-material, multi-layer simulations. We then extend this approach to 3D for further validation of this methodology (using the Gulf of Mexico scenario proposed by Horrillo et al., 2013) and to consider the effect of lateral spreading. This methodology is then used to simulate a series of hypothetical submarine slide events in the Arctic Ocean (based on evidence of historic slides) and examine the hazard posed to the UK coast.

An opportunity cost approach to sample size calculation in cost-effectiveness analysis.

PubMed

Gafni, A; Walter, S D; Birch, S; Sendi, P

2008-01-01

The inclusion of economic evaluations as part of clinical trials has led to concerns about the adequacy of trial sample size to support such analysis. The analytical tool of cost-effectiveness analysis is the incremental cost-effectiveness ratio (ICER), which is compared with a threshold value (lambda) as a method to determine the efficiency of a health-care intervention. Accordingly, many of the methods suggested to calculating the sample size requirements for the economic component of clinical trials are based on the properties of the ICER. However, use of the ICER and a threshold value as a basis for determining efficiency has been shown to be inconsistent with the economic concept of opportunity cost. As a result, the validity of the ICER-based approaches to sample size calculations can be challenged. Alternative methods for determining improvements in efficiency have been presented in the literature that does not depend upon ICER values. In this paper, we develop an opportunity cost approach to calculating sample size for economic evaluations alongside clinical trials, and illustrate the approach using a numerical example. We compare the sample size requirement of the opportunity cost method with the ICER threshold method. In general, either method may yield the larger required sample size. However, the opportunity cost approach, although simple to use, has additional data requirements. We believe that the additional data requirements represent a small price to pay for being able to perform an analysis consistent with both concept of opportunity cost and the problem faced by decision makers. Copyright (c) 2007 John Wiley & Sons, Ltd.

Dynamic coupling of subsurface and seepage flows solved within a regularized partition formulation

NASA Astrophysics Data System (ADS)

Marçais, J.; de Dreuzy, J.-R.; Erhel, J.

2017-11-01

Hillslope response to precipitations is characterized by sharp transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Locally, the transition between these two regimes is triggered by soil saturation. Here we develop an integrative approach to simultaneously solve the subsurface flow, locate the potential fully saturated areas and deduce the generated saturation excess overland flow. This approach combines the different dynamics and transitions in a single partition formulation using discontinuous functions. We propose to regularize the system of partial differential equations and to use classic spatial and temporal discretization schemes. We illustrate our methodology on the 1D hillslope storage Boussinesq equations (Troch et al., 2003). We first validate the numerical scheme on previous numerical experiments without saturation excess overland flow. Then we apply our model to a test case with dynamic transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Our results show that discretization respects mass balance both locally and globally, converges when the mesh or time step are refined. Moreover the regularization parameter can be taken small enough to ensure accuracy without suffering of numerical artefacts. Applied to some hundreds of realistic hillslope cases taken from Western side of France (Brittany), the developed method appears to be robust and efficient.

Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kudryashov, Nikolay A.; Shilnikov, Kirill E.

Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumormore » tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.« less

An adaptive multi-moment FVM approach for incompressible flows

NASA Astrophysics Data System (ADS)

Liu, Cheng; Hu, Changhong

2018-04-01

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder (Re = 3000 , 9500), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers (Re = 10000 , 45000), the predicted drag coefficient (CD) and lift coefficient (CL) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions (Re = 5000 , 40000), the predicted CD, CL and CM (moment coefficient) are in good agreement with those obtained by other numerical methods.

Numerical methods for large eddy simulation of acoustic combustion instabilities

NASA Astrophysics Data System (ADS)

Wall, Clifton T.

Acoustic combustion instabilities occur when interaction between the combustion process and acoustic modes in a combustor results in periodic oscillations in pressure, velocity, and heat release. If sufficiently large in amplitude, these instabilities can cause operational difficulties or the failure of combustor hardware. In many situations, the dominant instability is the result of the interaction between a low frequency acoustic mode of the combustor and the large scale hydrodynamics. Large eddy simulation (LES), therefore, is a promising tool for the prediction of these instabilities, since both the low frequency acoustic modes and the large scale hydrodynamics are well resolved in LES. Problems with the tractability of such simulations arise, however, due to the difficulty of solving the compressible Navier-Stokes equations efficiently at low Mach number and due to the large number of acoustic periods that are often required for such instabilities to reach limit cycles. An implicit numerical method for the solution of the compressible Navier-Stokes equations has been developed which avoids the acoustic CFL restriction, allowing for significant efficiency gains at low Mach number, while still resolving the low frequency acoustic modes of interest. In the limit of a uniform grid the numerical method causes no artificial damping of acoustic waves. New, non-reflecting boundary conditions have also been developed for use with the characteristic-based approach of Poinsot and Lele (1992). The new boundary conditions are implemented in a manner which allows for significant reduction of the computational domain of an LES by eliminating the need to perform LES in regions where one-dimensional acoustics significantly affect the instability but details of the hydrodynamics do not. These new numerical techniques have been demonstrated in an LES of an experimental combustor. The new techniques are shown to be an efficient means of performing LES of acoustic combustion instabilities and are shown to accurately predict the occurrence and frequency of the dominant mode of the instability observed in the experiment.

Correlating electroluminescence characterization and physics-based models of InGaN/GaN LEDs: Pitfalls and open issues

NASA Astrophysics Data System (ADS)

Calciati, Marco; Goano, Michele; Bertazzi, Francesco; Vallone, Marco; Zhou, Xiangyu; Ghione, Giovanni; Meneghini, Matteo; Meneghesso, Gaudenzio; Zanoni, Enrico; Bellotti, Enrico; Verzellesi, Giovanni; Zhu, Dandan; Humphreys, Colin

2014-06-01

Electroluminescence (EL) characterization of InGaN/GaN light-emitting diodes (LEDs), coupled with numerical device models of different sophistication, is routinely adopted not only to establish correlations between device efficiency and structural features, but also to make inferences about the loss mechanisms responsible for LED efficiency droop at high driving currents. The limits of this investigative approach are discussed here in a case study based on a comprehensive set of current- and temperature-dependent EL data from blue LEDs with low and high densities of threading dislocations (TDs). First, the effects limiting the applicability of simpler (closed-form and/or one-dimensional) classes of models are addressed, like lateral current crowding, vertical carrier distribution nonuniformity, and interband transition broadening. Then, the major sources of uncertainty affecting state-of-the-art numerical device simulation are reviewed and discussed, including (i) the approximations in the transport description through the multi-quantum-well active region, (ii) the alternative valence band parametrizations proposed to calculate the spontaneous emission rate, (iii) the difficulties in defining the Auger coefficients due to inadequacies in the microscopic quantum well description and the possible presence of extra, non-Auger high-current-density recombination mechanisms and/or Auger-induced leakage. In the case of the present LED structures, the application of three-dimensional numerical-simulation-based analysis to the EL data leads to an explanation of efficiency droop in terms of TD-related and Auger-like nonradiative losses, with a C coefficient in the 10-30 cm6/s range at room temperature, close to the larger theoretical calculations reported so far. However, a study of the combined effects of structural and model uncertainties suggests that the C values thus determined could be overestimated by about an order of magnitude. This preliminary attempt at uncertainty quantification confirms, beyond the present case, the need for an improved description of carrier transport and microscopic radiative and nonradiative recombination mechanisms in device-level LED numerical models.

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Reservoir simulation with the cubic plus (cross-) association equation of state for water, CO2, hydrocarbons, and tracers

NASA Astrophysics Data System (ADS)

Moortgat, Joachim

2018-04-01

This work presents an efficient reservoir simulation framework for multicomponent, multiphase, compressible flow, based on the cubic-plus-association (CPA) equation of state (EOS). CPA is an accurate EOS for mixtures that contain non-polar hydrocarbons, self-associating polar water, and cross-associating molecules like methane, ethane, unsaturated hydrocarbons, CO2, and H2S. While CPA is accurate, its mathematical formulation is highly non-linear, resulting in excessive computational costs that have made the EOS unfeasible for large scale reservoir simulations. This work presents algorithms that overcome these bottlenecks and achieve an efficiency comparable to the much simpler cubic EOS approach. The main applications that require such accurate phase behavior modeling are 1) the study of methane leakage from high-pressure production wells and its potential impact on groundwater resources, 2) modeling of geological CO2 sequestration in brine aquifers when one is interested in more than the CO2 and H2O components, e.g. methane, other light hydrocarbons, and various tracers, and 3) enhanced oil recovery by CO2 injection in reservoirs that have previously been waterflooded or contain connate water. We present numerical examples of all those scenarios, extensive validation of the CPA EOS with experimental data, and analyses of the efficiency of our proposed numerical schemes. The accuracy, efficiency, and robustness of the presented phase split computations pave the way to more widespread adoption of CPA in reservoir simulators.

Development of a High-Order Space-Time Matrix-Free Adjoint Solver

NASA Technical Reports Server (NTRS)

Ceze, Marco A.; Diosady, Laslo T.; Murman, Scott M.

2016-01-01

The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASA's Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods.

Characterization and effectiveness of pay-for-performance in ophthalmology: a systematic review.

PubMed

Herbst, Tim; Emmert, Martin

2017-06-05

To identify, characterize and compare existing pay-for-performance approaches and their impact on the quality of care and efficiency in ophthalmology. A systematic evidence-based review was conducted. English, French and German written literature published between 2000 and 2015 were searched in the following databases: Medline (via PubMed), NCBI web site, Scopus, Web of Knowledge, Econlit and the Cochrane Library. Empirical as well as descriptive articles were included. Controlled clinical trials, meta-analyses, randomized controlled studies as well as observational studies were included as empirical articles. Systematic characterization of identified pay-for-performance approaches (P4P approaches) was conducted according to the "Model for Implementing and Monitoring Incentives for Quality" (MIMIQ). Methodological quality of empirical articles was assessed according to the Critical Appraisal Skills Programme (CASP) checklists. Overall, 13 relevant articles were included. Eleven articles were descriptive and two articles included empirical analyses. Based on these articles, four different pay-for-performance approaches implemented in the United States were identified. With regard to quality and incentive elements, systematic comparison showed numerous differences between P4P approaches. Empirical studies showed isolated cost or quality effects, while a simultaneous examination of these effects was missing. Research results show that experiences with pay-for-performance approaches in ophthalmology are limited. Identified approaches differ with regard to quality and incentive elements restricting comparability. Two empirical studies are insufficient to draw strong conclusions about the effectiveness and efficiency of these approaches.

An efficient and scalable graph modeling approach for capturing information at different levels in next generation sequencing reads

PubMed Central

2013-01-01

Background Next generation sequencing technologies have greatly advanced many research areas of the biomedical sciences through their capability to generate massive amounts of genetic information at unprecedented rates. The advent of next generation sequencing has led to the development of numerous computational tools to analyze and assemble the millions to billions of short sequencing reads produced by these technologies. While these tools filled an important gap, current approaches for storing, processing, and analyzing short read datasets generally have remained simple and lack the complexity needed to efficiently model the produced reads and assemble them correctly. Results Previously, we presented an overlap graph coarsening scheme for modeling read overlap relationships on multiple levels. Most current read assembly and analysis approaches use a single graph or set of clusters to represent the relationships among a read dataset. Instead, we use a series of graphs to represent the reads and their overlap relationships across a spectrum of information granularity. At each information level our algorithm is capable of generating clusters of reads from the reduced graph, forming an integrated graph modeling and clustering approach for read analysis and assembly. Previously we applied our algorithm to simulated and real 454 datasets to assess its ability to efficiently model and cluster next generation sequencing data. In this paper we extend our algorithm to large simulated and real Illumina datasets to demonstrate that our algorithm is practical for both sequencing technologies. Conclusions Our overlap graph theoretic algorithm is able to model next generation sequencing reads at various levels of granularity through the process of graph coarsening. Additionally, our model allows for efficient representation of the read overlap relationships, is scalable for large datasets, and is practical for both Illumina and 454 sequencing technologies. PMID:24564333

Modelling water uptake efficiency of root systems

NASA Astrophysics Data System (ADS)

Leitner, Daniel; Tron, Stefania; Schröder, Natalie; Bodner, Gernot; Javaux, Mathieu; Vanderborght, Jan; Vereecken, Harry; Schnepf, Andrea

2016-04-01

Water uptake is crucial for plant productivity. Trait based breeding for more water efficient crops will enable a sustainable agricultural management under specific pedoclimatic conditions, and can increase drought resistance of plants. Mathematical modelling can be used to find suitable root system traits for better water uptake efficiency defined as amount of water taken up per unit of root biomass. This approach requires large simulation times and large number of simulation runs, since we test different root systems under different pedoclimatic conditions. In this work, we model water movement by the 1-dimensional Richards equation with the soil hydraulic properties described according to the van Genuchten model. Climatic conditions serve as the upper boundary condition. The root system grows during the simulation period and water uptake is calculated via a sink term (after Tron et al. 2015). The goal of this work is to compare different free software tools based on different numerical schemes to solve the model. We compare implementations using DUMUX (based on finite volumes), Hydrus 1D (based on finite elements), and a Matlab implementation of Van Dam, J. C., & Feddes 2000 (based on finite differences). We analyse the methods for accuracy, speed and flexibility. Using this model case study, we can clearly show the impact of various root system traits on water uptake efficiency. Furthermore, we can quantify frequent simplifications that are introduced in the modelling step like considering a static root system instead of a growing one, or considering a sink term based on root density instead of considering the full root hydraulic model (Javaux et al. 2008). References Tron, S., Bodner, G., Laio, F., Ridolfi, L., & Leitner, D. (2015). Can diversity in root architecture explain plant water use efficiency? A modeling study. Ecological modelling, 312, 200-210. Van Dam, J. C., & Feddes, R. A. (2000). Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation. Journal of Hydrology, 233(1), 72-85. Javaux, M., Schröder, T., Vanderborght, J., & Vereecken, H. (2008). Use of a three-dimensional detailed modeling approach for predicting root water uptake. Vadose Zone Journal, 7(3), 1079-1088.

Numerical analysis of unsteady 3D flow of Carreau nanofluid with variable thermal conductivity and heat source/sink

NASA Astrophysics Data System (ADS)

Irfan, M.; Khan, M.; Khan, W. A.

Inspired by modern deeds of nanotechnology and nanoscience and their abundant applications in the field of science and engineering, we establish a mathematical relation for unsteady 3D forced convective flow of Carreau nanofluid over a bidirectional stretched surface. Heat transfer phenomena of Carreau nanofluid is inspected through the variable thermal conductivity and heat generation/absorption impact. Furthermore, this research paper presents a more convincing approach for heat and mass transfer phenomenon of nanoliquid by utilizing new mass flux condition. Practically, zero mass flux condition is more adequate because in this approach we assume nanoparticle amends itself accordingly on the boundaries. Now the features of Buongiorno's relation for Carreau nanofluid can be applied in a more efficient way. An appropriate transformation is vacant to alter the PDEs into ODEs and then tackled numerically by employing bvp4c scheme. The numerous consequence of scheming parameters on the Carreau nanoliquid velocity components, temperature and concentration fields are portrayed graphically and deliberated in detail. The numerical outcomes for local skin friction and the wall temperature gradient for nanoliquid are intended and vacant through tables. The outcomes conveyed here manifest that impact of Brownian motion parameter Nb on the rate of heat transfer for nanoliquids becomes negligible for the recently recommended revised relation. Addationally, for authentication of the present relation, the achieved results are distinguished with earlier research works in specific cases and marvelous agreement has been noted.

Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation

NASA Astrophysics Data System (ADS)

Gasmi, Hatem; Hamdi, Essaïeb; Bouden Romdhane, Nejla

2014-07-01

Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young's modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young's modulus of equivalent medium for wave propagation analysis.

Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set

DOE PAGES

Pemmaraju, C. D.; Vila, F. D.; Kas, J. J.; ...

2018-02-07

The interaction of laser fields with solid-state systems can be modeled efficiently within the velocity-gauge formalism of real-time time dependent density functional theory (RT-TDDFT). In this article, we discuss the implementation of the velocity-gauge RT-TDDFT equations for electron dynamics within a linear combination of atomic orbitals (LCAO) basis set framework. Numerical results obtained from our LCAO implementation, for the electronic response of periodic systems to both weak and intense laser fields, are compared to those obtained from established real-space grid and Full-Potential Linearized Augmented Planewave approaches. As a result, potential applications of the LCAO based scheme in the context ofmore » extreme ultra-violet and soft X-ray spectroscopies involving core-electronic excitations are discussed.« less

Upwind and symmetric shock-capturing schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.

1987-01-01

The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pemmaraju, C. D.; Vila, F. D.; Kas, J. J.

The interaction of laser fields with solid-state systems can be modeled efficiently within the velocity-gauge formalism of real-time time dependent density functional theory (RT-TDDFT). In this article, we discuss the implementation of the velocity-gauge RT-TDDFT equations for electron dynamics within a linear combination of atomic orbitals (LCAO) basis set framework. Numerical results obtained from our LCAO implementation, for the electronic response of periodic systems to both weak and intense laser fields, are compared to those obtained from established real-space grid and Full-Potential Linearized Augmented Planewave approaches. As a result, potential applications of the LCAO based scheme in the context ofmore » extreme ultra-violet and soft X-ray spectroscopies involving core-electronic excitations are discussed.« less

A new potential for the numerical simulations of electrolyte solutions on a hypersphere

NASA Astrophysics Data System (ADS)

Caillol, Jean-Michel

1993-12-01

We propose a new way of performing numerical simulations of the restricted primitive model of electrolytes—and related models—on a hypersphere. In this new approach, the system is viewed as a single component fluid of charged bihard spheres constrained to move at the surface of a four dimensional sphere. A charged bihard sphere is defined as the rigid association of two antipodal charged hard spheres of opposite signs. These objects interact via a simple analytical potential obtained by solving the Poisson-Laplace equation on the hypersphere. This new technique of simulation enables a precise determination of the chemical potential of the charged species in the canonical ensemble by a straightforward application of Widom's insertion method. Comparisons with previous simulations demonstrate the efficiency and the reliability of the method.

The Osher scheme for non-equilibrium reacting flows

NASA Technical Reports Server (NTRS)

Suresh, Ambady; Liou, Meng-Sing

1992-01-01

An extension of the Osher upwind scheme to nonequilibrium reacting flows is presented. Owing to the presence of source terms, the Riemann problem is no longer self-similar and therefore its approximate solution becomes tedious. With simplicity in mind, a linearized approach which avoids an iterative solution is used to define the intermediate states and sonic points. The source terms are treated explicitly. Numerical computations are presented to demonstrate the feasibility, efficiency and accuracy of the proposed method. The test problems include a ZND (Zeldovich-Neumann-Doring) detonation problem for which spurious numerical solutions which propagate at mesh speed have been observed on coarse grids. With the present method, a change of limiter causes the solution to change from the physically correct CJ detonation solution to the spurious weak detonation solution.

Online machining error estimation method of numerical control gear grinding machine tool based on data analysis of internal sensors

NASA Astrophysics Data System (ADS)

Zhao, Fei; Zhang, Chi; Yang, Guilin; Chen, Chinyin

2016-12-01

This paper presents an online estimation method of cutting error by analyzing of internal sensor readings. The internal sensors of numerical control (NC) machine tool are selected to avoid installation problem. The estimation mathematic model of cutting error was proposed to compute the relative position of cutting point and tool center point (TCP) from internal sensor readings based on cutting theory of gear. In order to verify the effectiveness of the proposed model, it was simulated and experimented in gear generating grinding process. The cutting error of gear was estimated and the factors which induce cutting error were analyzed. The simulation and experiments verify that the proposed approach is an efficient way to estimate the cutting error of work-piece during machining process.

Multiple crack detection in 3D using a stable XFEM and global optimization

NASA Astrophysics Data System (ADS)

Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane P. A.

2018-02-01

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

Gain and power optimization of the wireless optical system with multilevel modulation.

PubMed

Liu, Xian

2008-06-01

When used in an outdoor environment to expedite networking access, the performance of wireless optical communication systems is affected by transmitter sway. In the design of such systems, much attention has been paid to developing power-efficient schemes. However, the bandwidth efficiency is also an important issue. One of the most natural approaches to promote bandwidth efficiency is to use multilevel modulation. This leads to multilevel pulse amplitude modulation in the context of intensity modulation and direct detection. We develop a model based on the four-level pulse amplitude modulation. We show that the model can be formulated as an optimization problem in terms of the transmitter power, bit error probability, transmitter gain, and receiver gain. The technical challenges raised by modeling and solving the problem include the analytical and numerical treatments for the improper integrals of the Gaussian functions coupled with the erfc function. The results demonstrate that, at the optimal points, the power penalty paid to the doubled bandwidth efficiency is around 3 dB.

Brush seal numerical simulation: Concepts and advances

NASA Technical Reports Server (NTRS)

Braun, M. J.; Kudriavtsev, V. V.

1994-01-01

The development of the brush seal is considered to be most promising among the advanced type seals that are presently in use in the high speed turbomachinery. The brush is usually mounted on the stationary portions of the engine and has direct contact with the rotating element, in the process of limiting the 'unwanted' leakage flows between stages, or various engine cavities. This type of sealing technology is providing high (in comparison with conventional seals) pressure drops due mainly to the high packing density (around 100 bristles/sq mm), and brush compliance with the rotor motions. In the design of modern aerospace turbomachinery leakage flows between the stages must be minimal, thus contributing to the higher efficiency of the engine. Use of the brush seal instead of the labyrinth seal reduces the leakage flow by one order of magnitude. Brush seals also have been found to enhance dynamic performance, cost less, and are lighter than labyrinth seals. Even though industrial brush seals have been successfully developed through extensive experimentation, there is no comprehensive numerical methodology for the design or prediction of their performance. The existing analytical/numerical approaches are based on bulk flow models and do not allow the investigation of the effects of brush morphology (bristle arrangement), or brushes arrangement (number of brushes, spacing between them), on the pressure drops and flow leakage. An increase in the brush seal efficiency is clearly a complex problem that is closely related to the brush geometry and arrangement, and can be solved most likely only by means of a numerically distributed model.

An efficient numerical solution of the transient storage equations for solute transport in small streams

USGS Publications Warehouse

Runkel, Robert L.; Chapra, Steven C.

1993-01-01

Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.

A characteristics-based method for solving the transport equation and its application to the process of mantle differentiation and continental root growth

NASA Astrophysics Data System (ADS)

de Smet, Jeroen H.; van den Berg, Arie P.; Vlaar, Nico J.; Yuen, David A.

2000-03-01

Purely advective transport of composition is of major importance in the Geosciences, and efficient and accurate solution methods are needed. A characteristics-based method is used to solve the transport equation. We employ a new hybrid interpolation scheme, which allows for the tuning of stability and accuracy through a threshold parameter ɛth. Stability is established by bilinear interpolations, and bicubic splines are used to maintain accuracy. With this scheme, numerical instabilities can be suppressed by allowing numerical diffusion to work in time and locally in space. The scheme can be applied efficiently for preliminary modelling purposes. This can be followed by detailed high-resolution experiments. First, the principal effects of this hybrid interpolation method are illustrated and some tests are presented for numerical solutions of the transport equation. Second, we illustrate that this approach works successfully for a previously developed continental evolution model for the convecting upper mantle. In this model the transport equation contains a source term, which describes the melt production in pressure-released partial melting. In this model, a characteristic phenomenon of small-scale melting diapirs is observed (De Smet et al.1998; De Smet et al. 1999). High-resolution experiments with grid cells down to 700m horizontally and 515m vertically result in highly detailed observations of the diapiric melting phenomenon.

Low-Complexity User Selection for Rate Maximization in MIMO Broadcast Channels with Downlink Beamforming

PubMed Central

Silva, Adão; Gameiro, Atílio

2014-01-01

We present in this work a low-complexity algorithm to solve the sum rate maximization problem in multiuser MIMO broadcast channels with downlink beamforming. Our approach decouples the user selection problem from the resource allocation problem and its main goal is to create a set of quasiorthogonal users. The proposed algorithm exploits physical metrics of the wireless channels that can be easily computed in such a way that a null space projection power can be approximated efficiently. Based on the derived metrics we present a mathematical model that describes the dynamics of the user selection process which renders the user selection problem into an integer linear program. Numerical results show that our approach is highly efficient to form groups of quasiorthogonal users when compared to previously proposed algorithms in the literature. Our user selection algorithm achieves a large portion of the optimum user selection sum rate (90%) for a moderate number of active users. PMID:24574928

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Framework to trade optimality for local processing in large-scale wavefront reconstruction problems.

PubMed

Haber, Aleksandar; Verhaegen, Michel

2016-11-15

We show that the minimum variance wavefront estimation problems permit localized approximate solutions, in the sense that the wavefront value at a point (excluding unobservable modes, such as the piston mode) can be approximated by a linear combination of the wavefront slope measurements in the point's neighborhood. This enables us to efficiently compute a wavefront estimate by performing a single sparse matrix-vector multiplication. Moreover, our results open the possibility for the development of wavefront estimators that can be easily implemented in a decentralized/distributed manner, and in which the estimate optimality can be easily traded for computational efficiency. We numerically validate our approach on Hudgin wavefront sensor geometries, and the results can be easily generalized to Fried geometries.

Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria

NASA Astrophysics Data System (ADS)

Sun, Zhigang; Wang, Changxi; Niu, Xuming; Song, Yingdong

2017-08-01

In this paper, a Reliability-Sensitivity Based Design Optimization (RSBDO) methodology for the design of the ceramic matrix composites (CMCs) components has been proposed. A practical and efficient method for reliability analysis and sensitivity analysis of complex components with arbitrary distribution parameters are investigated by using the perturbation method, the respond surface method, the Edgeworth series and the sensitivity analysis approach. The RSBDO methodology is then established by incorporating sensitivity calculation model into RBDO methodology. Finally, the proposed RSBDO methodology is applied to the design of the CMCs components. By comparing with Monte Carlo simulation, the numerical results demonstrate that the proposed methodology provides an accurate, convergent and computationally efficient method for reliability-analysis based finite element modeling engineering practice.

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train-track interaction and inelastic deformations

NASA Astrophysics Data System (ADS)

Andersson, Robin; Torstensson, Peter T.; Kabo, Elena; Larsson, Fredrik

2015-11-01

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle-track interaction accounting for transient non-Hertzian wheel-rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang-Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.

Genetic engineering of Ganoderma lucidum for the efficient production of ganoderic acids.

PubMed

Xu, Jun-Wei; Zhong, Jian-Jiang

2015-01-01

Ganoderma lucidum is a well-known traditional medicinal mushroom that produces ganoderic acids with numerous interesting bioactivities. Genetic engineering is an efficient approach to improve ganoderic acid biosynthesis. However, reliable genetic transformation methods and appropriate genetic manipulation strategies remain underdeveloped and thus should be enhanced. We previously established a homologous genetic transformation method for G. lucidum; we also applied the established method to perform the deregulated overexpression of a homologous 3-hydroxy-3-methyl-glutaryl coenzyme A reductase gene in G. lucidum. Engineered strains accumulated more ganoderic acids than wild-type strains. In this report, the genetic transformation systems of G. lucidum are described; current trends are also presented to improve ganoderic acid production through the genetic manipulation of G. lucidum.

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

A variational dynamic programming approach to robot-path planning with a distance-safety criterion

NASA Technical Reports Server (NTRS)

Suh, Suk-Hwan; Shin, Kang G.

1988-01-01

An approach to robot-path planning is developed by considering both the traveling distance and the safety of the robot. A computationally-efficient algorithm is developed to find a near-optimal path with a weighted distance-safety criterion by using a variational calculus and dynamic programming (VCDP) method. The algorithm is readily applicable to any factory environment by representing the free workspace as channels. A method for deriving these channels is also proposed. Although it is developed mainly for two-dimensional problems, this method can be easily extended to a class of three-dimensional problems. Numerical examples are presented to demonstrate the utility and power of this method.

Scalable pumping approach for extracting the maximum TEM(00) solar laser power.

PubMed

Liang, Dawei; Almeida, Joana; Vistas, Cláudia R

2014-10-20

A scalable TEM(00) solar laser pumping approach is composed of four pairs of first-stage Fresnel lens-folding mirror collectors, four fused-silica secondary concentrators with light guides of rectangular cross-section for radiation homogenization, four hollow two-dimensional compound parabolic concentrators for further concentration of uniform radiations from the light guides to a 3 mm diameter, 76 mm length Nd:YAG rod within four V-shaped pumping cavities. An asymmetric resonator ensures an efficient large-mode matching between pump light and oscillating laser light. Laser power of 59.1 W TEM(00) is calculated by ZEMAX and LASCAD numerical analysis, revealing 20 times improvement in brightness figure of merit.

Real-Space Analysis of Scanning Tunneling Microscopy Topography Datasets Using Sparse Modeling Approach

NASA Astrophysics Data System (ADS)

Miyama, Masamichi J.; Hukushima, Koji

2018-04-01

A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contain numerous peaks originating from the electron density of surface atoms and/or impurities. The method, based on the relevance vector machine with L1 regularization and k-means clustering, enables separation of the peaks and peak center positioning with accuracy beyond the resolution of the measurement grid. The validity and efficiency of the proposed method are demonstrated using synthetic data in comparison with the conventional least-squares method. An application of the proposed method to experimental data of a metallic oxide thin-film clearly indicates the existence of defects and corresponding local lattice distortions.

Approximation of Nash equilibria and the network community structure detection problem

PubMed Central

2017-01-01

Game theory based methods designed to solve the problem of community structure detection in complex networks have emerged in recent years as an alternative to classical and optimization based approaches. The Mixed Nash Extremal Optimization uses a generative relation for the characterization of Nash equilibria to identify the community structure of a network by converting the problem into a non-cooperative game. This paper proposes a method to enhance this algorithm by reducing the number of payoff function evaluations. Numerical experiments performed on synthetic and real-world networks show that this approach is efficient, with results better or just as good as other state-of-the-art methods. PMID:28467496

Turbine blade profile design method based on Bezier curves

NASA Astrophysics Data System (ADS)

Alexeev, R. A.; Tishchenko, V. A.; Gribin, V. G.; Gavrilov, I. Yu.

2017-11-01

In this paper, the technique of two-dimensional parametric blade profile design is presented. Bezier curves are used to create the profile geometry. The main feature of the proposed method is an adaptive approach of curve fitting to given geometric conditions. Calculation of the profile shape is produced by multi-dimensional minimization method with a number of restrictions imposed on the blade geometry.The proposed method has been used to describe parametric geometry of known blade profile. Then the baseline geometry was modified by varying some parameters of the blade. The numerical calculation of obtained designs has been carried out. The results of calculations have shown the efficiency of chosen approach.