Fast algorithm for bilinear transforms in optics

NASA Astrophysics Data System (ADS)

Ostrovsky, Andrey S.; Martinez-Niconoff, Gabriel C.; Ramos Romero, Obdulio; Cortes, Liliana

2000-10-01

The fast algorithm for calculating the bilinear transform in the optical system is proposed. This algorithm is based on the coherent-mode representation of the cross-spectral density function of the illumination. The algorithm is computationally efficient when the illumination is partially coherent. Numerical examples are studied and compared with the theoretical results.

An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis.

PubMed

Xu, Z N

2014-12-01

In this study, an error analysis is performed to study real water drop images and the corresponding numerically generated water drop profiles for three widely used static contact angle algorithms: the circle- and ellipse-fitting algorithms and the axisymmetric drop shape analysis-profile (ADSA-P) algorithm. The results demonstrate the accuracy of the numerically generated drop profiles based on the Laplace equation. A significant number of water drop profiles with different volumes, contact angles, and noise levels are generated, and the influences of the three factors on the accuracies of the three algorithms are systematically investigated. The results reveal that the above-mentioned three algorithms are complementary. In fact, the circle- and ellipse-fitting algorithms show low errors and are highly resistant to noise for water drops with small/medium volumes and contact angles, while for water drop with large volumes and contact angles just the ADSA-P algorithm can meet accuracy requirement. However, this algorithm introduces significant errors in the case of small volumes and contact angles because of its high sensitivity to noise. The critical water drop volumes of the circle- and ellipse-fitting algorithms corresponding to a certain contact angle error are obtained through a significant amount of computation. To improve the precision of the static contact angle measurement, a more accurate algorithm based on a combination of the three algorithms is proposed. Following a systematic investigation, the algorithm selection rule is described in detail, while maintaining the advantages of the three algorithms and overcoming their deficiencies. In general, static contact angles over the entire hydrophobicity range can be accurately evaluated using the proposed algorithm. The ease of erroneous judgment in static contact angle measurements is avoided. The proposed algorithm is validated by a static contact angle evaluation of real and numerically generated water drop images with different hydrophobicity values and volumes.

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

DOE PAGES

Lehe, Remi; Kirchen, Manuel; Andriyash, Igor A.; ...

2016-02-17

We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of spurious numerical dispersion, in vacuum. This algorithm is benchmarked in several situations that are of interest for laser-plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm - including the zero-order numerical Cherenkov effect.

Effects of illumination on image reconstruction via Fourier ptychography

NASA Astrophysics Data System (ADS)

Cao, Xinrui; Sinzinger, Stefan

2017-12-01

The Fourier ptychographic microscopy (FPM) technique provides high-resolution images by combining a traditional imaging system, e.g. a microscope or a 4f-imaging system, with a multiplexing illumination system, e.g. an LED array and numerical image processing for enhanced image reconstruction. In order to numerically combine images that are captured under varying illumination angles, an iterative phase-retrieval algorithm is often applied. However, in practice, the performance of the FPM algorithm degrades due to the imperfections of the optical system, the image noise caused by the camera, etc. To eliminate the influence of the aberrations of the imaging system, an embedded pupil function recovery (EPRY)-FPM algorithm has been proposed [Opt. Express 22, 4960-4972 (2014)]. In this paper, we study how the performance of FPM and EPRY-FPM algorithms are affected by imperfections of the illumination system using both numerical simulations and experiments. The investigated imperfections include varying and non-uniform intensities, and wavefront aberrations. Our study shows that the aberrations of the illumination system significantly affect the performance of both FPM and EPRY-FPM algorithms. Hence, in practice, aberrations in the illumination system gain significant influence on the resulting image quality.

The generalization ability of online SVM classification based on Markov sampling.

PubMed

Xu, Jie; Yan Tang, Yuan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang

2015-03-01

In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

A Parallel Compact Multi-Dimensional Numerical Algorithm with Aeroacoustics Applications

NASA Technical Reports Server (NTRS)

Povitsky, Alex; Morris, Philip J.

1999-01-01

In this study we propose a novel method to parallelize high-order compact numerical algorithms for the solution of three-dimensional PDEs (Partial Differential Equations) in a space-time domain. For this numerical integration most of the computer time is spent in computation of spatial derivatives at each stage of the Runge-Kutta temporal update. The most efficient direct method to compute spatial derivatives on a serial computer is a version of Gaussian elimination for narrow linear banded systems known as the Thomas algorithm. In a straightforward pipelined implementation of the Thomas algorithm processors are idle due to the forward and backward recurrences of the Thomas algorithm. To utilize processors during this time, we propose to use them for either non-local data independent computations, solving lines in the next spatial direction, or local data-dependent computations by the Runge-Kutta method. To achieve this goal, control of processor communication and computations by a static schedule is adopted. Thus, our parallel code is driven by a communication and computation schedule instead of the usual "creative, programming" approach. The obtained parallelization speed-up of the novel algorithm is about twice as much as that for the standard pipelined algorithm and close to that for the explicit DRP algorithm.

Faster and more accurate transport procedures for HZETRN

NASA Astrophysics Data System (ADS)

Slaba, T. C.; Blattnig, S. R.; Badavi, F. F.

2010-12-01

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle ( A ⩽ 4) and heavy ion ( A > 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete description of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms to 100 g/cm 2 in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100 g/cm 2 of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Faster and more accurate transport procedures for HZETRN

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

Slaba, T.C., E-mail: Tony.C.Slaba@nasa.go; Blattnig, S.R., E-mail: Steve.R.Blattnig@nasa.go; Badavi, F.F., E-mail: Francis.F.Badavi@nasa.go

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle (A {<=} 4) and heavy ion (A > 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete descriptionmore » of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms to 100 g/cm{sup 2} in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100 g/cm{sup 2} of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.« less

An algorithm for the split-feasibility problems with application to the split-equality problem.

PubMed

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

Number Partitioning via Quantum Adiabatic Computation

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadim N.; Toussaint, Udo

2002-01-01

We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.

Trees, bialgebras and intrinsic numerical algorithms

NASA Technical Reports Server (NTRS)

Crouch, Peter; Grossman, Robert; Larson, Richard

1990-01-01

Preliminary work about intrinsic numerical integrators evolving on groups is described. Fix a finite dimensional Lie group G; let g denote its Lie algebra, and let Y(sub 1),...,Y(sub N) denote a basis of g. A class of numerical algorithms is presented that approximate solutions to differential equations evolving on G of the form: dot-x(t) = F(x(t)), x(0) = p is an element of G. The algorithms depend upon constants c(sub i) and c(sub ij), for i = 1,...,k and j is less than i. The algorithms have the property that if the algorithm starts on the group, then it remains on the group. In addition, they also have the property that if G is the abelian group R(N), then the algorithm becomes the classical Runge-Kutta algorithm. The Cayley algebra generated by labeled, ordered trees is used to generate the equations that the coefficients c(sub i) and c(sub ij) must satisfy in order for the algorithm to yield an rth order numerical integrator and to analyze the resulting algorithms.

Reliable numerical computation in an optimal output-feedback design

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

Multiple-source multiple-harmonic active vibration control of variable section cylindrical structures: A numerical study

NASA Astrophysics Data System (ADS)

Liu, Jinxin; Chen, Xuefeng; Gao, Jiawei; Zhang, Xingwu

2016-12-01

Air vehicles, space vehicles and underwater vehicles, the cabins of which can be viewed as variable section cylindrical structures, have multiple rotational vibration sources (e.g., engines, propellers, compressors and motors), making the spectrum of noise multiple-harmonic. The suppression of such noise has been a focus of interests in the field of active vibration control (AVC). In this paper, a multiple-source multiple-harmonic (MSMH) active vibration suppression algorithm with feed-forward structure is proposed based on reference amplitude rectification and conjugate gradient method (CGM). An AVC simulation scheme called finite element model in-loop simulation (FEMILS) is also proposed for rapid algorithm verification. Numerical studies of AVC are conducted on a variable section cylindrical structure based on the proposed MSMH algorithm and FEMILS scheme. It can be seen from the numerical studies that: (1) the proposed MSMH algorithm can individually suppress each component of the multiple-harmonic noise with an unified and improved convergence rate; (2) the FEMILS scheme is convenient and straightforward for multiple-source simulations with an acceptable loop time. Moreover, the simulations have similar procedure to real-life control and can be easily extended to physical model platform.

An improved cylindrical FDTD method and its application to field-tissue interaction study in MRI.

PubMed

Chi, Jieru; Liu, Feng; Xia, Ling; Shao, Tingting; Mason, David G; Crozier, Stuart

2010-01-01

This paper presents a three dimensional finite-difference time-domain (FDTD) scheme in cylindrical coordinates with an improved algorithm for accommodating the numerical singularity associated with the polar axis. The regularization of this singularity problem is entirely based on Ampere's law. The proposed algorithm has been detailed and verified against a problem with a known solution obtained from a commercial electromagnetic simulation package. The numerical scheme is also illustrated by modeling high-frequency RF field-human body interactions in MRI. The results demonstrate the accuracy and capability of the proposed algorithm.

Performance-Based Seismic Design of Steel Frames Utilizing Colliding Bodies Algorithm

PubMed Central

Veladi, H.

2014-01-01

A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm. PMID:25202717

Performance-based seismic design of steel frames utilizing colliding bodies algorithm.

PubMed

Veladi, H

2014-01-01

A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm.

Research on numerical algorithms for large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1982-01-01

Numerical algorithms for large space structures were investigated with particular emphasis on decoupling method for analysis and design. Numerous aspects of the analysis of large systems ranging from the algebraic theory to lambda matrices to identification algorithms were considered. A general treatment of the algebraic theory of lambda matrices is presented and the theory is applied to second order lambda matrices.

A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients

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

Alex, Arne; Delft, Jan von; Kalus, Matthias

2011-02-15

We present an algorithm for the explicit numerical calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients, based on the Gelfand-Tsetlin pattern calculus. Our algorithm is well suited for numerical implementation; we include a computer code in an appendix. Our exposition presumes only familiarity with the representation theory of SU(2).

Recent numerical and algorithmic advances within the volume tracking framework for modeling interfacial flows

DOE PAGES

François, Marianne M.

2015-05-28

A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented. The volume tracking method, also known as the volume-of-fluid method has become an established numerical approach to model and simulate interfacial flows. Its advantage is its strict mass conservation. However, because the interface is not explicitly tracked but captured via the material volume fraction on a fixed mesh, accurate estimation of the interface position, its geometric properties and modeling of interfacial physics in the volume tracking framework remain difficult. Several improvements have been made over the last decade to address these challenges.more » In this study, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted.« less

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Numerical implementation of the S-matrix algorithm for modeling of relief diffraction gratings

NASA Astrophysics Data System (ADS)

Yaremchuk, Iryna; Tamulevičius, Tomas; Fitio, Volodymyr; Gražulevičiūte, Ieva; Bobitski, Yaroslav; Tamulevičius, Sigitas

2013-11-01

A new numerical implementation is developed to calculate the diffraction efficiency of relief diffraction gratings. In the new formulation, vectors containing the expansion coefficients of electric and magnetic fields on boundaries of the grating layer are expressed by additional constants. An S-matrix algorithm has been systematically described in detail and adapted to a simple matrix form. This implementation is suitable for the study of optical characteristics of periodic structures by using modern object-oriented programming languages and different standard mathematical software. The modeling program has been developed on the basis of this numerical implementation and tested by comparison with other commercially available programs and experimental data. Numerical examples are given to show the usefulness of the new implementation.

Probing numerical Laplace inversion methods for two and three-site molecular exchange between interconnected pore structures.

PubMed

Silletta, Emilia V; Franzoni, María B; Monti, Gustavo A; Acosta, Rodolfo H

2018-01-01

Two-dimension (2D) Nuclear Magnetic Resonance relaxometry experiments are a powerful tool extensively used to probe the interaction among different pore structures, mostly in inorganic systems. The analysis of the collected experimental data generally consists of a 2D numerical inversion of time-domain data where T 2 -T 2 maps are generated. Through the years, different algorithms for the numerical inversion have been proposed. In this paper, two different algorithms for numerical inversion are tested and compared under different conditions of exchange dynamics; the method based on Butler-Reeds-Dawson (BRD) algorithm and the fast-iterative shrinkage-thresholding algorithm (FISTA) method. By constructing a theoretical model, the algorithms were tested for a two- and three-site porous media, varying the exchange rates parameters, the pore sizes and the signal to noise ratio. In order to test the methods under realistic experimental conditions, a challenging organic system was chosen. The molecular exchange rates of water confined in hierarchical porous polymeric networks were obtained, for a two- and three-site porous media. Data processed with the BRD method was found to be accurate only under certain conditions of the exchange parameters, while data processed with the FISTA method is precise for all the studied parameters, except when SNR conditions are extreme. Copyright © 2017 Elsevier Inc. All rights reserved.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

Inverse Problems in Geodynamics Using Machine Learning Algorithms

NASA Astrophysics Data System (ADS)

Shahnas, M. H.; Yuen, D. A.; Pysklywec, R. N.

2018-01-01

During the past few decades numerical studies have been widely employed to explore the style of circulation and mixing in the mantle of Earth and other planets. However, in geodynamical studies there are many properties from mineral physics, geochemistry, and petrology in these numerical models. Machine learning, as a computational statistic-related technique and a subfield of artificial intelligence, has rapidly emerged recently in many fields of sciences and engineering. We focus here on the application of supervised machine learning (SML) algorithms in predictions of mantle flow processes. Specifically, we emphasize on estimating mantle properties by employing machine learning techniques in solving an inverse problem. Using snapshots of numerical convection models as training samples, we enable machine learning models to determine the magnitude of the spin transition-induced density anomalies that can cause flow stagnation at midmantle depths. Employing support vector machine algorithms, we show that SML techniques can successfully predict the magnitude of mantle density anomalies and can also be used in characterizing mantle flow patterns. The technique can be extended to more complex geodynamic problems in mantle dynamics by employing deep learning algorithms for putting constraints on properties such as viscosity, elastic parameters, and the nature of thermal and chemical anomalies.

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Verification of Numerical Programs: From Real Numbers to Floating Point Numbers

NASA Technical Reports Server (NTRS)

Goodloe, Alwyn E.; Munoz, Cesar; Kirchner, Florent; Correnson, Loiec

2013-01-01

Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

A parallel time integrator for noisy nonlinear oscillatory systems

NASA Astrophysics Data System (ADS)

Subber, Waad; Sarkar, Abhijit

2018-06-01

In this paper, we adapt a parallel time integration scheme to track the trajectories of noisy non-linear dynamical systems. Specifically, we formulate a parallel algorithm to generate the sample path of nonlinear oscillator defined by stochastic differential equations (SDEs) using the so-called parareal method for ordinary differential equations (ODEs). The presence of Wiener process in SDEs causes difficulties in the direct application of any numerical integration techniques of ODEs including the parareal algorithm. The parallel implementation of the algorithm involves two SDEs solvers, namely a fine-level scheme to integrate the system in parallel and a coarse-level scheme to generate and correct the required initial conditions to start the fine-level integrators. For the numerical illustration, a randomly excited Duffing oscillator is investigated in order to study the performance of the stochastic parallel algorithm with respect to a range of system parameters. The distributed implementation of the algorithm exploits Massage Passing Interface (MPI).

Real Time Optima Tracking Using Harvesting Models of the Genetic Algorithm

NASA Technical Reports Server (NTRS)

Baskaran, Subbiah; Noever, D.

1999-01-01

Tracking optima in real time propulsion control, particularly for non-stationary optimization problems is a challenging task. Several approaches have been put forward for such a study including the numerical method called the genetic algorithm. In brief, this approach is built upon Darwinian-style competition between numerical alternatives displayed in the form of binary strings, or by analogy to 'pseudogenes'. Breeding of improved solution is an often cited parallel to natural selection in.evolutionary or soft computing. In this report we present our results of applying a novel model of a genetic algorithm for tracking optima in propulsion engineering and in real time control. We specialize the algorithm to mission profiling and planning optimizations, both to select reduced propulsion needs through trajectory planning and to explore time or fuel conservation strategies.

Direct variational data assimilation algorithm for atmospheric chemistry data with transport and transformation model

NASA Astrophysics Data System (ADS)

Penenko, Alexey; Penenko, Vladimir; Nuterman, Roman; Baklanov, Alexander; Mahura, Alexander

2015-11-01

Atmospheric chemistry dynamics is studied with convection-diffusion-reaction model. The numerical Data Assimilation algorithm presented is based on the additive-averaged splitting schemes. It carries out ''fine-grained'' variational data assimilation on the separate splitting stages with respect to spatial dimensions and processes i.e. the same measurement data is assimilated to different parts of the split model. This design has efficient implementation due to the direct data assimilation algorithms of the transport process along coordinate lines. Results of numerical experiments with chemical data assimilation algorithm of in situ concentration measurements on real data scenario have been presented. In order to construct the scenario, meteorological data has been taken from EnviroHIRLAM model output, initial conditions from MOZART model output and measurements from Airbase database.

Splitting algorithm for numerical simulation of Li-ion battery electrochemical processes

NASA Astrophysics Data System (ADS)

Iliev, Oleg; Nikiforova, Marina A.; Semenov, Yuri V.; Zakharov, Petr E.

2017-11-01

In this paper we present a splitting algorithm for a numerical simulation of Li-ion battery electrochemical processes. Liion battery consists of three domains: anode, cathode and electrolyte. Mathematical model of electrochemical processes is described on a microscopic scale, and contains nonlinear equations for concentration and potential in each domain. On the interface of electrodes and electrolyte there are the Lithium ions intercalation and deintercalation processes, which are described by Butler-Volmer nonlinear equation. To approximate in spatial coordinates we use finite element methods with discontinues Galerkin elements. To simplify numerical simulations we develop the splitting algorithm, which split the original problem into three independent subproblems. We investigate the numerical convergence of the algorithm on 2D model problem.

Advanced rotorcraft control using parameter optimization

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.

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

Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio

2011-12-01

This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

NASA Astrophysics Data System (ADS)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational

DOE PAGES

Ellison, C. L.; Burby, J. W.; Qin, H.

2015-11-01

One popular technique for the numerical time advance of charged particles interacting with electric and magnetic fields according to the Lorentz force law [1], [2], [3] and [4] is the Boris algorithm. Its popularity stems from simple implementation, rapid iteration, and excellent long-term numerical fidelity [1] and [5]. Excellent long-term behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6]. Moreover, without conserved quantities to constrain the numerical dynamics, algorithms typically dissipate or accumulate important observables such as energy and momentum over long periods of simulated time [6]. Identification of themore » conservative properties of an algorithm is important for establishing rigorous expectations on the long-term behavior; energy-preserving, symplectic, and volume-preserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].« less

Parallel Algorithm Solves Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

A combination chaotic system and application in color image encryption

NASA Astrophysics Data System (ADS)

Parvaz, R.; Zarebnia, M.

2018-05-01

In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

NASA Technical Reports Server (NTRS)

Liandrat, J.; Tchamitchian, PH.

1990-01-01

The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.

Model of a Frame of Dynamic Routing and Its Equilibrium

NASA Astrophysics Data System (ADS)

Zhang, Shu; Yuan, Yuan; Xu, Jian

Dynamic routing algorithm based on the shortest path principle is criticized due to the oscillation induced by such routing scheme. In the present work, we propose the model of TCP/RED algorithm by a new frame of dynamic routing, based on the measurement of occupation ratio of router buffer for different links, which only requires the information of the queue size at the buffer of the router, to stabilize the system. We classify several types of equilibrium and employ the numerical method to study the stability of the steady state. Our numerical results show that the careful selection of the parameters characterizing the dynamic routing algorithm can stabilize the system in some cases.

Theoretical study on electronic excitation spectra: A matrix form of numerical algorithm for spectral shift

NASA Astrophysics Data System (ADS)

Ming, Mei-Jun; Xu, Long-Kun; Wang, Fan; Bi, Ting-Jun; Li, Xiang-Yuan

2017-07-01

In this work, a matrix form of numerical algorithm for spectral shift is presented based on the novel nonequilibrium solvation model that is established by introducing the constrained equilibrium manipulation. This form is convenient for the development of codes for numerical solution. By means of the integral equation formulation polarizable continuum model (IEF-PCM), a subroutine has been implemented to compute spectral shift numerically. Here, the spectral shifts of absorption spectra for several popular chromophores, N,N-diethyl-p-nitroaniline (DEPNA), methylenecyclopropene (MCP), acrolein (ACL) and p-nitroaniline (PNA) were investigated in different solvents with various polarities. The computed spectral shifts can explain the available experimental findings reasonably. Discussions were made on the contributions of solute geometry distortion, electrostatic polarization and other non-electrostatic interactions to spectral shift.

Algorithms and Libraries

NASA Technical Reports Server (NTRS)

Dongarra, Jack

1998-01-01

This exploratory study initiated our inquiry into algorithms and applications that would benefit by latency tolerant approach to algorithm building, including the construction of new algorithms where appropriate. In a multithreaded execution, when a processor reaches a point where remote memory access is necessary, the request is sent out on the network and a context--switch occurs to a new thread of computation. This effectively masks a long and unpredictable latency due to remote loads, thereby providing tolerance to remote access latency. We began to develop standards to profile various algorithm and application parameters, such as the degree of parallelism, granularity, precision, instruction set mix, interprocessor communication, latency etc. These tools will continue to develop and evolve as the Information Power Grid environment matures. To provide a richer context for this research, the project also focused on issues of fault-tolerance and computation migration of numerical algorithms and software. During the initial phase we tried to increase our understanding of the bottlenecks in single processor performance. Our work began by developing an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. Based on the results we achieved in this study we are planning to study other architectures of interest, including development of cost models, and developing code generators appropriate to these architectures.

Numerical model updating technique for structures using firefly algorithm

NASA Astrophysics Data System (ADS)

Sai Kubair, K.; Mohan, S. C.

2018-03-01

Numerical model updating is a technique used for updating the existing experimental models for any structures related to civil, mechanical, automobiles, marine, aerospace engineering, etc. The basic concept behind this technique is updating the numerical models to closely match with experimental data obtained from real or prototype test structures. The present work involves the development of numerical model using MATLAB as a computational tool and with mathematical equations that define the experimental model. Firefly algorithm is used as an optimization tool in this study. In this updating process a response parameter of the structure has to be chosen, which helps to correlate the numerical model developed with the experimental results obtained. The variables for the updating can be either material or geometrical properties of the model or both. In this study, to verify the proposed technique, a cantilever beam is analyzed for its tip deflection and a space frame has been analyzed for its natural frequencies. Both the models are updated with their respective response values obtained from experimental results. The numerical results after updating show that there is a close relationship that can be brought between the experimental and the numerical models.

Multi-objective optimal design of sandwich panels using a genetic algorithm

NASA Astrophysics Data System (ADS)

Xu, Xiaomei; Jiang, Yiping; Pueh Lee, Heow

2017-10-01

In this study, an optimization problem concerning sandwich panels is investigated by simultaneously considering the two objectives of minimizing the panel mass and maximizing the sound insulation performance. First of all, the acoustic model of sandwich panels is discussed, which provides a foundation to model the acoustic objective function. Then the optimization problem is formulated as a bi-objective programming model, and a solution algorithm based on the non-dominated sorting genetic algorithm II (NSGA-II) is provided to solve the proposed model. Finally, taking an example of a sandwich panel that is expected to be used as an automotive roof panel, numerical experiments are carried out to verify the effectiveness of the proposed model and solution algorithm. Numerical results demonstrate in detail how the core material, geometric constraints and mechanical constraints impact the optimal designs of sandwich panels.

Numerical simulation of steady supersonic flow. [spatial marching

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Steger, J. L.

1981-01-01

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Modifying a numerical algorithm for solving the matrix equation X + AX T B = C

NASA Astrophysics Data System (ADS)

Vorontsov, Yu. O.

2013-06-01

Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.

Numerical stability of the error diffusion concept

NASA Astrophysics Data System (ADS)

Weissbach, Severin; Wyrowski, Frank

1992-10-01

The error diffusion algorithm is an easy implementable mean to handle nonlinearities in signal processing, e.g. in picture binarization and coding of diffractive elements. The numerical stability of the algorithm depends on the choice of the diffusion weights. A criterion for the stability of the algorithm is presented and evaluated for some examples.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

Algorithms For Integrating Nonlinear Differential Equations

NASA Technical Reports Server (NTRS)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

A study of metaheuristic algorithms for high dimensional feature selection on microarray data

NASA Astrophysics Data System (ADS)

Dankolo, Muhammad Nasiru; Radzi, Nor Haizan Mohamed; Sallehuddin, Roselina; Mustaffa, Noorfa Haszlinna

2017-11-01

Microarray systems enable experts to examine gene profile at molecular level using machine learning algorithms. It increases the potentials of classification and diagnosis of many diseases at gene expression level. Though, numerous difficulties may affect the efficiency of machine learning algorithms which includes vast number of genes features comprised in the original data. Many of these features may be unrelated to the intended analysis. Therefore, feature selection is necessary to be performed in the data pre-processing. Many feature selection algorithms are developed and applied on microarray which including the metaheuristic optimization algorithms. This paper discusses the application of the metaheuristics algorithms for feature selection in microarray dataset. This study reveals that, the algorithms have yield an interesting result with limited resources thereby saving computational expenses of machine learning algorithms.

e-DMDAV: A new privacy preserving algorithm for wearable enterprise information systems

NASA Astrophysics Data System (ADS)

Zhang, Zhenjiang; Wang, Xiaoni; Uden, Lorna; Zhang, Peng; Zhao, Yingsi

2018-04-01

Wearable devices have been widely used in many fields to improve the quality of people's lives. More and more data on individuals and businesses are collected by statistical organizations though those devices. Almost all of this data holds confidential information. Statistical Disclosure Control (SDC) seeks to protect statistical data in such a way that it can be released without giving away confidential information that can be linked to specific individuals or entities. The MDAV (Maximum Distance to Average Vector) algorithm is an efficient micro-aggregation algorithm belonging to SDC. However, the MDAV algorithm cannot survive homogeneity and background knowledge attacks because it was designed for static numerical data. This paper proposes a systematic dynamic-updating anonymity algorithm based on MDAV called the e-DMDAV algorithm. This algorithm introduces a new parameter and a table to ensure that the k records in one cluster with the range of the distinct values in each cluster is no less than e for numerical and non-numerical datasets. This new algorithm has been evaluated and compared with the MDAV algorithm. The simulation results show that the new algorithm outperforms MDAV in terms of minimizing distortion and disclosure risk with a similar computational cost.

The development of efficient numerical time-domain modeling methods for geophysical wave propagation

NASA Astrophysics Data System (ADS)

Zhu, Lieyuan

This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The numerical AVO study reveals that the normalized residual polarization (NRP) variation with offset does not respond to subsurface NAPL existence when the offset is close to or larger than its critical value (which corresponds to critical incident angle) because the air and head waves dominate the recorded wave field and severely interfere with reflected waves in the TEz wave field. Thus it can be concluded that the NRP AVO/GPR method is invalid when source-receiver angle offset is close to or greater than its critical value due to incomplete and severely distorted reflection information. In other words, AVO is not a promising technique for detection of the subsurface NAPL, as claimed by some researchers. In addition, the robustness of the newly developed numerical algorithms is also verified by the AVO study for randomly-arranged layered media. Meanwhile, this case study also demonstrates again that the full-wave numerical modeling algorithms are superior to ray tracing method. The second case study focuses on the effect of the existence of a near-surface fault on the vertically incident P- and S- plane waves. The modeling results show that both P-wave vertical incidence and S-wave vertical incidence cases are qualified fault indicators. For the plane S-wave vertical incidence case, the horizontal location of the upper tip of the fault (the footwall side) can be identified without much effort, because all the recorded parameters on the surface including the maximum velocities and the maximum accelerations, and even their ratios H/V, have shown dramatic changes when crossing the upper tip of the fault. The centers of the transition zone of the all the curves of parameters are almost directly above the fault tip (roughly the horizontal center of the model). Compared with the case of the vertically incident P-wave source, it has been found that the S-wave vertical source is a better indicator for fault location, because the horizontal location of the tip of that fault cannot be clearly identified with the ratio of the horizontal to vertical velocity for the P-wave incident case.

Computer simulation of solutions of polyharmonic equations in plane domain

NASA Astrophysics Data System (ADS)

Kazakova, A. O.

2018-05-01

A systematic study of plane problems of the theory of polyharmonic functions is presented. A method of reducing boundary problems for polyharmonic functions to the system of integral equations on the boundary of the domain is given and a numerical algorithm for simulation of solutions of this system is suggested. Particular attention is paid to the numerical solution of the main tasks when the values of the function and its derivatives are given. Test examples are considered that confirm the effectiveness and accuracy of the suggested algorithm.

Optimal placement of excitations and sensors for verification of large dynamical systems

NASA Technical Reports Server (NTRS)

Salama, M.; Rose, T.; Garba, J.

1987-01-01

The computationally difficult problem of the optimal placement of excitations and sensors to maximize the observed measurements is studied within the framework of combinatorial optimization, and is solved numerically using a variation of the simulated annealing heuristic algorithm. Results of numerical experiments including a square plate and a 960 degrees-of-freedom Control of Flexible Structure (COFS) truss structure, are presented. Though the algorithm produces suboptimal solutions, its generality and simplicity allow the treatment of complex dynamical systems which would otherwise be difficult to handle.

A case study of view-factor rectification procedures for diffuse-gray radiation enclosure computations

NASA Technical Reports Server (NTRS)

Taylor, Robert P.; Luck, Rogelio

1995-01-01

The view factors which are used in diffuse-gray radiation enclosure calculations are often computed by approximate numerical integrations. These approximately calculated view factors will usually not satisfy the important physical constraints of reciprocity and closure. In this paper several view-factor rectification algorithms are reviewed and a rectification algorithm based on a least-squares numerical filtering scheme is proposed with both weighted and unweighted classes. A Monte-Carlo investigation is undertaken to study the propagation of view-factor and surface-area uncertainties into the heat transfer results of the diffuse-gray enclosure calculations. It is found that the weighted least-squares algorithm is vastly superior to the other rectification schemes for the reduction of the heat-flux sensitivities to view-factor uncertainties. In a sample problem, which has proven to be very sensitive to uncertainties in view factor, the heat transfer calculations with weighted least-squares rectified view factors are very good with an original view-factor matrix computed to only one-digit accuracy. All of the algorithms had roughly equivalent effects on the reduction in sensitivity to area uncertainty in this case study.

The NLO jet vertex in the small-cone approximation for kt and cone algorithms

NASA Astrophysics Data System (ADS)

Colferai, D.; Niccoli, A.

2015-04-01

We determine the jet vertex for Mueller-Navelet jets and forward jets in the small-cone approximation for two particular choices of jet algoritms: the kt algorithm and the cone algorithm. These choices are motivated by the extensive use of such algorithms in the phenomenology of jets. The differences with the original calculations of the small-cone jet vertex by Ivanov and Papa, which is found to be equivalent to a formerly algorithm proposed by Furman, are shown at both analytic and numerical level, and turn out to be sizeable. A detailed numerical study of the error introduced by the small-cone approximation is also presented, for various observables of phenomenological interest. For values of the jet "radius" R = 0 .5, the use of the small-cone approximation amounts to an error of about 5% at the level of cross section, while it reduces to less than 2% for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets.

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

UDU/T/ covariance factorization for Kalman filtering

NASA Technical Reports Server (NTRS)

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

1980-01-01

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Numerical method for computing Maass cusp forms on triply punctured two-sphere

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

Chan, K. T.; Kamari, H. M.; Zainuddin, H.

2014-03-05

A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triplymore » punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm.« less

Second-order Poisson Nernst-Planck solver for ion channel transport

PubMed Central

Zheng, Qiong; Chen, Duan; Wei, Guo-Wei

2010-01-01

The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements. PMID:21552336

Adaptive Grid Refinement for Atmospheric Boundary Layer Simulations

NASA Astrophysics Data System (ADS)

van Hooft, Antoon; van Heerwaarden, Chiel; Popinet, Stephane; van der linden, Steven; de Roode, Stephan; van de Wiel, Bas

2017-04-01

We validate and benchmark an adaptive mesh refinement (AMR) algorithm for numerical simulations of the atmospheric boundary layer (ABL). The AMR technique aims to distribute the computational resources efficiently over a domain by refining and coarsening the numerical grid locally and in time. This can be beneficial for studying cases in which length scales vary significantly in time and space. We present the results for a case describing the growth and decay of a convective boundary layer. The AMR results are benchmarked against two runs using a fixed, fine meshed grid. First, with the same numerical formulation as the AMR-code and second, with a code dedicated to ABL studies. Compared to the fixed and isotropic grid runs, the AMR algorithm can coarsen and refine the grid such that accurate results are obtained whilst using only a fraction of the grid cells. Performance wise, the AMR run was cheaper than the fixed and isotropic grid run with similar numerical formulations. However, for this specific case, the dedicated code outperformed both aforementioned runs.

On recent advances and future research directions for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Soliman, M. O.; Manhardt, P. D.

1986-01-01

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Numerical Algorithms for Acoustic Integrals - The Devil is in the Details

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1996-01-01

The accurate prediction of the aeroacoustic field generated by aerospace vehicles or nonaerospace machinery is necessary for designers to control and reduce source noise. Powerful computational aeroacoustic methods, based on various acoustic analogies (primarily the Lighthill acoustic analogy) and Kirchhoff methods, have been developed for prediction of noise from complicated sources, such as rotating blades. Both methods ultimately predict the noise through a numerical evaluation of an integral formulation. In this paper, we consider three generic acoustic formulations and several numerical algorithms that have been used to compute the solutions to these formulations. Algorithms for retarded-time formulations are the most efficient and robust, but they are difficult to implement for supersonic-source motion. Collapsing-sphere and emission-surface formulations are good alternatives when supersonic-source motion is present, but the numerical implementations of these formulations are more computationally demanding. New algorithms - which utilize solution adaptation to provide a specified error level - are needed.

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

NASA Astrophysics Data System (ADS)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Design and Implementation of Hybrid CORDIC Algorithm Based on Phase Rotation Estimation for NCO

PubMed Central

Zhang, Chaozhu; Han, Jinan; Li, Ke

2014-01-01

The numerical controlled oscillator has wide application in radar, digital receiver, and software radio system. Firstly, this paper introduces the traditional CORDIC algorithm. Then in order to improve computing speed and save resources, this paper proposes a kind of hybrid CORDIC algorithm based on phase rotation estimation applied in numerical controlled oscillator (NCO). Through estimating the direction of part phase rotation, the algorithm reduces part phase rotation and add-subtract unit, so that it decreases delay. Furthermore, the paper simulates and implements the numerical controlled oscillator by Quartus II software and Modelsim software. Finally, simulation results indicate that the improvement over traditional CORDIC algorithm is achieved in terms of ease of computation, resource utilization, and computing speed/delay while maintaining the precision. It is suitable for high speed and precision digital modulation and demodulation. PMID:25110750

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

NASA Astrophysics Data System (ADS)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Application of the stochastic parallel gradient descent algorithm for numerical simulation and analysis of the coherent summation of radiation from fibre amplifiers

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Li, Xiao; Chen, Zilum; Xu, Xiaojun; Liu, Zejin

2009-10-01

Coherent summation of fibre laser beams, which can be scaled to a relatively large number of elements, is simulated by using the stochastic parallel gradient descent (SPGD) algorithm. The applicability of this algorithm for coherent summation is analysed and its optimisaton parameters and bandwidth limitations are studied.

Flood predictions using the parallel version of distributed numerical physical rainfall-runoff model TOPKAPI

NASA Astrophysics Data System (ADS)

Boyko, Oleksiy; Zheleznyak, Mark

2015-04-01

The original numerical code TOPKAPI-IMMS of the distributed rainfall-runoff model TOPKAPI ( Todini et al, 1996-2014) is developed and implemented in Ukraine. The parallel version of the code has been developed recently to be used on multiprocessors systems - multicore/processors PC and clusters. Algorithm is based on binary-tree decomposition of the watershed for the balancing of the amount of computation for all processors/cores. Message passing interface (MPI) protocol is used as a parallel computing framework. The numerical efficiency of the parallelization algorithms is demonstrated for the case studies for the flood predictions of the mountain watersheds of the Ukrainian Carpathian regions. The modeling results is compared with the predictions based on the lumped parameters models.

Comparing performance of centerline algorithms for quantitative assessment of brain vascular anatomy.

PubMed

Diedrich, Karl T; Roberts, John A; Schmidt, Richard H; Parker, Dennis L

2012-12-01

Attributes like length, diameter, and tortuosity of tubular anatomical structures such as blood vessels in medical images can be measured from centerlines. This study develops methods for comparing the accuracy and stability of centerline algorithms. Sample data included numeric phantoms simulating arteries and clinical human brain artery images. Centerlines were calculated from segmented phantoms and arteries with shortest paths centerline algorithms developed with different cost functions. The cost functions were the inverse modified distance from edge (MDFE(i) ), the center of mass (COM), the binary-thinned (BT)-MDFE(i) , and the BT-COM. The accuracy of the centerline algorithms were measured by the root mean square error from known centerlines of phantoms. The stability of the centerlines was measured by starting the centerline tree from different points and measuring the differences between trees. The accuracy and stability of the centerlines were visualized by overlaying centerlines on vasculature images. The BT-COM cost function centerline was the most stable in numeric phantoms and human brain arteries. The MDFE(i) -based centerline was most accurate in the numeric phantoms. The COM-based centerline correctly handled the "kissing" artery in 16 of 16 arteries in eight subjects whereas the BT-COM was correct in 10 of 16 and MDFE(i) was correct in 6 of 16. The COM-based centerline algorithm was selected for future use based on the ability to handle arteries where the initial binary vessels segmentation exhibits closed loops. The selected COM centerline was found to measure numerical phantoms to within 2% of the known length. Copyright © 2012 Wiley Periodicals, Inc.

Numerical study of time domain analogy applied to noise prediction from rotating blades

NASA Astrophysics Data System (ADS)

Fedala, D.; Kouidri, S.; Rey, R.

2009-04-01

Aeroacoustic formulations in time domain are frequently used to model the aerodynamic sound of airfoils, the time data being more accessible. The formulation 1A developed by Farassat, an integral solution of the Ffowcs Williams and Hawkings equation, holds great interest because of its ability to handle surfaces in arbitrary motion. The aim of this work is to study the numerical sensitivity of this model to specified parameters used in the calculation. The numerical algorithms, spatial and time discretizations, and approximations used for far-field acoustic simulation are presented. An approach of quantifying of the numerical errors resulting from implementation of formulation 1A is carried out based on Isom's and Tam's test cases. A helicopter blade airfoil, as defined by Farassat to investigate Isom's case, is used in this work. According to Isom, the acoustic response of a dipole source with a constant aerodynamic load, ρ0c02, is equal to the thickness noise contribution. Discrepancies are observed when the two contributions are computed numerically. In this work, variations of these errors, which depend on the temporal resolution, Mach number, source-observer distance, and interpolation algorithm type, are investigated. The results show that the spline interpolating algorithm gives the minimum error. The analysis is then extended to Tam's test case. Tam's test case has the advantage of providing an analytical solution for the first harmonic of the noise produced by a specific force distribution.

An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids

NASA Astrophysics Data System (ADS)

Xu, Xiaoyang; Deng, Xiao-Long

2016-04-01

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field.

Feasibility of using the Massively Parallel Processor for large eddy simulations and other Computational Fluid Dynamics applications

NASA Technical Reports Server (NTRS)

Bruno, John

1984-01-01

The results of an investigation into the feasibility of using the MPP for direct and large eddy simulations of the Navier-Stokes equations is presented. A major part of this study was devoted to the implementation of two of the standard numerical algorithms for CFD. These implementations were not run on the Massively Parallel Processor (MPP) since the machine delivered to NASA Goddard does not have sufficient capacity. Instead, a detailed implementation plan was designed and from these were derived estimates of the time and space requirements of the algorithms on a suitably configured MPP. In addition, other issues related to the practical implementation of these algorithms on an MPP-like architecture were considered; namely, adaptive grid generation, zonal boundary conditions, the table lookup problem, and the software interface. Performance estimates show that the architectural components of the MPP, the Staging Memory and the Array Unit, appear to be well suited to the numerical algorithms of CFD. This combined with the prospect of building a faster and larger MMP-like machine holds the promise of achieving sustained gigaflop rates that are required for the numerical simulations in CFD.

Research on numerical algorithms for large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1981-01-01

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

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.

Physiology driven adaptivity for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2007-09-01

Previous work [Whiteley, J. P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006] derived a stable, semi-implicit numerical scheme for solving the bidomain equations. This scheme allows the timestep used when solving the bidomain equations numerically to be chosen by accuracy considerations rather than stability considerations. In this study we modify this scheme to allow an adaptive numerical solution in both time and space. The spatial mesh size is determined by the gradient of the transmembrane and extracellular potentials while the timestep is determined by the values of: (i) the fast sodium current; and (ii) the calcium release from junctional sarcoplasmic reticulum to myoplasm current. For two-dimensional simulations presented here, combining the numerical algorithm in the paper cited above with the adaptive algorithm presented here leads to an increase in computational efficiency by a factor of around 250 over previous work, together with significantly less computational memory being required. The speedup for three-dimensional simulations is likely to be more impressive.

Numerical Algorithms Based on Biorthogonal Wavelets

NASA Technical Reports Server (NTRS)

Ponenti, Pj.; Liandrat, J.

1996-01-01

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Algorithms for computing the geopotential using a simple density layer

NASA Technical Reports Server (NTRS)

Morrison, F.

1976-01-01

Several algorithms have been developed for computing the potential and attraction of a simple density layer. These are numerical cubature, Taylor series, and a mixed analytic and numerical integration using a singularity-matching technique. A computer program has been written to combine these techniques for computing the disturbing acceleration on an artificial earth satellite. A total of 1640 equal-area, constant surface density blocks on an oblate spheroid are used. The singularity-matching algorithm is used in the subsatellite region, Taylor series in the surrounding zone, and numerical cubature on the rest of the earth.

Multidisciplinary Optimization of a Transport Aircraft Wing using Particle Swarm Optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Venter, Gerhard

2002-01-01

The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The paper's new contributions to multidisciplinary optimization is the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations as to the utility of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and truly discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented here. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization as well as the numerical noise and truly discrete variables present in the current example problem.

An approach of traffic signal control based on NLRSQP algorithm

NASA Astrophysics Data System (ADS)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

Self-learning Monte Carlo method and cumulative update in fermion systems

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

Liu, Junwei; Shen, Huitao; Qi, Yang

2017-06-07

In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far lessmore » than the conventional algorithm with local updates.« less

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

An intercomparison study of TSM, SEBS, and SEBAL using high-resolution imagery and lysimetric data

USDA-ARS?s Scientific Manuscript database

Over the past three decades, numerous remote sensing based ET mapping algorithms were developed. These algorithms provided a robust, economical, and efficient tool for ET estimations at field and regional scales. The Two Source Model (TSM), Surface Energy Balance System (SEBS), and Surface Energy Ba...

Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers.

PubMed

Gong, Mali; Yuan, Yanyang; Li, Chen; Yan, Ping; Zhang, Haitao; Liao, Suying

2007-03-19

A model based on propagation-rate equations with consideration of transverse gain distribution is built up to describe the transverse mode competition in strongly pumped multimode fiber lasers and amplifiers. An approximate practical numerical algorithm by multilayer method is presented. Based on the model and the numerical algorithm, the behaviors of multitransverse mode competition are demonstrated and individual transverse modes power distributions of output are simulated numerically for both fiber lasers and amplifiers under various conditions.

Nonlinear Computational Aeroelasticity: Formulations and Solution Algorithms

DTIC Science & Technology

2003-03-01

problem is proposed. Fluid-structure coupling algorithms are then discussed with some emphasis on distributed computing strategies. Numerical results...the structure and the exchange of structure motion to the fluid. The computational fluid dynamics code PFES is our finite element code for the numerical ...unstructured meshes). It was numerically demonstrated [1-3] that EBS can be less diffusive than SUPG [4-6] and the standard Finite Volume schemes

Numerical Analysis of Ginzburg-Landau Models for Superconductivity.

NASA Astrophysics Data System (ADS)

Coskun, Erhan

Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.

A numerically-stable algorithm for calibrating single six-ports for national microwave reflectometry

NASA Astrophysics Data System (ADS)

Hodgetts, T. E.

1990-11-01

A full description and analysis of the numerically stable algorithm currently used for calibrating single six ports or multi states for national microwave reflectometry, employing as standards four one port devices having known voltage reflection coefficients, is given.

Automatic extraction of numeric strings in unconstrained handwritten document images

NASA Astrophysics Data System (ADS)

Haji, M. Mehdi; Bui, Tien D.; Suen, Ching Y.

2011-01-01

Numeric strings such as identification numbers carry vital pieces of information in documents. In this paper, we present a novel algorithm for automatic extraction of numeric strings in unconstrained handwritten document images. The algorithm has two main phases: pruning and verification. In the pruning phase, the algorithm first performs a new segment-merge procedure on each text line, and then using a new regularity measure, it prunes all sequences of characters that are unlikely to be numeric strings. The segment-merge procedure is composed of two modules: a new explicit character segmentation algorithm which is based on analysis of skeletal graphs and a merging algorithm which is based on graph partitioning. All the candidate sequences that pass the pruning phase are sent to a recognition-based verification phase for the final decision. The recognition is based on a coarse-to-fine approach using probabilistic RBF networks. We developed our algorithm for the processing of real-world documents where letters and digits may be connected or broken in a document. The effectiveness of the proposed approach is shown by extensive experiments done on a real-world database of 607 documents which contains handwritten, machine-printed and mixed documents with different types of layouts and levels of noise.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

NASA Astrophysics Data System (ADS)

Block, Martin M.; Durand, Loyal

2011-11-01

We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function F2^{γ p}(x,Q2). We numerically inverted the function g( s), s being the variable in Laplace space, to G( v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g( s)→0 less rapidly than 1/ s as s→∞, e.g., as 1/ s β for 0< β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G( v) is given by the product of a power v β-1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10-6 obtaining numerical results that imitate the Dirac delta function δ( v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q 2=5 GeV2 down to the lower virtuality Q 2=1.69 GeV2. For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.

Kalman filters for assimilating near-surface observations into the Richards equation - Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

NASA Astrophysics Data System (ADS)

Chirico, G. B.; Medina, H.; Romano, N.

2014-07-01

This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.

A modified three-term PRP conjugate gradient algorithm for optimization models.

PubMed

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

The 3-D numerical simulation research of vacuum injector for linear induction accelerator

NASA Astrophysics Data System (ADS)

Liu, Dagang; Xie, Mengjun; Tang, Xinbing; Liao, Shuqing

2017-01-01

Simulation method for voltage in-feed and electron injection of vacuum injector is given, and verification of the simulated voltage and current is carried out. The numerical simulation for the magnetic field of solenoid is implemented, and a comparative analysis is conducted between the simulation results and experimental results. A semi-implicit difference algorithm is adopted to suppress the numerical noise, and a parallel acceleration algorithm is used for increasing the computation speed. The RMS emittance calculation method of the beam envelope equations is analyzed. In addition, the simulated results of RMS emittance are compared with the experimental data. Finally, influences of the ferromagnetic rings on the radial and axial magnetic fields of solenoid as well as the emittance of beam are studied.

A multi-level solution algorithm for steady-state Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham; Leutenegger, Scott T.

1993-01-01

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

A priori mesh grading for the numerical calculation of the head-related transfer functions

PubMed Central

Ziegelwanger, Harald; Kreuzer, Wolfgang; Majdak, Piotr

2017-01-01

Head-related transfer functions (HRTFs) describe the directional filtering of the incoming sound caused by the morphology of a listener’s head and pinnae. When an accurate model of a listener’s morphology exists, HRTFs can be calculated numerically with the boundary element method (BEM). However, the general recommendation to model the head and pinnae with at least six elements per wavelength renders the BEM as a time-consuming procedure when calculating HRTFs for the full audible frequency range. In this study, a mesh preprocessing algorithm is proposed, viz., a priori mesh grading, which reduces the computational costs in the HRTF calculation process significantly. The mesh grading algorithm deliberately violates the recommendation of at least six elements per wavelength in certain regions of the head and pinnae and varies the size of elements gradually according to an a priori defined grading function. The evaluation of the algorithm involved HRTFs calculated for various geometric objects including meshes of three human listeners and various grading functions. The numerical accuracy and the predicted sound-localization performance of calculated HRTFs were analyzed. A-priori mesh grading appeared to be suitable for the numerical calculation of HRTFs in the full audible frequency range and outperformed uniform meshes in terms of numerical errors, perception based predictions of sound-localization performance, and computational costs. PMID:28239186

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

USGS Publications Warehouse

Haney, M.M.

2007-01-01

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model - that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable. ?? 2007 Society of Exploration Geophysicists.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation

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

Braumann, Andreas; Kraft, Markus, E-mail: mk306@cam.ac.u; Wagner, Wolfgang

2010-10-01

This paper is concerned with computational aspects of a multidimensional population balance model of a wet granulation process. Wet granulation is a manufacturing method to form composite particles, granules, from small particles and binders. A detailed numerical study of a stochastic particle algorithm for the solution of a five-dimensional population balance model for wet granulation is presented. Each particle consists of two types of solids (containing pores) and of external and internal liquid (located in the pores). Several transformations of particles are considered, including coalescence, compaction and breakage. A convergence study is performed with respect to the parameter that determinesmore » the number of numerical particles. Averaged properties of the system are computed. In addition, the ensemble is subdivided into practically relevant size classes and analysed with respect to the amount of mass and the particle porosity in each class. These results illustrate the importance of the multidimensional approach. Finally, the kinetic equation corresponding to the stochastic model is discussed.« less

Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

Highly uniform parallel microfabrication using a large numerical aperture system

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

Zhang, Zi-Yu; Su, Ya-Hui, E-mail: ustcsyh@ahu.edu.cn, E-mail: dongwu@ustc.edu.cn; Zhang, Chen-Chu

In this letter, we report an improved algorithm to produce accurate phase patterns for generating highly uniform diffraction-limited multifocal arrays in a large numerical aperture objective system. It is shown that based on the original diffraction integral, the uniformity of the diffraction-limited focal arrays can be improved from ∼75% to >97%, owing to the critical consideration of the aperture function and apodization effect associated with a large numerical aperture objective. The experimental results, e.g., 3 × 3 arrays of square and triangle, seven microlens arrays with high uniformity, further verify the advantage of the improved algorithm. This algorithm enables the laser parallelmore » processing technology to realize uniform microstructures and functional devices in the microfabrication system with a large numerical aperture objective.« less

Parallel language constructs for tensor product computations on loosely coupled architectures

NASA Technical Reports Server (NTRS)

Mehrotra, Piyush; Van Rosendale, John

1989-01-01

A set of language primitives designed to allow the specification of parallel numerical algorithms at a higher level is described. The authors focus on tensor product array computations, a simple but important class of numerical algorithms. They consider first the problem of programming one-dimensional kernel routines, such as parallel tridiagonal solvers, and then look at how such parallel kernels can be combined to form parallel tensor product algorithms.

Hidden Markov Model-Based CNV Detection Algorithms for Illumina Genotyping Microarrays.

PubMed

Seiser, Eric L; Innocenti, Federico

2014-01-01

Somatic alterations in DNA copy number have been well studied in numerous malignancies, yet the role of germline DNA copy number variation in cancer is still emerging. Genotyping microarrays generate allele-specific signal intensities to determine genotype, but may also be used to infer DNA copy number using additional computational approaches. Numerous tools have been developed to analyze Illumina genotype microarray data for copy number variant (CNV) discovery, although commonly utilized algorithms freely available to the public employ approaches based upon the use of hidden Markov models (HMMs). QuantiSNP, PennCNV, and GenoCN utilize HMMs with six copy number states but vary in how transition and emission probabilities are calculated. Performance of these CNV detection algorithms has been shown to be variable between both genotyping platforms and data sets, although HMM approaches generally outperform other current methods. Low sensitivity is prevalent with HMM-based algorithms, suggesting the need for continued improvement in CNV detection methodologies.

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

NASA Technical Reports Server (NTRS)

Bui, Trong T.

1999-01-01

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Parallel-vector unsymmetric Eigen-Solver on high performance computers

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Jiangning, Qin

1993-01-01

The popular QR algorithm for solving all eigenvalues of an unsymmetric matrix is reviewed. Among the basic components in the QR algorithm, it was concluded from this study, that the reduction of an unsymmetric matrix to a Hessenberg form (before applying the QR algorithm itself) can be done effectively by exploiting the vector speed and multiple processors offered by modern high-performance computers. Numerical examples of several test cases have indicated that the proposed parallel-vector algorithm for converting a given unsymmetric matrix to a Hessenberg form offers computational advantages over the existing algorithm. The time saving obtained by the proposed methods is increased as the problem size increased.

Focusing light through random scattering media by four-element division algorithm

NASA Astrophysics Data System (ADS)

Fang, Longjie; Zhang, Xicheng; Zuo, Haoyi; Pang, Lin

2018-01-01

The focusing of light through random scattering materials using wavefront shaping is studied in detail. We propose a newfangled approach namely four-element division algorithm to improve the average convergence rate and signal-to-noise ratio of focusing. Using 4096 independently controlled segments of light, the intensity at the target is 72 times enhanced over the original intensity at the same position. The four-element division algorithm and existing phase control algorithms of focusing through scattering media are compared by both of the numerical simulation and the experiment. It is found that four-element division algorithm is particularly advantageous to improve the average convergence rate of focusing.

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.

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

EPA Science Inventory

Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

A scale space based algorithm for automated segmentation of single shot tagged MRI of shearing deformation.

PubMed

Sprengers, Andre M J; Caan, Matthan W A; Moerman, Kevin M; Nederveen, Aart J; Lamerichs, Rolf M; Stoker, Jaap

2013-04-01

This study proposes a scale space based algorithm for automated segmentation of single-shot tagged images of modest SNR. Furthermore the algorithm was designed for analysis of discontinuous or shearing types of motion, i.e. segmentation of broken tag patterns. The proposed algorithm utilises non-linear scale space for automatic segmentation of single-shot tagged images. The algorithm's ability to automatically segment tagged shearing motion was evaluated in a numerical simulation and in vivo. A typical shearing deformation was simulated in a Shepp-Logan phantom allowing for quantitative evaluation of the algorithm's success rate as a function of both SNR and the amount of deformation. For a qualitative in vivo evaluation tagged images showing deformations in the calf muscles and eye movement in a healthy volunteer were acquired. Both the numerical simulation and the in vivo tagged data demonstrated the algorithm's ability for automated segmentation of single-shot tagged MR provided that SNR of the images is above 10 and the amount of deformation does not exceed the tag spacing. The latter constraint can be met by adjusting the tag delay or the tag spacing. The scale space based algorithm for automatic segmentation of single-shot tagged MR enables the application of tagged MR to complex (shearing) deformation and the processing of datasets with relatively low SNR.

Differential evolution algorithm based photonic structure design: numerical and experimental verification of subwavelength λ/5 focusing of light.

PubMed

Bor, E; Turduev, M; Kurt, H

2016-08-01

Photonic structure designs based on optimization algorithms provide superior properties compared to those using intuition-based approaches. In the present study, we numerically and experimentally demonstrate subwavelength focusing of light using wavelength scale absorption-free dielectric scattering objects embedded in an air background. An optimization algorithm based on differential evolution integrated into the finite-difference time-domain method was applied to determine the locations of each circular dielectric object with a constant radius and refractive index. The multiobjective cost function defined inside the algorithm ensures strong focusing of light with low intensity side lobes. The temporal and spectral responses of the designed compact photonic structure provided a beam spot size in air with a full width at half maximum value of 0.19λ, where λ is the wavelength of light. The experiments were carried out in the microwave region to verify numerical findings, and very good agreement between the two approaches was found. The subwavelength light focusing is associated with a strong interference effect due to nonuniformly arranged scatterers and an irregular index gradient. Improving the focusing capability of optical elements by surpassing the diffraction limit of light is of paramount importance in optical imaging, lithography, data storage, and strong light-matter interaction.

Differential evolution algorithm based photonic structure design: numerical and experimental verification of subwavelength λ/5 focusing of light

PubMed Central

Bor, E.; Turduev, M.; Kurt, H.

2016-01-01

Photonic structure designs based on optimization algorithms provide superior properties compared to those using intuition-based approaches. In the present study, we numerically and experimentally demonstrate subwavelength focusing of light using wavelength scale absorption-free dielectric scattering objects embedded in an air background. An optimization algorithm based on differential evolution integrated into the finite-difference time-domain method was applied to determine the locations of each circular dielectric object with a constant radius and refractive index. The multiobjective cost function defined inside the algorithm ensures strong focusing of light with low intensity side lobes. The temporal and spectral responses of the designed compact photonic structure provided a beam spot size in air with a full width at half maximum value of 0.19λ, where λ is the wavelength of light. The experiments were carried out in the microwave region to verify numerical findings, and very good agreement between the two approaches was found. The subwavelength light focusing is associated with a strong interference effect due to nonuniformly arranged scatterers and an irregular index gradient. Improving the focusing capability of optical elements by surpassing the diffraction limit of light is of paramount importance in optical imaging, lithography, data storage, and strong light-matter interaction. PMID:27477060

A Comparison of Three Algorithms for Orion Drogue Parachute Release

NASA Technical Reports Server (NTRS)

Matz, Daniel A.; Braun, Robert D.

2015-01-01

The Orion Multi-Purpose Crew Vehicle is susceptible to ipping apex forward between drogue parachute release and main parachute in ation. A smart drogue release algorithm is required to select a drogue release condition that will not result in an apex forward main parachute deployment. The baseline algorithm is simple and elegant, but does not perform as well as desired in drogue failure cases. A simple modi cation to the baseline algorithm can improve performance, but can also sometimes fail to identify a good release condition. A new algorithm employing simpli ed rotational dynamics and a numeric predictor to minimize a rotational energy metric is proposed. A Monte Carlo analysis of a drogue failure scenario is used to compare the performance of the algorithms. The numeric predictor prevents more of the cases from ipping apex forward, and also results in an improvement in the capsule attitude at main bag extraction. The sensitivity of the numeric predictor to aerodynamic dispersions, errors in the navigated state, and execution rate is investigated, showing little degradation in performance.

Multiresolution representation and numerical algorithms: A brief review

NASA Technical Reports Server (NTRS)

Harten, Amiram

1994-01-01

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

Random sequential adsorption of cubes

NASA Astrophysics Data System (ADS)

Cieśla, Michał; Kubala, Piotr

2018-01-01

Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Analysis of data mining classification by comparison of C4.5 and ID algorithms

NASA Astrophysics Data System (ADS)

Sudrajat, R.; Irianingsih, I.; Krisnawan, D.

2017-01-01

The rapid development of information technology, triggered by the intensive use of information technology. For example, data mining widely used in investment. Many techniques that can be used assisting in investment, the method that used for classification is decision tree. Decision tree has a variety of algorithms, such as C4.5 and ID3. Both algorithms can generate different models for similar data sets and different accuracy. C4.5 and ID3 algorithms with discrete data provide accuracy are 87.16% and 99.83% and C4.5 algorithm with numerical data is 89.69%. C4.5 and ID3 algorithms with discrete data provides 520 and 598 customers and C4.5 algorithm with numerical data is 546 customers. From the analysis of the both algorithm it can classified quite well because error rate less than 15%.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models

NASA Astrophysics Data System (ADS)

Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng

2012-09-01

Our goal in this paper is to improve the computational performance of the proximity algorithms for the L1/TV denoising model. This leads us to a new characterization of all solutions to the L1/TV model via fixed-point equations expressed in terms of the proximity operators. Based upon this observation we develop an algorithm for solving the model and establish its convergence. Furthermore, we demonstrate that the proposed algorithm can be accelerated through the use of the componentwise Gauss-Seidel iteration so that the CPU time consumed is significantly reduced. Numerical experiments using the proposed algorithm for impulsive noise removal are included, with a comparison to three recently developed algorithms. The numerical results show that while the proposed algorithm enjoys a high quality of the restored images, as the other three known algorithms do, it performs significantly better in terms of computational efficiency measured in the CPU time consumed.

Study of the Z{sub 3} symmetry in QCD at finite temperature and chemical potential using a worm algorithm

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

Krein, Gastao; Leme, Rafael R.; Woitek, Marcio

Traditional Monte Carlo simulations of QCD in the presence of a baryon chemical potential are plagued by the complex phase problem and new numerical approaches are necessary for studying the phase diagram of the theory. In this work we consider a Z{sub 3} Polyakov loop model for the deconfining phase transition in QCD and discuss how a flux representation of the model in terms of dimer and monomer variable solves the complex action problem. We present results of numerical simulations using a worm algorithm for the specific heat and two-point correlation function of Polyakov loops. Evidences of a first ordermore » deconfinement phase transition are discussed.« less

Numerical simulations of detonation propagation in gaseous fuel-air mixtures

NASA Astrophysics Data System (ADS)

Honhar, Praveen; Kaplan, Carolyn; Houim, Ryan; Oran, Elaine

2017-11-01

Unsteady multidimensional numerical simulations of detonation propagation and survival in mixtures of fuel (hydrogen or methane) diluted with air were carried out with a fully compressible Navier-Stokes solver using a simplified chemical-diffusive model (CDM). The CDM was derived using a genetic algorithm combined with the Nelder-Mead optimization algorithm and reproduces physically correct laminar flame and detonation properties. Cases studied are overdriven detonations propagating through confined mediums, with or without gradients in composition. Results from simulations confirm that the survival of the detonation depends on the channel heights. In addition, the simulations show that the propagation of the detonation waves depends on the steepness in composition gradients.

Forebody and base region real gas flow in severe planetary entry by a factored implicit numerical method. II - Equilibrium reactive gas

NASA Technical Reports Server (NTRS)

Davy, W. C.; Green, M. J.; Lombard, C. K.

1981-01-01

The factored-implicit, gas-dynamic algorithm has been adapted to the numerical simulation of equilibrium reactive flows. Changes required in the perfect gas version of the algorithm are developed, and the method of coupling gas-dynamic and chemistry variables is discussed. A flow-field solution that approximates a Jovian entry case was obtained by this method and compared with the same solution obtained by HYVIS, a computer program much used for the study of planetary entry. Comparison of surface pressure distribution and stagnation line shock-layer profiles indicates that the two solutions agree well.

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for Circular Current Loops in Cylindrical Coordinates

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

Walstrom, Peter Lowell

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for circular current loops is described. An algorithm for computing the vector potential is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations (especially for the field derivatives) are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. Since cel can evaluate complete elliptic integrals of a fairlymore » general type, in some cases the elliptic integrals can be evaluated without first reducing them to forms containing standard Legendre forms. The algorithms avoid the numerical difficulties that many of the textbook solutions have for points near the axis because of explicit factors of 1=r or 1=r 2 in the some of the expressions.« less

Automatic Boosted Flood Mapping from Satellite Data

NASA Technical Reports Server (NTRS)

Coltin, Brian; McMichael, Scott; Smith, Trey; Fong, Terrence

2016-01-01

Numerous algorithms have been proposed to map floods from Moderate Resolution Imaging Spectroradiometer (MODIS) imagery. However, most require human input to succeed, either to specify a threshold value or to manually annotate training data. We introduce a new algorithm based on Adaboost which effectively maps floods without any human input, allowing for a truly rapid and automatic response. The Adaboost algorithm combines multiple thresholds to achieve results comparable to state-of-the-art algorithms which do require human input. We evaluate Adaboost, as well as numerous previously proposed flood mapping algorithms, on multiple MODIS flood images, as well as on hundreds of non-flood MODIS lake images, demonstrating its effectiveness across a wide variety of conditions.

Research on the control of large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1983-01-01

The research effort on the control of large space structures at the University of Houston has concentrated on the mathematical theory of finite-element models; identification of the mass, damping, and stiffness matrix; assignment of damping to structures; and decoupling of structure dynamics. The objective of the work has been and will continue to be the development of efficient numerical algorithms for analysis, control, and identification of large space structures. The major consideration in the development of the algorithms has been the large number of equations that must be handled by the algorithm as well as sensitivity of the algorithms to numerical errors.

Seven-spot ladybird optimization: a novel and efficient metaheuristic algorithm for numerical optimization.

PubMed

Wang, Peng; Zhu, Zhouquan; Huang, Shuai

2013-01-01

This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions.

Seven-Spot Ladybird Optimization: A Novel and Efficient Metaheuristic Algorithm for Numerical Optimization

PubMed Central

Zhu, Zhouquan

2013-01-01

This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions. PMID:24385879

On the impact of communication complexity in the design of parallel numerical algorithms

NASA Technical Reports Server (NTRS)

Gannon, D.; Vanrosendale, J.

1984-01-01

This paper describes two models of the cost of data movement in parallel numerical algorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In the second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm independent upper bounds on system performance are derived for several problems that are important to scientific computation.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.

PubMed

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-11-25

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

A hybrid artificial bee colony algorithm for numerical function optimization

NASA Astrophysics Data System (ADS)

Alqattan, Zakaria N.; Abdullah, Rosni

2015-02-01

Artificial Bee Colony (ABC) algorithm is one of the swarm intelligence algorithms; it has been introduced by Karaboga in 2005. It is a meta-heuristic optimization search algorithm inspired from the intelligent foraging behavior of the honey bees in nature. Its unique search process made it as one of the most competitive algorithm with some other search algorithms in the area of optimization, such as Genetic algorithm (GA) and Particle Swarm Optimization (PSO). However, the ABC performance of the local search process and the bee movement or the solution improvement equation still has some weaknesses. The ABC is good in avoiding trapping at the local optimum but it spends its time searching around unpromising random selected solutions. Inspired by the PSO, we propose a Hybrid Particle-movement ABC algorithm called HPABC, which adapts the particle movement process to improve the exploration of the original ABC algorithm. Numerical benchmark functions were used in order to experimentally test the HPABC algorithm. The results illustrate that the HPABC algorithm can outperform the ABC algorithm in most of the experiments (75% better in accuracy and over 3 times faster).

Theory and algorithms for image reconstruction on chords and within regions of interest

NASA Astrophysics Data System (ADS)

Zou, Yu; Pan, Xiaochuan; Sidky, Emilâ Y.

2005-11-01

We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.

Multiphysics phase field modeling of hydrogen diffusion and delta-hydride precipitation in alpha-zirconium

NASA Astrophysics Data System (ADS)

Jokisaari, Andrea M.

Hydride precipitation in zirconium is a significant factor limiting the lifetime of nuclear fuel cladding, because hydride microstructures play a key role in the degradation of fuel cladding. However, the behavior of hydrogen in zirconium has typically been modeled using mean field approaches, which do not consider microstructural evolution. This thesis describes a quantitative microstructural evolution model for the alpha-zirconium/delta-hydride system and the associated numerical methods and algorithms that were developed. The multiphysics, phase field-based model incorporates CALPHAD free energy descriptions, linear elastic solid mechanics, and classical nucleation theory. A flexible simulation software implementing the model, Hyrax, is built on the Multiphysics Object Oriented Simulation Environment (MOOSE) finite element framework. Hyrax is open-source and freely available; moreover, the numerical methods and algorithms that have been developed are generalizable to other systems. The algorithms are described in detail, and verification studies for each are discussed. In addition, analyses of the sensitivity of the simulation results to the choice of numerical parameters are presented. For example, threshold values for the CALPHAD free energy algorithm and the use of mesh and time adaptivity when employing the nucleation algorithm are studied. Furthermore, preliminary insights into the nucleation behavior of delta-hydrides are described. These include a) the sensitivities of the nucleation rate to temperature, interfacial energy, composition and elastic energy, b) the spatial variation of the nucleation rate around a single precipitate, and c) the effect of interfacial energy and nucleation rate on the precipitate microstructure. Finally, several avenues for future work are discussed. Topics encompass the terminal solid solubility hysteresis of hydrogen in zirconium and the effects of the alpha/delta interfacial energy, as well as thermodiffusion, plasticity, and irradiation, which are not yet accounted for in the model.

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

NASA Astrophysics Data System (ADS)

Ehrhardt, Matthias J.; Markiewicz, Pawel; Chambolle, Antonin; Richtárik, Peter; Schott, Jonathan; Schönlieb, Carola-Bibiane

2017-08-01

Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.

Consumers' Kansei Needs Clustering Method for Product Emotional Design Based on Numerical Design Structure Matrix and Genetic Algorithms.

PubMed

Yang, Yan-Pu; Chen, Deng-Kai; Gu, Rong; Gu, Yu-Feng; Yu, Sui-Huai

2016-01-01

Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design.

Consumers' Kansei Needs Clustering Method for Product Emotional Design Based on Numerical Design Structure Matrix and Genetic Algorithms

PubMed Central

Chen, Deng-kai; Gu, Rong; Gu, Yu-feng; Yu, Sui-huai

2016-01-01

Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design. PMID:27630709

An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

2017-11-01

Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

Analytical and numerical algorthms for revelation and investigation of secular resonances in the motion of near earth space objects. (Russian Title: Численно-аналитическая методика выявления и исследования вековых резонансов в движении околоземных объектов)

NASA Astrophysics Data System (ADS)

Bordovitsyna, T. V.; Tomilova, I. V.; Chuvashov, I. N.

2011-07-01

In this paper complex of analytical and numerical algorithms for revelation and investigation of secular resonances in the motion of near Earth space objects are presented. Analytical numerical algorithm for revelation secular resonances and numerical ones for study of object's long-time orbital evolution are applied. Small denominators are used as indicators of the secular resonances presence. The program complex "The numerical model of the motion of the Earth artificial satellite systems" are used for investigation of the orbital evolution.

Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms

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

Lebensohn, Ricardo A.; Needleman, Alan

Here, we present the numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012). Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influencemore » of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.« less

Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms

DOE PAGES

Lebensohn, Ricardo A.; Needleman, Alan

2016-03-28

Here, we present the numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012). Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influencemore » of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.« less

Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions. Numerical Analysis in Continuous Time

NASA Astrophysics Data System (ADS)

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors the rare trajectories of interest. However, such algorithms are plagued by finite simulation time- and finite population size- effects that can render their use delicate. Using the continuous-time cloning algorithm, we analyze the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. We use these scalings in order to propose a numerical approach which allows to extract the infinite-time and infinite-size limit of these estimators.

New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method

PubMed Central

Doha, E.H.; Abd-Elhameed, W.M.; Youssri, Y.H.

2014-01-01

Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient. PMID:26425358

An Optimization Study of Hot Stamping Operation

NASA Astrophysics Data System (ADS)

Ghoo, Bonyoung; Umezu, Yasuyoshi; Watanabe, Yuko; Ma, Ninshu; Averill, Ron

2010-06-01

In the present study, 3-dimensional finite element analyses for hot-stamping processes of Audi B-pillar product are conducted using JSTAMP/NV and HEEDS. Special attention is paid to the optimization of simulation technology coupling with thermal-mechanical formulations. Numerical simulation based on FEM technology and optimization design using the hybrid adaptive SHERPA algorithm are applied to hot stamping operation to improve productivity. The robustness of the SHERPA algorithm is found through the results of the benchmark example. The SHERPA algorithm is shown to be far superior to the GA (Genetic Algorithm) in terms of efficiency, whose calculation time is about 7 times faster than that of the GA. The SHERPA algorithm could show high performance in a large scale problem having complicated design space and long calculation time.

In Praise of Numerical Computation

NASA Astrophysics Data System (ADS)

Yap, Chee K.

Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms’ design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name “numerical computational geometry” for such activities.

Single-step methods for predicting orbital motion considering its periodic components

NASA Astrophysics Data System (ADS)

Lavrov, K. N.

1989-01-01

Modern numerical methods for integration of ordinary differential equations can provide accurate and universal solutions to celestial mechanics problems. The implicit single sequence algorithms of Everhart and multiple step computational schemes using a priori information on periodic components can be combined to construct implicit single sequence algorithms which combine their advantages. The construction and analysis of the properties of such algorithms are studied, utilizing trigonometric approximation of the solutions of differential equations containing periodic components. The algorithms require 10 percent more machine memory than the Everhart algorithms, but are twice as fast, and yield short term predictions valid for five to ten orbits with good accuracy and five to six times faster than algorithms using other methods.

Minimal-scan filtered backpropagation algorithms for diffraction tomography.

PubMed

Pan, X; Anastasio, M A

1999-12-01

The filtered backpropagation (FBPP) algorithm, originally developed by Devaney [Ultrason. Imaging 4, 336 (1982)], has been widely used for reconstructing images in diffraction tomography. It is generally known that the FBPP algorithm requires scattered data from a full angular range of 2 pi for exact reconstruction of a generally complex-valued object function. However, we reveal that one needs scattered data only over the angular range 0 < or = phi < or = 3 pi/2 for exact reconstruction of a generally complex-valued object function. Using this insight, we develop and analyze a family of minimal-scan filtered backpropagation (MS-FBPP) algorithms, which, unlike the FBPP algorithm, use scattered data acquired from view angles over the range 0 < or = phi < or = 3 pi/2. We show analytically that these MS-FBPP algorithms are mathematically identical to the FBPP algorithm. We also perform computer simulation studies for validation, demonstration, and comparison of these MS-FBPP algorithms. The numerical results in these simulation studies corroborate our theoretical assertions.

Numerical Modeling of One-Dimensional Steady-State Flow and Contaminant Transport in a Horizontally Heterogeneous Unconfined Aquifer with an Uneven Base

EPA Science Inventory

Algorithms and a short description of the D1_Flow program for numerical modeling of one-dimensional steady-state flow in horizontally heterogeneous aquifers with uneven sloping bases are presented. The algorithms are based on the Dupuit-Forchheimer approximations. The program per...

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

A numerical solution of Duffing's equations including the prediction of jump phenomena

NASA Technical Reports Server (NTRS)

Moyer, E. T., Jr.; Ghasghai-Abdi, E.

1987-01-01

Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.

Density-matrix-based algorithm for solving eigenvalue problems

NASA Astrophysics Data System (ADS)

Polizzi, Eric

2009-03-01

A fast and stable numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques and takes its inspiration from the contour integration and density-matrix representation in quantum mechanics. It will be shown that this algorithm—named FEAST—exhibits high efficiency, robustness, accuracy, and scalability on parallel architectures. Examples from electronic structure calculations of carbon nanotubes are presented, and numerical performances and capabilities are discussed.

The Construction of 3-d Neutral Density for Arbitrary Data Sets

NASA Astrophysics Data System (ADS)

Riha, S.; McDougall, T. J.; Barker, P. M.

2014-12-01

The Neutral Density variable allows inference of water pathways from thermodynamic properties in the global ocean, and is therefore an essential component of global ocean circulation analysis. The widely used algorithm for the computation of Neutral Density yields accurate results for data sets which are close to the observed climatological ocean. Long-term numerical climate simulations, however, often generate a significant drift from present-day climate, which renders the existing algorithm inaccurate. To remedy this problem, new algorithms which operate on arbitrary data have been developed, which may potentially be used to compute Neutral Density during runtime of a numerical model.We review existing approaches for the construction of Neutral Density in arbitrary data sets, detail their algorithmic structure, and present an analysis of the computational cost for implementations on a single-CPU computer. We discuss possible strategies for the implementation in state-of-the-art numerical models, with a focus on distributed computing environments.

Formation Flight of Multiple UAVs via Onboard Sensor Information Sharing.

PubMed

Park, Chulwoo; Cho, Namhoon; Lee, Kyunghyun; Kim, Youdan

2015-07-17

To monitor large areas or simultaneously measure multiple points, multiple unmanned aerial vehicles (UAVs) must be flown in formation. To perform such flights, sensor information generated by each UAV should be shared via communications. Although a variety of studies have focused on the algorithms for formation flight, these studies have mainly demonstrated the performance of formation flight using numerical simulations or ground robots, which do not reflect the dynamic characteristics of UAVs. In this study, an onboard sensor information sharing system and formation flight algorithms for multiple UAVs are proposed. The communication delays of radiofrequency (RF) telemetry are analyzed to enable the implementation of the onboard sensor information sharing system. Using the sensor information sharing, the formation guidance law for multiple UAVs, which includes both a circular and close formation, is designed. The hardware system, which includes avionics and an airframe, is constructed for the proposed multi-UAV platform. A numerical simulation is performed to demonstrate the performance of the formation flight guidance and control system for multiple UAVs. Finally, a flight test is conducted to verify the proposed algorithm for the multi-UAV system.

Formation Flight of Multiple UAVs via Onboard Sensor Information Sharing

PubMed Central

Park, Chulwoo; Cho, Namhoon; Lee, Kyunghyun; Kim, Youdan

2015-01-01

To monitor large areas or simultaneously measure multiple points, multiple unmanned aerial vehicles (UAVs) must be flown in formation. To perform such flights, sensor information generated by each UAV should be shared via communications. Although a variety of studies have focused on the algorithms for formation flight, these studies have mainly demonstrated the performance of formation flight using numerical simulations or ground robots, which do not reflect the dynamic characteristics of UAVs. In this study, an onboard sensor information sharing system and formation flight algorithms for multiple UAVs are proposed. The communication delays of radiofrequency (RF) telemetry are analyzed to enable the implementation of the onboard sensor information sharing system. Using the sensor information sharing, the formation guidance law for multiple UAVs, which includes both a circular and close formation, is designed. The hardware system, which includes avionics and an airframe, is constructed for the proposed multi-UAV platform. A numerical simulation is performed to demonstrate the performance of the formation flight guidance and control system for multiple UAVs. Finally, a flight test is conducted to verify the proposed algorithm for the multi-UAV system. PMID:26193281

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

Developing Information Power Grid Based Algorithms and Software

NASA Technical Reports Server (NTRS)

Dongarra, Jack

1998-01-01

This exploratory study initiated our effort to understand performance modeling on parallel systems. The basic goal of performance modeling is to understand and predict the performance of a computer program or set of programs on a computer system. Performance modeling has numerous applications, including evaluation of algorithms, optimization of code implementations, parallel library development, comparison of system architectures, parallel system design, and procurement of new systems. Our work lays the basis for the construction of parallel libraries that allow for the reconstruction of application codes on several distinct architectures so as to assure performance portability. Following our strategy, once the requirements of applications are well understood, one can then construct a library in a layered fashion. The top level of this library will consist of architecture-independent geometric, numerical, and symbolic algorithms that are needed by the sample of applications. These routines should be written in a language that is portable across the targeted architectures.

Simulation of two-dimensional turbulent flows in a rotating annulus

NASA Astrophysics Data System (ADS)

Storey, Brian D.

2004-05-01

Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments.

Understanding disordered systems through numerical simulation and algorithm development

NASA Astrophysics Data System (ADS)

Sweeney, Sean Michael

Disordered systems arise in many physical contexts. Not all matter is uniform, and impurities or heterogeneities can be modeled by fixed random disorder. Numerous complex networks also possess fixed disorder, leading to applications in transportation systems, telecommunications, social networks, and epidemic modeling, to name a few. Due to their random nature and power law critical behavior, disordered systems are difficult to study analytically. Numerical simulation can help overcome this hurdle by allowing for the rapid computation of system states. In order to get precise statistics and extrapolate to the thermodynamic limit, large systems must be studied over many realizations. Thus, innovative algorithm development is essential in order reduce memory or running time requirements of simulations. This thesis presents a review of disordered systems, as well as a thorough study of two particular systems through numerical simulation, algorithm development and optimization, and careful statistical analysis of scaling properties. Chapter 1 provides a thorough overview of disordered systems, the history of their study in the physics community, and the development of techniques used to study them. Topics of quenched disorder, phase transitions, the renormalization group, criticality, and scale invariance are discussed. Several prominent models of disordered systems are also explained. Lastly, analysis techniques used in studying disordered systems are covered. In Chapter 2, minimal spanning trees on critical percolation clusters are studied, motivated in part by an analytic perturbation expansion by Jackson and Read that I check against numerical calculations. This system has a direct mapping to the ground state of the strongly disordered spin glass. We compute the path length fractal dimension of these trees in dimensions d = {2, 3, 4, 5} and find our results to be compatible with the analytic results suggested by Jackson and Read. In Chapter 3, the random bond Ising ferromagnet is studied, which is especially useful since it serves as a prototype for more complicated disordered systems such as the random field Ising model and spin glasses. We investigate the effect that changing boundary spins has on the locations of domain walls in the interior of the random ferromagnet system. We provide an analytic proof that ground state domain walls in the two dimensional system are decomposable, and we map these domain walls to a shortest paths problem. By implementing a multiple-source shortest paths algorithm developed by Philip Klein, we are able to efficiently probe domain wall locations for all possible configurations of boundary spins. We consider lattices with uncorrelated dis- order, as well as disorder that is spatially correlated according to a power law. We present numerical results for the scaling exponent governing the probability that a domain wall can be induced that passes through a particular location in the system's interior, and we compare these results to previous results on the directed polymer problem.

An Adaptive Numeric Predictor-corrector Guidance Algorithm for Atmospheric Entry Vehicles. M.S. Thesis - MIT, Cambridge

NASA Technical Reports Server (NTRS)

Spratlin, Kenneth Milton

1987-01-01

An adaptive numeric predictor-corrector guidance is developed for atmospheric entry vehicles which utilize lift to achieve maximum footprint capability. Applicability of the guidance design to vehicles with a wide range of performance capabilities is desired so as to reduce the need for algorithm redesign with each new vehicle. Adaptability is desired to minimize mission-specific analysis and planning. The guidance algorithm motivation and design are presented. Performance is assessed for application of the algorithm to the NASA Entry Research Vehicle (ERV). The dispersions the guidance must be designed to handle are presented. The achievable operational footprint for expected worst-case dispersions is presented. The algorithm performs excellently for the expected dispersions and captures most of the achievable footprint.

Positive dwell time algorithm with minimum equal extra material removal in deterministic optical surfacing technology.

PubMed

Li, Longxiang; Xue, Donglin; Deng, Weijie; Wang, Xu; Bai, Yang; Zhang, Feng; Zhang, Xuejun

2017-11-10

In deterministic computer-controlled optical surfacing, accurate dwell time execution by computer numeric control machines is crucial in guaranteeing a high-convergence ratio for the optical surface error. It is necessary to consider the machine dynamics limitations in the numerical dwell time algorithms. In this paper, these constraints on dwell time distribution are analyzed, and a model of the equal extra material removal is established. A positive dwell time algorithm with minimum equal extra material removal is developed. Results of simulations based on deterministic magnetorheological finishing demonstrate the necessity of considering machine dynamics performance and illustrate the validity of the proposed algorithm. Indeed, the algorithm effectively facilitates the determinacy of sub-aperture optical surfacing processes.

Mixed formulation for seismic analysis of composite steel-concrete frame structures

NASA Astrophysics Data System (ADS)

Ayoub, Ashraf Salah Eldin

This study presents a new finite element model for the nonlinear analysis of structures made up of steel and concrete under monotonic and cyclic loads. The new formulation is based on a two-field mixed formulation. In the formulation, both forces and deformations are simultaneously approximated within the element through independent interpolation functions. The main advantages of the model is the accuracy in global and local response with very few elements while maintaining rapid numerical convergence and robustness even under severe cyclic loading. Overall four elements were developed based on the new formulation: an element that describes the behavior of anchored reinforcing bars, an element that describes the behavior of composite steel-concrete beams with deformable shear connectors, an element that describes the behavior of reinforced concrete beam-columns with bond-slip, and an element that describes the behavior of pretensioned or posttensioned, bonded or unbonded prestressed concrete structures. The models use fiber discretization of beam sections to describe nonlinear material response. The transfer of forces between steel and concrete is described with bond elements. Bond elements are modeled with distributed spring elements. The non-linear behavior of the composite element derives entirely from the constitutive laws of the steel, concrete and bond elements. Two additional elements are used for the prestressed concrete models, a friction element that models the effect of friction between the tendon and the duct during the posttensioning operation, and an anchorage element that describes the behavior of the prestressing tendon anchorage in posttensioned structures. Two algorithms for the numerical implementation of the new proposed model are presented; an algorithm that enforces stress continuity at element boundaries, and an algorithm in which stress continuity is relaxed locally inside the element. Stability of both algorithms is discussed. Comparison with standard displacement based models and earlier flexibility based models is presented through numerical studies. The studies prove the superiority of the mixed model over both displacement and flexibility models. Correlation studies of the proposed model with experimental results of structural specimens are conducted. The studies show the accuracy of the model and its numerical robustness even under severe cyclic loading conditions.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

PubMed Central

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-01-01

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design. PMID:25404761

The upwind control volume scheme for unstructured triangular grids

NASA Technical Reports Server (NTRS)

Giles, Michael; Anderson, W. Kyle; Roberts, Thomas W.

1989-01-01

A new algorithm for the numerical solution of the Euler equations is presented. This algorithm is particularly suited to the use of unstructured triangular meshes, allowing geometric flexibility. Solutions are second-order accurate in the steady state. Implementation of the algorithm requires minimal grid connectivity information, resulting in modest storage requirements, and should enhance the implementation of the scheme on massively parallel computers. A novel form of upwind differencing is developed, and is shown to yield sharp resolution of shocks. Two new artificial viscosity models are introduced that enhance the performance of the new scheme. Numerical results for transonic airfoil flows are presented, which demonstrate the performance of the algorithm.

On the efficient and reliable numerical solution of rate-and-state friction problems

NASA Astrophysics Data System (ADS)

Pipping, Elias; Kornhuber, Ralf; Rosenau, Matthias; Oncken, Onno

2016-03-01

We present a mathematically consistent numerical algorithm for the simulation of earthquake rupture with rate-and-state friction. Its main features are adaptive time stepping, a novel algebraic solution algorithm involving nonlinear multigrid and a fixed point iteration for the rate-and-state decoupling. The algorithm is applied to a laboratory scale subduction zone which allows us to compare our simulations with experimental results. Using physical parameters from the experiment, we find a good fit of recurrence time of slip events as well as their rupture width and peak slip. Computations in 3-D confirm efficiency and robustness of our algorithm.

A Fast EM Algorithm for Fitting Joint Models of a Binary Response and Multiple Longitudinal Covariates Subject to Detection Limits

PubMed Central

Bernhardt, Paul W.; Zhang, Daowen; Wang, Huixia Judy

2014-01-01

Joint modeling techniques have become a popular strategy for studying the association between a response and one or more longitudinal covariates. Motivated by the GenIMS study, where it is of interest to model the event of survival using censored longitudinal biomarkers, a joint model is proposed for describing the relationship between a binary outcome and multiple longitudinal covariates subject to detection limits. A fast, approximate EM algorithm is developed that reduces the dimension of integration in the E-step of the algorithm to one, regardless of the number of random effects in the joint model. Numerical studies demonstrate that the proposed approximate EM algorithm leads to satisfactory parameter and variance estimates in situations with and without censoring on the longitudinal covariates. The approximate EM algorithm is applied to analyze the GenIMS data set. PMID:25598564

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.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

The MINERVA Software Development Process

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony; Munoz, Cesar A.; Dutle, Aaron M.

2017-01-01

This paper presents a software development process for safety-critical software components of cyber-physical systems. The process is called MINERVA, which stands for Mirrored Implementation Numerically Evaluated against Rigorously Verified Algorithms. The process relies on formal methods for rigorously validating code against its requirements. The software development process uses: (1) a formal specification language for describing the algorithms and their functional requirements, (2) an interactive theorem prover for formally verifying the correctness of the algorithms, (3) test cases that stress the code, and (4) numerical evaluation on these test cases of both the algorithm specifications and their implementations in code. The MINERVA process is illustrated in this paper with an application to geo-containment algorithms for unmanned aircraft systems. These algorithms ensure that the position of an aircraft never leaves a predetermined polygon region and provide recovery maneuvers when the region is inadvertently exited.

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

PubMed Central

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-01-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. PMID:23271835

Introduction to Numerical Methods

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

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Numerical analysis of moving contact line with contact angle hysteresis using feedback deceleration technique

NASA Astrophysics Data System (ADS)

Park, Jun Kwon; Kang, Kwan Hyoung

2012-04-01

Contact angle (CA) hysteresis is important in many natural and engineering wetting processes, but predicting it numerically is difficult. We developed an algorithm that considers CA hysteresis when analyzing the motion of the contact line (CL). This algorithm employs feedback control of CA which decelerates CL speed to make the CL stationary in the hysteretic range of CA, and one control coefficient should be heuristically determined depending on characteristic time of the simulated system. The algorithm requires embedding only a simple additional routine with little modification of a code which considers the dynamic CA. The method is non-iterative and explicit, and also has less computational load than other algorithms. For a drop hanging on a wire, the proposed algorithm accurately predicts the theoretical equilibrium CA. For the drop impacting on a dry surface, the results of the proposed algorithm agree well with experimental results including the intermittent occurrence of the pinning of CL. The proposed algorithm is as accurate as other algorithms, but faster.

Spherical gyroscopic moment stabilizer for attitude control of microsatellites

NASA Astrophysics Data System (ADS)

Keshtkar, Sajjad; Moreno, Jaime A.; Kojima, Hirohisa; Uchiyama, Kenji; Nohmi, Masahiro; Takaya, Keisuke

2018-02-01

This paper presents a new and improved concept of recently proposed two-degrees of freedom spherical stabilizer for triaxial orientation of microsatellites. The analytical analysis of the advantages of the proposed mechanism over the existing inertial attitude control devices are introduced. The extended equations of motion of the stabilizing satellite including the spherical gyroscope, for control law design and numerical simulations, are studied in detail. A new control algorithm based on continuous high-order sliding mode algorithms, for managing the torque produced by the stabilizer and therefore the attitude control of the satellite in the presence of perturbations/uncertainties, is presented. Some numerical simulations are carried out to prove the performance of the proposed mechanism and control laws.

Determining residual reduction algorithm kinematic tracking weights for a sidestep cut via numerical optimization.

PubMed

Samaan, Michael A; Weinhandl, Joshua T; Bawab, Sebastian Y; Ringleb, Stacie I

2016-12-01

Musculoskeletal modeling allows for the determination of various parameters during dynamic maneuvers by using in vivo kinematic and ground reaction force (GRF) data as inputs. Differences between experimental and model marker data and inconsistencies in the GRFs applied to these musculoskeletal models may not produce accurate simulations. Therefore, residual forces and moments are applied to these models in order to reduce these differences. Numerical optimization techniques can be used to determine optimal tracking weights of each degree of freedom of a musculoskeletal model in order to reduce differences between the experimental and model marker data as well as residual forces and moments. In this study, the particle swarm optimization (PSO) and simplex simulated annealing (SIMPSA) algorithms were used to determine optimal tracking weights for the simulation of a sidestep cut. The PSO and SIMPSA algorithms were able to produce model kinematics that were within 1.4° of experimental kinematics with residual forces and moments of less than 10 N and 18 Nm, respectively. The PSO algorithm was able to replicate the experimental kinematic data more closely and produce more dynamically consistent kinematic data for a sidestep cut compared to the SIMPSA algorithm. Future studies should use external optimization routines to determine dynamically consistent kinematic data and report the differences between experimental and model data for these musculoskeletal simulations.

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.; Molvig, K.

2015-09-01

In this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional Rosenbluth-Fokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single- and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and to exhibit manifestly positive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

ERIC Educational Resources Information Center

Gonzalez-Vega, Laureano

1999-01-01

Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

NASA Technical Reports Server (NTRS)

Verhaegen, M. H.

1987-01-01

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.

An algorithm for the numerical solution of linear differential games

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

Polovinkin, E S; Ivanov, G E; Balashov, M V

2001-10-31

A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented andmore » estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.« less

Numerical simulation of deformation and fracture of space protective shell structures from concrete and fiber concrete under pulse loading

NASA Astrophysics Data System (ADS)

Radchenko, P. A.; Batuev, S. P.; Radchenko, A. V.; Plevkov, V. S.

2015-11-01

This paper presents results of numerical simulation of interaction between aircraft Boeing 747-400 and protective shell of nuclear power plant. The shell is presented as complex multilayered cellular structure comprising layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was held three-dimensionally using the author's algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. The dynamics of stress-strain state and fracture of structure were studied. Destruction is described using two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of shell cellular structure—cells start to destruct in unloading wave, originating after output of compression wave to the free surfaces of cells.

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.

A reconstruction method for cone-beam differential x-ray phase-contrast computed tomography.

PubMed

Fu, Jian; Velroyen, Astrid; Tan, Renbo; Zhang, Junwei; Chen, Liyuan; Tapfer, Arne; Bech, Martin; Pfeiffer, Franz

2012-09-10

Most existing differential phase-contrast computed tomography (DPC-CT) approaches are based on three kinds of scanning geometries, described by parallel-beam, fan-beam and cone-beam. Due to the potential of compact imaging systems with magnified spatial resolution, cone-beam DPC-CT has attracted significant interest. In this paper, we report a reconstruction method based on a back-projection filtration (BPF) algorithm for cone-beam DPC-CT. Due to the differential nature of phase contrast projections, the algorithm restrains from differentiation of the projection data prior to back-projection, unlike BPF algorithms commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a micro-focus x-ray tube source. Moreover, the numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated cone-beam datasets. We believe that this feature is of particular interest for future medical cone-beam phase-contrast CT imaging applications.

Efficient Numerical Diagonalization of Hermitian 3 × 3 Matrices

NASA Astrophysics Data System (ADS)

Kopp, Joachim

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3 × 3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an alytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from .

Navigation strategy and filter design for solar electric missions

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Hagar, H., Jr.

1972-01-01

Methods which have been proposed to improve the navigation accuracy for the low-thrust space vehicle include modifications to the standard Sequential- and Batch-type orbit determination procedures and the use of inertial measuring units (IMU) which measures directly the acceleration applied to the vehicle. The navigation accuracy obtained using one of the more promising modifications to the orbit determination procedures is compared with a combined IMU-Standard. The unknown accelerations are approximated as both first-order and second-order Gauss-Markov processes. The comparison is based on numerical results obtained in a study of the navigation requirements of a numerically simulated 152-day low-thrust mission to the asteroid Eros. The results obtained in the simulation indicate that the DMC algorithm will yield a significant improvement over the navigation accuracies achieved with previous estimation algorithms. In addition, the DMC algorithms will yield better navigation accuracies than the IMU-Standard Orbit Determination algorithm, except for extremely precise IMU measurements, i.e., gyroplatform alignment .01 deg and accelerometer signal-to-noise ratio .07. Unless these accuracies are achieved, the IMU navigation accuracies are generally unacceptable.

Parallel Algorithms for Computational Models of Geophysical Systems

NASA Astrophysics Data System (ADS)

Carrillo Ledesma, A.; Herrera, I.; de la Cruz, L. M.; Hernández, G.; Grupo de Modelacion Matematica y Computacional

2013-05-01

Mathematical models of many systems of interest, including very important continuous systems of Earth Sciences and Engineering, lead to a great variety of partial differential equations (PDEs) whose solution methods are based on the computational processing of large-scale algebraic systems. Furthermore, the incredible expansion experienced by the existing computational hardware and software has made amenable to effective treatment problems of an ever increasing diversity and complexity, posed by scientific and engineering applications. Parallel computing is outstanding among the new computational tools and, in order to effectively use the most advanced computers available today, massively parallel software is required. Domain decomposition methods (DDMs) have been developed precisely for effectively treating PDEs in paralle. Ideally, the main objective of domain decomposition research is to produce algorithms capable of 'obtaining the global solution by exclusively solving local problems', but up-to-now this has only been an aspiration; that is, a strong desire for achieving such a property and so we call it 'the DDM-paradigm'. In recent times, numerically competitive DDM-algorithms are non-overlapping, preconditioned and necessarily incorporate constraints which pose an additional challenge for achieving the DDM-paradigm. Recently a group of four algorithms, referred to as the 'DVS-algorithms', which fulfill the DDM-paradigm, was developed. To derive them a new discretization method, which uses a non-overlapping system of nodes (the derived-nodes), was introduced. This discretization procedure can be applied to any boundary-value problem, or system of such equations. In turn, the resulting system of discrete equations can be treated using any available DDM-algorithm. In particular, two of the four DVS-algorithms mentioned above were obtained by application of the well-known and very effective algorithms BDDC and FETI-DP; these will be referred to as the DVS-BDDC and DVS-FETI-DP algorithms. The other two, which will be referred to as the DVS-PRIMAL and DVS-DUAL algorithms, were obtained by application of two new algorithms that had not been previously reported in the literature. As said before, the four DVS-algorithms constitute a group of preconditioned and constrained algorithms that, for the first time, fulfill the DDM-paradigm. Both, BDDC and FETI-DP, are very well-known; and both are highly efficient. Recently, it was established that these two methods are closely related and its numerical performance is quite similar. On the other hand, through numerical experiments, we have established that the numerical performances of each one of the members of DVS-algorithms group (DVS-BDDC, DVS-FETI-DP, DVS-PRIMAL and DVS-DUAL) are very similar too. Furthermore, we have carried out comparisons of the performances of the standard versions of BDDC and FETI-DP with DVS-BDDC and DVS-FETI-DP, and in all such numerical experiments the DVS algorithms have performed significantly better.

A study of hydrogen diffusion flames using PDF turbulence model

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1991-01-01

The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

A study of hydrogen diffusion flames using PDF turbulence model

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1991-01-01

The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

Topology of large-scale structure. IV - Topology in two dimensions

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Cohen, Alexander P.; Hamilton, Andrew J. S.; Gott, J. Richard, III; Weinberg, David H.

1989-01-01

In a recent series of papers, an algorithm was developed for quantitatively measuring the topology of the large-scale structure of the universe and this algorithm was applied to numerical models and to three-dimensional observational data sets. In this paper, it is shown that topological information can be derived from a two-dimensional cross section of a density field, and analytic expressions are given for a Gaussian random field. The application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models is demonstrated.

Interior point techniques for LP and NLP

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

Evtushenko, Y.

By using surjective mapping the initial constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem we use the generalized gradient-projection method and Newton`s method. After inverse transformation to the initial space we obtain the family of numerical methods for solving optimization problems with equality and inequality constraints. In the linear programming case after some simplification we obtain Dikin`s algorithm, affine scaling algorithm and generalized primal dual interior point linear programming algorithm.

A numerical study of axisymmetric compressible non-isothermal and reactive swirling flow

NASA Astrophysics Data System (ADS)

Tavernetti, William E.; Hafez, Mohamed M.

2017-09-01

Non-linear dynamical phenomena in combustion processes is an active area of experimental and theoretical research. This is in large part due to increasingly strict environmental pressures to make gas turbine engines and industrial burners more efficient. Using numerical methods, for steady and unsteady confined and unconfined compressible flow, this study examines the modeling influence of compressibility for axisymmetric swirling flow. The compressible reactive Navier-Stokes equations in terms of stream function, vorticity, circulation are used. Results, details of the numerical algorithms, as well as numerical verification techniques and validation with sources from the literature will be presented. Understanding how vortex breakdown phenomena are affected by modeling reactant consumption with compressibility effect is the main goal of this study.

Continued Research into Characterizing the Preturbulence Environment for Sensor Development, New Hazard Algorithms and Experimental Flight Planning

NASA Technical Reports Server (NTRS)

Kaplan, Michael L.; Lin, Yuh-Lang

2005-01-01

The purpose of the research was to develop and test improved hazard algorithms that could result in the development of sensors that are better able to anticipate potentially severe atmospheric turbulence, which affects aircraft safety. The research focused on employing numerical simulation models to develop improved algorithms for the prediction of aviation turbulence. This involved producing both research simulations and real-time simulations of environments predisposed to moderate and severe aviation turbulence. The research resulted in the following fundamental advancements toward the aforementioned goal: 1) very high resolution simulations of turbulent environments indicated how predictive hazard indices could be improved resulting in a candidate hazard index that indicated the potential for improvement over existing operational indices, 2) a real-time turbulence hazard numerical modeling system was improved by correcting deficiencies in its simulation of moist convection and 3) the same real-time predictive system was tested by running the code twice daily and the hazard prediction indices updated and improved. Additionally, a simple validation study was undertaken to determine how well a real time hazard predictive index performed when compared to commercial pilot observations of aviation turbulence. Simple statistical analyses were performed in this validation study indicating potential skill in employing the hazard prediction index to predict regions of varying intensities of aviation turbulence. Data sets from a research numerical model where provided to NASA for use in a large eddy simulation numerical model. A NASA contractor report and several refereed journal articles where prepared and submitted for publication during the course of this research.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Does the Acquisition of Mathematical Knowledge Make Students Better Problem Solvers? An Examination of Third Graders' Solutions of Division-with-Remainder (DWR) Problems.

ERIC Educational Resources Information Center

Guerrero, Lourdes; Rivera, Antonio

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

Translation and integration of numerical atomic orbitals in linear molecules

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

Heinäsmäki, Sami, E-mail: sami.heinasmaki@gmail.com

2014-02-14

We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.

Exploring the spectrum of planar AdS4 /CFT3 at finite coupling

NASA Astrophysics Data System (ADS)

Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto

2018-04-01

The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

Recent advances in numerical PDEs

NASA Astrophysics Data System (ADS)

Zuev, Julia Michelle

In this thesis, we investigate four neighboring topics, all in the general area of numerical methods for solving Partial Differential Equations (PDEs). Topic 1. Radial Basis Functions (RBF) are widely used for multi-dimensional interpolation of scattered data. This methodology offers smooth and accurate interpolants, which can be further refined, if necessary, by clustering nodes in select areas. We show, however, that local refinements with RBF (in a constant shape parameter [varepsilon] regime) may lead to the oscillatory errors associated with the Runge phenomenon (RP). RP is best known in the case of high-order polynomial interpolation, where its effects can be accurately predicted via Lebesgue constant L (which is based solely on the node distribution). We study the RP and the applicability of Lebesgue constant (as well as other error measures) in RBF interpolation. Mainly, we allow for a spatially variable shape parameter, and demonstrate how it can be used to suppress RP-like edge effects and to improve the overall stability and accuracy. Topic 2. Although not as versatile as RBFs, cubic splines are useful for interpolating grid-based data. In 2-D, we consider a patch representation via Hermite basis functions s i,j ( u, v ) = [Special characters omitted.] h mn H m ( u ) H n ( v ), as opposed to the standard bicubic representation. Stitching requirements for the rectangular non-equispaced grid yield a 2-D tridiagonal linear system AX = B, where X represents the unknown first derivatives. We discover that the standard methods for solving this NxM system do not take advantage of the spline-specific format of the matrix B. We develop an alternative approach using this specialization of the RHS, which allows us to pre-compute coefficients only once, instead of N times. MATLAB implementation of our fast 2-D cubic spline algorithm is provided. We confirm analytically and numerically that for large N ( N > 200), our method is at least 3 times faster than the standard algorithm and is just as accurate. Topic 3. The well-known ADI-FDTD method for solving Maxwell's curl equations is second-order accurate in space/time, unconditionally stable, and computationally efficient. We research Richardson extrapolation -based techniques to improve time discretization accuracy for spatially oversampled ADI-FDTD. A careful analysis of temporal accuracy, computational efficiency, and the algorithm's overall stability is presented. Given the context of wave- type PDEs, we find that only a limited number of extrapolations to the ADI-FDTD method are beneficial, if its unconditional stability is to be preserved. We propose a practical approach for choosing the size of a time step that can be used to improve the efficiency of the ADI-FDTD algorithm, while maintaining its accuracy and stability. Topic 4. Shock waves and their energy dissipation properties are critical to understanding the dynamics controlling the MHD turbulence. Numerical advection algorithms used in MHD solvers (e.g. the ZEUS package) introduce undesirable numerical viscosity. To counteract its effects and to resolve shocks numerically, Richtmyer and von Neumann's artificial viscosity is commonly added to the model. We study shock power by analyzing the influence of both artificial and numerical viscosity on energy decay rates. Also, we analytically characterize the numerical diffusivity of various advection algorithms by quantifying their diffusion coefficients e.

Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

NASA Astrophysics Data System (ADS)

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-11-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

Tests of a Semi-Analytical Case 1 and Gelbstoff Case 2 SeaWiFS Algorithm with a Global Data Set

NASA Technical Reports Server (NTRS)

Carder, Kendall L.; Hawes, Steve K.; Lee, Zhongping

1997-01-01

A semi-analytical algorithm was tested with a total of 733 points of either unpackaged or packaged-pigment data, with corresponding algorithm parameters for each data type. The 'unpackaged' type consisted of data sets that were generally consistent with the Case 1 CZCS algorithm and other well calibrated data sets. The 'packaged' type consisted of data sets apparently containing somewhat more packaged pigments, requiring modification of the absorption parameters of the model consistent with the CalCOFI study area. This resulted in two equally divided data sets. A more thorough scrutiny of these and other data sets using a semianalytical model requires improved knowledge of the phytoplankton and gelbstoff of the specific environment studied. Since the semi-analytical algorithm is dependent upon 4 spectral channels including the 412 nm channel, while most other algorithms are not, a means of testing data sets for consistency was sought. A numerical filter was developed to classify data sets into the above classes. The filter uses reflectance ratios, which can be determined from space. The sensitivity of such numerical filters to measurement resulting from atmospheric correction and sensor noise errors requires further study. The semi-analytical algorithm performed superbly on each of the data sets after classification, resulting in RMS1 errors of 0.107 and 0.121, respectively, for the unpackaged and packaged data-set classes, with little bias and slopes near 1.0. In combination, the RMS1 performance was 0.114. While these numbers appear rather sterling, one must bear in mind what mis-classification does to the results. Using an average or compromise parameterization on the modified global data set yielded an RMS1 error of 0.171, while using the unpackaged parameterization on the global evaluation data set yielded an RMS1 error of 0.284. So, without classification, the algorithm performs better globally using the average parameters than it does using the unpackaged parameters. Finally, the effects of even more extreme pigment packaging must be examined in order to improve algorithm performance at high latitudes. Note, however, that the North Sea and Mississippi River plume studies contributed data to the packaged and unpackaged classess, respectively, with little effect on algorithm performance. This suggests that gelbstoff-rich Case 2 waters do not seriously degrade performance of the semi-analytical algorithm.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

NASA Astrophysics Data System (ADS)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

A loop-counting method for covariate-corrected low-rank biclustering of gene-expression and genome-wide association study data.

PubMed

Rangan, Aaditya V; McGrouther, Caroline C; Kelsoe, John; Schork, Nicholas; Stahl, Eli; Zhu, Qian; Krishnan, Arjun; Yao, Vicky; Troyanskaya, Olga; Bilaloglu, Seda; Raghavan, Preeti; Bergen, Sarah; Jureus, Anders; Landen, Mikael

2018-05-14

A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices (i.e., 'loops') within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS).

influx_s: increasing numerical stability and precision for metabolic flux analysis in isotope labelling experiments.

PubMed

Sokol, Serguei; Millard, Pierre; Portais, Jean-Charles

2012-03-01

The problem of stationary metabolic flux analysis based on isotope labelling experiments first appeared in the early 1950s and was basically solved in early 2000s. Several algorithms and software packages are available for this problem. However, the generic stochastic algorithms (simulated annealing or evolution algorithms) currently used in these software require a lot of time to achieve acceptable precision. For deterministic algorithms, a common drawback is the lack of convergence stability for ill-conditioned systems or when started from a random point. In this article, we present a new deterministic algorithm with significantly increased numerical stability and accuracy of flux estimation compared with commonly used algorithms. It requires relatively short CPU time (from several seconds to several minutes with a standard PC architecture) to estimate fluxes in the central carbon metabolism network of Escherichia coli. The software package influx_s implementing this algorithm is distributed under an OpenSource licence at http://metasys.insa-toulouse.fr/software/influx/. Supplementary data are available at Bioinformatics online.

Image reconstruction algorithms for electrical capacitance tomography based on ROF model using new numerical techniques

NASA Astrophysics Data System (ADS)

Chen, Jiaoxuan; Zhang, Maomao; Liu, Yinyan; Chen, Jiaoliao; Li, Yi

2017-03-01

Electrical capacitance tomography (ECT) is a promising technique applied in many fields. However, the solutions for ECT are not unique and highly sensitive to the measurement noise. To remain a good shape of reconstructed object and endure a noisy data, a Rudin-Osher-Fatemi (ROF) model with total variation regularization is applied to image reconstruction in ECT. Two numerical methods, which are simplified augmented Lagrangian (SAL) and accelerated alternating direction method of multipliers (AADMM), are innovatively introduced to try to solve the above mentioned problems in ECT. The effect of the parameters and the number of iterations for different algorithms, and the noise level in capacitance data are discussed. Both simulation and experimental tests were carried out to validate the feasibility of the proposed algorithms, compared to the Landweber iteration (LI) algorithm. The results show that the SAL and AADMM algorithms can handle a high level of noise and the AADMM algorithm outperforms other algorithms in identifying the object from its background.

Analytic reconstruction algorithms for triple-source CT with horizontal data truncation

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

Chen, Ming; Yu, Hengyong, E-mail: hengyong-yu@ieee.org

2015-10-15

Purpose: This paper explores a triple-source imaging method with horizontal data truncation to enlarge the field of view (FOV) for big objects. Methods: The study is conducted by using theoretical analysis, mathematical deduction, and numerical simulations. The proposed algorithms are implemented in c + + and MATLAB. While the basic platform is constructed in MATLAB, the computationally intensive segments are coded in c + +, which are linked via a MEX interface. Results: A triple-source circular scanning configuration with horizontal data truncation is developed, where three pairs of x-ray sources and detectors are unevenly distributed on the same circle tomore » cover the whole imaging object. For this triple-source configuration, a fan-beam filtered backprojection-type algorithm is derived for truncated full-scan projections without data rebinning. The algorithm is also extended for horizontally truncated half-scan projections and cone-beam projections in a Feldkamp-type framework. Using their method, the FOV is enlarged twofold to threefold to scan bigger objects with high speed and quality. The numerical simulation results confirm the correctness and effectiveness of the developed algorithms. Conclusions: The triple-source scanning configuration with horizontal data truncation cannot only keep most of the advantages of a traditional multisource system but also cover a larger FOV for big imaging objects. In addition, because the filtering is shift-invariant, the proposed algorithms are very fast and easily parallelized on graphic processing units.« less

Analytic reconstruction algorithms for triple-source CT with horizontal data truncation.

PubMed

Chen, Ming; Yu, Hengyong

2015-10-01

This paper explores a triple-source imaging method with horizontal data truncation to enlarge the field of view (FOV) for big objects. The study is conducted by using theoretical analysis, mathematical deduction, and numerical simulations. The proposed algorithms are implemented in c + + and matlab. While the basic platform is constructed in matlab, the computationally intensive segments are coded in c + +, which are linked via a mex interface. A triple-source circular scanning configuration with horizontal data truncation is developed, where three pairs of x-ray sources and detectors are unevenly distributed on the same circle to cover the whole imaging object. For this triple-source configuration, a fan-beam filtered backprojection-type algorithm is derived for truncated full-scan projections without data rebinning. The algorithm is also extended for horizontally truncated half-scan projections and cone-beam projections in a Feldkamp-type framework. Using their method, the FOV is enlarged twofold to threefold to scan bigger objects with high speed and quality. The numerical simulation results confirm the correctness and effectiveness of the developed algorithms. The triple-source scanning configuration with horizontal data truncation cannot only keep most of the advantages of a traditional multisource system but also cover a larger FOV for big imaging objects. In addition, because the filtering is shift-invariant, the proposed algorithms are very fast and easily parallelized on graphic processing units.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

A multistage time-stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1985-01-01

A class of explicit multistage time-stepping schemes is used to construct an algorithm for solving the compressible Navier-Stokes equations. Flexibility in treating arbitrary geometries is obtained with a finite-volume formulation. Numerical efficiency is achieved by employing techniques for accelerating convergence to steady state. Computer processing is enhanced through vectorization of the algorithm. The scheme is evaluated by solving laminar and turbulent flows over a flat plate and an NACA 0012 airfoil. Numerical results are compared with theoretical solutions or other numerical solutions and/or experimental data.

Analytical and numerical analysis of frictional damage in quasi brittle materials

NASA Astrophysics Data System (ADS)

Zhu, Q. Z.; Zhao, L. Y.; Shao, J. F.

2016-07-01

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori-Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress-strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

Development of a new metal artifact reduction algorithm by using an edge preserving method for CBCT imaging

NASA Astrophysics Data System (ADS)

Kim, Juhye; Nam, Haewon; Lee, Rena

2015-07-01

CT (computed tomography) images, metal materials such as tooth supplements or surgical clips can cause metal artifact and degrade image quality. In severe cases, this may lead to misdiagnosis. In this research, we developed a new MAR (metal artifact reduction) algorithm by using an edge preserving filter and the MATLAB program (Mathworks, version R2012a). The proposed algorithm consists of 6 steps: image reconstruction from projection data, metal segmentation, forward projection, interpolation, applied edge preserving smoothing filter, and new image reconstruction. For an evaluation of the proposed algorithm, we obtained both numerical simulation data and data for a Rando phantom. In the numerical simulation data, four metal regions were added into the Shepp Logan phantom for metal artifacts. The projection data of the metal-inserted Rando phantom were obtained by using a prototype CBCT scanner manufactured by medical engineering and medical physics (MEMP) laboratory research group in medical science at Ewha Womans University. After these had been adopted the proposed algorithm was performed, and the result were compared with the original image (with metal artifact without correction) and with a corrected image based on linear interpolation. Both visual and quantitative evaluations were done. Compared with the original image with metal artifacts and with the image corrected by using linear interpolation, both the numerical and the experimental phantom data demonstrated that the proposed algorithm reduced the metal artifact. In conclusion, the evaluation in this research showed that the proposed algorithm outperformed the interpolation based MAR algorithm. If an optimization and a stability evaluation of the proposed algorithm can be performed, the developed algorithm is expected to be an effective tool for eliminating metal artifacts even in commercial CT systems.

A Food Chain Algorithm for Capacitated Vehicle Routing Problem with Recycling in Reverse Logistics

NASA Astrophysics Data System (ADS)

Song, Qiang; Gao, Xuexia; Santos, Emmanuel T.

2015-12-01

This paper introduces the capacitated vehicle routing problem with recycling in reverse logistics, and designs a food chain algorithm for it. Some illustrative examples are selected to conduct simulation and comparison. Numerical results show that the performance of the food chain algorithm is better than the genetic algorithm, particle swarm optimization as well as quantum evolutionary algorithm.

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, W. R.; Nguyen, D. T.; Reddy, C. J.; Vatsa, V. N.; Tang, W. H.

2001-01-01

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Seeding the initial population with feasible solutions in metaheuristic optimization of steel trusses

NASA Astrophysics Data System (ADS)

Kazemzadeh Azad, Saeid

2018-01-01

In spite of considerable research work on the development of efficient algorithms for discrete sizing optimization of steel truss structures, only a few studies have addressed non-algorithmic issues affecting the general performance of algorithms. For instance, an important question is whether starting the design optimization from a feasible solution is fruitful or not. This study is an attempt to investigate the effect of seeding the initial population with feasible solutions on the general performance of metaheuristic techniques. To this end, the sensitivity of recently proposed metaheuristic algorithms to the feasibility of initial candidate designs is evaluated through practical discrete sizing of real-size steel truss structures. The numerical experiments indicate that seeding the initial population with feasible solutions can improve the computational efficiency of metaheuristic structural optimization algorithms, especially in the early stages of the optimization. This paves the way for efficient metaheuristic optimization of large-scale structural systems.

PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release

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

Pizzocri, D.; Rabiti, C.; Luzzi, L.

2016-09-01

This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of themore » corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.« less

NOTE: A BPF-type algorithm for CT with a curved PI detector

NASA Astrophysics Data System (ADS)

Tang, Jie; Zhang, Li; Chen, Zhiqiang; Xing, Yuxiang; Cheng, Jianping

2006-08-01

Helical cone-beam CT is used widely nowadays because of its rapid scan speed and efficient utilization of x-ray dose. Recently, an exact reconstruction algorithm for helical cone-beam CT was proposed (Zou and Pan 2004a Phys. Med. Biol. 49 941 59). The algorithm is referred to as a backprojection-filtering (BPF) algorithm. This BPF algorithm for a helical cone-beam CT with a flat-panel detector (FPD-HCBCT) requires minimum data within the Tam Danielsson window and can naturally address the problem of ROI reconstruction from data truncated in both longitudinal and transversal directions. In practical CT systems, detectors are expensive and always take a very important position in the total cost. Hence, we work on an exact reconstruction algorithm for a CT system with a detector of the smallest size, i.e., a curved PI detector fitting the Tam Danielsson window. The reconstruction algorithm is derived following the framework of the BPF algorithm. Numerical simulations are done to validate our algorithm in this study.

A BPF-type algorithm for CT with a curved PI detector.

PubMed

Tang, Jie; Zhang, Li; Chen, Zhiqiang; Xing, Yuxiang; Cheng, Jianping

2006-08-21

Helical cone-beam CT is used widely nowadays because of its rapid scan speed and efficient utilization of x-ray dose. Recently, an exact reconstruction algorithm for helical cone-beam CT was proposed (Zou and Pan 2004a Phys. Med. Biol. 49 941-59). The algorithm is referred to as a backprojection-filtering (BPF) algorithm. This BPF algorithm for a helical cone-beam CT with a flat-panel detector (FPD-HCBCT) requires minimum data within the Tam-Danielsson window and can naturally address the problem of ROI reconstruction from data truncated in both longitudinal and transversal directions. In practical CT systems, detectors are expensive and always take a very important position in the total cost. Hence, we work on an exact reconstruction algorithm for a CT system with a detector of the smallest size, i.e., a curved PI detector fitting the Tam-Danielsson window. The reconstruction algorithm is derived following the framework of the BPF algorithm. Numerical simulations are done to validate our algorithm in this study.

Efficient calculation of higher-order optical waveguide dispersion.

PubMed

Mores, J A; Malheiros-Silveira, G N; Fragnito, H L; Hernández-Figueroa, H E

2010-09-13

An efficient numerical strategy to compute the higher-order dispersion parameters of optical waveguides is presented. For the first time to our knowledge, a systematic study of the errors involved in the higher-order dispersions' numerical calculation process is made, showing that the present strategy can accurately model those parameters. Such strategy combines a full-vectorial finite element modal solver and a proper finite difference differentiation algorithm. Its performance has been carefully assessed through the analysis of several key geometries. In addition, the optimization of those higher-order dispersion parameters can also be carried out by coupling to the present scheme a genetic algorithm, as shown here through the design of a photonic crystal fiber suitable for parametric amplification applications.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Numerical algorithm for rigid body position estimation using the quaternion approach

NASA Astrophysics Data System (ADS)

Zigic, Miodrag; Grahovac, Nenad

2017-11-01

This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

NASA Astrophysics Data System (ADS)

Bartuccelli, Michele; Deane, Jonathan; Gentile, Guido

2017-08-01

We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C^1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 10^6-10^7 years. The proposed algorithm is based on the high-order Euler method which was described in Bartuccelli et al. (Celest Mech Dyn Astron 121(3):233-260, 2015), and it requires computer algebra to set up the code for its implementation. The payoff is an overall increase in speed by a factor of about 7.5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Application of symbolic/numeric matrix solution techniques to the NASTRAN program

NASA Technical Reports Server (NTRS)

Buturla, E. M.; Burroughs, S. H.

1977-01-01

The matrix solving algorithm of any finite element algorithm is extremely important since solution of the matrix equations requires a large amount of elapse time due to null calculations and excessive input/output operations. An alternate method of solving the matrix equations is presented. A symbolic processing step followed by numeric solution yields the solution very rapidly and is especially useful for nonlinear problems.

A sensitivity equation approach to shape optimization in fluid flows

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1994-01-01

A sensitivity equation method to shape optimization problems is applied. An algorithm is developed and tested on a problem of designing optimal forebody simulators for a 2D, inviscid supersonic flow. The algorithm uses a BFGS/Trust Region optimization scheme with sensitivities computed by numerically approximating the linear partial differential equations that determine the flow sensitivities. Numerical examples are presented to illustrate the method.

Loading relativistic Maxwell distributions in particle simulations

NASA Astrophysics Data System (ADS)

Zenitani, S.

2015-12-01

In order to study energetic plasma phenomena by using particle-in-cell (PIC) and Monte-Carlo simulations, we need to deal with relativistic velocity distributions in these simulations. However, numerical algorithms to deal with relativistic distributions are not well known. In this contribution, we overview basic algorithms to load relativistic Maxwell distributions in PIC and Monte-Carlo simulations. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are newly proposed in a physically transparent manner. Their acceptance efficiencies are 􏰅50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.

Fuzzy logic-based approach to detecting a passive RFID tag in an outpatient clinic.

PubMed

Min, Daiki; Yih, Yuehwern

2011-06-01

This study is motivated by the observations on the data collected by radio frequency identification (RFID) readers in a pilot study, which was used to investigate the feasibility of implementing an RFID-based monitoring system in an outpatient eye clinic. The raw RFID data collected from RFID readers contain noise and missing reads, which prevent us from determining the tag location. In this paper, fuzzy logic-based algorithms are proposed to interpret the raw RFID data to extract accurate information. The proposed algorithms determine the location of an RFID tag by evaluating its possibility of presence and absence. To evaluate the performance of the proposed algorithms, numerical experiments are conducted using the data observed in the outpatient eye clinic. Experiments results showed that the proposed algorithms outperform existing static smoothing method in terms of minimizing both false positives and false negatives. Furthermore, the proposed algorithms are applied to a set of simulated data to show the robustness of the proposed algorithms at various levels of RFID reader reliability.

Three-Dimensional Imaging and Numerical Reconstruction of Graphite/Epoxy Composite Microstructure Based on Ultra-High Resolution X-Ray Computed Tomography

NASA Technical Reports Server (NTRS)

Czabaj, M. W.; Riccio, M. L.; Whitacre, W. W.

2014-01-01

A combined experimental and computational study aimed at high-resolution 3D imaging, visualization, and numerical reconstruction of fiber-reinforced polymer microstructures at the fiber length scale is presented. To this end, a sample of graphite/epoxy composite was imaged at sub-micron resolution using a 3D X-ray computed tomography microscope. Next, a novel segmentation algorithm was developed, based on concepts adopted from computer vision and multi-target tracking, to detect and estimate, with high accuracy, the position of individual fibers in a volume of the imaged composite. In the current implementation, the segmentation algorithm was based on Global Nearest Neighbor data-association architecture, a Kalman filter estimator, and several novel algorithms for virtualfiber stitching, smoothing, and overlap removal. The segmentation algorithm was used on a sub-volume of the imaged composite, detecting 508 individual fibers. The segmentation data were qualitatively compared to the tomographic data, demonstrating high accuracy of the numerical reconstruction. Moreover, the data were used to quantify a) the relative distribution of individual-fiber cross sections within the imaged sub-volume, and b) the local fiber misorientation relative to the global fiber axis. Finally, the segmentation data were converted using commercially available finite element (FE) software to generate a detailed FE mesh of the composite volume. The methodology described herein demonstrates the feasibility of realizing an FE-based, virtual-testing framework for graphite/fiber composites at the constituent level.

New algorithm and system for measuring size distribution of blood cells

NASA Astrophysics Data System (ADS)

Yao, Cuiping; Li, Zheng; Zhang, Zhenxi

2004-06-01

In optical scattering particle sizing, a numerical transform is sought so that a particle size distribution can be determined from angular measurements of near forward scattering, which has been adopted in the measurement of blood cells. In this paper a new method of counting and classification of blood cell, laser light scattering method from stationary suspensions, is presented. The genetic algorithm combined with nonnegative least squared algorithm is employed to inverse the size distribution of blood cells. Numerical tests show that these techniques can be successfully applied to measuring size distribution of blood cell with high stability.

On the impact of communication complexity on the design of parallel numerical algorithms

NASA Technical Reports Server (NTRS)

Gannon, D. B.; Van Rosendale, J.

1984-01-01

This paper describes two models of the cost of data movement in parallel numerical alorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In this second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm-independent upper bounds on system performance are derived for several problems that are important to scientific computation.

An extension of the QZ algorithm for solving the generalized matrix eigenvalue problem

NASA Technical Reports Server (NTRS)

Ward, R. C.

1973-01-01

This algorithm is an extension of Moler and Stewart's QZ algorithm with some added features for saving time and operations. Also, some additional properties of the QR algorithm which were not practical to implement in the QZ algorithm can be generalized with the combination shift QZ algorithm. Numerous test cases are presented to give practical application tests for algorithm. Based on results, this algorithm should be preferred over existing algorithms which attempt to solve the class of generalized eigenproblems where both matrices are singular or nearly singular.

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.

Final Technical Report [Scalable methods for electronic excitations and optical responses of nanostructures: mathematics to algorithms to observables

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

Saad, Yousef

2014-03-19

The master project under which this work is funded had as its main objective to develop computational methods for modeling electronic excited-state and optical properties of various nanostructures. The specific goals of the computer science group were primarily to develop effective numerical algorithms in Density Functional Theory (DFT) and Time Dependent Density Functional Theory (TDDFT). There were essentially four distinct stated objectives. The first objective was to study and develop effective numerical algorithms for solving large eigenvalue problems such as those that arise in Density Functional Theory (DFT) methods. The second objective was to explore so-called linear scaling methods ormore » Methods that avoid diagonalization. The third was to develop effective approaches for Time-Dependent DFT (TDDFT). Our fourth and final objective was to examine effective solution strategies for other problems in electronic excitations, such as the GW/Bethe-Salpeter method, and quantum transport problems.« less

Estimation of interfacial heat transfer coefficient in inverse heat conduction problems based on artificial fish swarm algorithm

NASA Astrophysics Data System (ADS)

Wang, Xiaowei; Li, Huiping; Li, Zhichao

2018-04-01

The interfacial heat transfer coefficient (IHTC) is one of the most important thermal physical parameters which have significant effects on the calculation accuracy of physical fields in the numerical simulation. In this study, the artificial fish swarm algorithm (AFSA) was used to evaluate the IHTC between the heated sample and the quenchant in a one-dimensional heat conduction problem. AFSA is a global optimization method. In order to speed up the convergence speed, a hybrid method which is the combination of AFSA and normal distribution method (ZAFSA) was presented. The IHTC evaluated by ZAFSA were compared with those attained by AFSA and the advanced-retreat method and golden section method. The results show that the reasonable IHTC is obtained by using ZAFSA, the convergence of hybrid method is well. The algorithm based on ZAFSA can not only accelerate the convergence speed, but also reduce the numerical oscillation in the evaluation of IHTC.

Optimal design of solidification processes

NASA Technical Reports Server (NTRS)

Dantzig, Jonathan A.; Tortorelli, Daniel A.

1991-01-01

An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem.

Numerical investigation of field enhancement by metal nano-particles using a hybrid FDTD-PSTD algorithm.

PubMed

Pernice, W H; Payne, F P; Gallagher, D F

2007-09-03

We present a novel numerical scheme for the simulation of the field enhancement by metal nano-particles in the time domain. The algorithm is based on a combination of the finite-difference time-domain method and the pseudo-spectral time-domain method for dispersive materials. The hybrid solver leads to an efficient subgridding algorithm that does not suffer from spurious field spikes as do FDTD schemes. Simulation of the field enhancement by gold particles shows the expected exponential field profile. The enhancement factors are computed for single particles and particle arrays. Due to the geometry conforming mesh the algorithm is stable for long integration times and thus suitable for the simulation of resonance phenomena in coupled nano-particle structures.

Genetic algorithms for the vehicle routing problem

NASA Astrophysics Data System (ADS)

Volna, Eva

2016-06-01

The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing the optimal set of routes for fleet of vehicles in order to serve a given set of customers. Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper we have performed an experimental study that indicates the suitable use of genetic algorithms for the vehicle routing problem.

The high performance parallel algorithm for Unified Gas-Kinetic Scheme

NASA Astrophysics Data System (ADS)

Li, Shiyi; Li, Qibing; Fu, Song; Xu, Jinxiu

2016-11-01

A high performance parallel algorithm for UGKS is developed to simulate three-dimensional flows internal and external on arbitrary grid system. The physical domain and velocity domain are divided into different blocks and distributed according to the two-dimensional Cartesian topology with intra-communicators in physical domain for data exchange and other intra-communicators in velocity domain for sum reduction to moment integrals. Numerical results of three-dimensional cavity flow and flow past a sphere agree well with the results from the existing studies and validate the applicability of the algorithm. The scalability of the algorithm is tested both on small (1-16) and large (729-5832) scale processors. The tested speed-up ratio is near linear ashind thus the efficiency is around 1, which reveals the good scalability of the present algorithm.

Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems

DOE PAGES

Chen, Qiang; Qin, Hong; Liu, Jian; ...

2017-08-24

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

Comparison Study of Three Different Image Reconstruction Algorithms for MAT-MI

PubMed Central

Xia, Rongmin; Li, Xu

2010-01-01

We report a theoretical study on magnetoacoustic tomography with magnetic induction (MAT-MI). According to the description of signal generation mechanism using Green’s function, the acoustic dipole model was proposed to describe acoustic source excited by the Lorentz force. Using Green’s function, three kinds of reconstruction algorithms based on different models of acoustic source (potential energy, vectored acoustic pressure, and divergence of Lorenz force) are deduced and compared, and corresponding numerical simulations were conducted to compare these three kinds of reconstruction algorithms. The computer simulation results indicate that the potential energy method and vectored pressure method can directly reconstruct the Lorentz force distribution and give a more accurate reconstruction of electrical conductivity. PMID:19846363

Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence

NASA Astrophysics Data System (ADS)

Belli, Emily Ann

Advanced numerical algorithms for gyrokinetic simulations are explored for more effective studies of plasma turbulent transport. The gyrokinetic equations describe the dynamics of particles in 5-dimensional phase space, averaging over the fast gyromotion, and provide a foundation for studying plasma microturbulence in fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/continuum gyrokinetic solvers are compared. An iterative implicit scheme based on numerical approximations of the plasma response is developed. This method reduces the long time needed to set-up implicit arrays, yet still has larger time step advantages similar to a fully implicit method. Various model preconditioners and iteration schemes, including Krylov-based solvers, are explored. An Alternating Direction Implicit algorithm is also studied and is surprisingly found to yield a severe stability restriction on the time step. Overall, an iterative Krylov algorithm might be the best approach for extensions of core tokamak gyrokinetic simulations to edge kinetic formulations and may be particularly useful for studies of large-scale ExB shear effects. The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic equilibria based on interpolations of representative JET-like shapes. High shaping is found to be a stabilizing influence on both the linear ITG instability and nonlinear ITG turbulence. A scaling of the heat flux with elongation of chi ˜ kappa-1.5 or kappa-2 (depending on the triangularity) is observed, which is consistent with previous gyrofluid simulations. Thus, the GS2 turbulence simulations are explaining a significant fraction, but not all, of the empirical elongation scaling. The remainder of the scaling may come from (1) the edge boundary conditions for core turbulence, and (2) the larger Dimits nonlinear critical temperature gradient shift due to the enhancement of zonal flows with shaping, which is observed with the GS2 simulations. Finally, a local linear trial function-based gyrokinetic code is developed to aid in fast scoping studies of gyrokinetic linear stability. This code is successfully benchmarked with the full GS2 code in the collisionless, electrostatic limit, as well as in the more general electromagnetic description with higher-order Hermite basis functions.

Mountain bicycle frame testing as an example of practical implementation of hybrid simulation using RTFEM

NASA Astrophysics Data System (ADS)

Mucha, Waldemar; Kuś, Wacław

2018-01-01

The paper presents a practical implementation of hybrid simulation using Real Time Finite Element Method (RTFEM). Hybrid simulation is a technique for investigating dynamic material and structural properties of mechanical systems by performing numerical analysis and experiment at the same time. It applies to mechanical systems with elements too difficult or impossible to model numerically. These elements are tested experimentally, while the rest of the system is simulated numerically. Data between the experiment and numerical simulation are exchanged in real time. Authors use Finite Element Method to perform the numerical simulation. The following paper presents the general algorithm for hybrid simulation using RTFEM and possible improvements of the algorithm for computation time reduction developed by the authors. The paper focuses on practical implementation of presented methods, which involves testing of a mountain bicycle frame, where the shock absorber is tested experimentally while the rest of the frame is simulated numerically.

Heuristics and biases: interactions among numeracy, ability, and reflectiveness predict normative responding

PubMed Central

Klaczynski, Paul A.

2014-01-01

In Stanovich's (2009a, 2011) dual-process theory, analytic processing occurs in the algorithmic and reflective minds. Thinking dispositions, indexes of reflective mind functioning, are believed to regulate operations at the algorithmic level, indexed by general cognitive ability. General limitations at the algorithmic level impose constraints on, and affect the adequacy of, specific strategies and abilities (e.g., numeracy). In a study of 216 undergraduates, the hypothesis that thinking dispositions and general ability moderate the relationship between numeracy (understanding of mathematical concepts and attention to numerical information) and normative responses on probabilistic heuristics and biases (HB) problems was tested. Although all three individual difference measures predicted normative responses, the numeracy-normative response association depended on thinking dispositions and general ability. Specifically, numeracy directly affected normative responding only at relatively high levels of thinking dispositions and general ability. At low levels of thinking dispositions, neither general ability nor numeric skills related to normative responses. Discussion focuses on the consistency of these findings with the hypothesis that the implementation of specific skills is constrained by limitations at both the reflective level and the algorithmic level, methodological limitations that prohibit definitive conclusions, and alternative explanations. PMID:25071639

Uniqueness and reconstruction in magnetic resonance-electrical impedance tomography (MR-EIT).

PubMed

Ider, Y Ziya; Onart, Serkan; Lionheart, William R B

2003-05-01

Magnetic resonance-electrical impedance tomography (MR-EIT) was first proposed in 1992. Since then various reconstruction algorithms have been suggested and applied. These algorithms use peripheral voltage measurements and internal current density measurements in different combinations. In this study the problem of MR-EIT is treated as a hyperbolic system of first-order partial differential equations, and three numerical methods are proposed for its solution. This approach is not utilized in any of the algorithms proposed earlier. The numerical solution methods are integration along equipotential surfaces (method of characteristics), integration on a Cartesian grid, and inversion of a system matrix derived by a finite difference formulation. It is shown that if some uniqueness conditions are satisfied, then using at least two injected current patterns, resistivity can be reconstructed apart from a multiplicative constant. This constant can then be identified using a single voltage measurement. The methods proposed are direct, non-iterative, and valid and feasible for 3D reconstructions. They can also be used to easily obtain slice and field-of-view images from a 3D object. 2D simulations are made to illustrate the performance of the algorithms.

Heuristics and biases: interactions among numeracy, ability, and reflectiveness predict normative responding.

PubMed

Klaczynski, Paul A

2014-01-01

In Stanovich's (2009a, 2011) dual-process theory, analytic processing occurs in the algorithmic and reflective minds. Thinking dispositions, indexes of reflective mind functioning, are believed to regulate operations at the algorithmic level, indexed by general cognitive ability. General limitations at the algorithmic level impose constraints on, and affect the adequacy of, specific strategies and abilities (e.g., numeracy). In a study of 216 undergraduates, the hypothesis that thinking dispositions and general ability moderate the relationship between numeracy (understanding of mathematical concepts and attention to numerical information) and normative responses on probabilistic heuristics and biases (HB) problems was tested. Although all three individual difference measures predicted normative responses, the numeracy-normative response association depended on thinking dispositions and general ability. Specifically, numeracy directly affected normative responding only at relatively high levels of thinking dispositions and general ability. At low levels of thinking dispositions, neither general ability nor numeric skills related to normative responses. Discussion focuses on the consistency of these findings with the hypothesis that the implementation of specific skills is constrained by limitations at both the reflective level and the algorithmic level, methodological limitations that prohibit definitive conclusions, and alternative explanations.

Algorithms for the Fractional Calculus: A Selection of Numerical Methods

NASA Technical Reports Server (NTRS)

Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.

2003-01-01

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

KAM Tori Construction Algorithms

NASA Astrophysics Data System (ADS)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

A composite experimental dynamic substructuring method based on partitioned algorithms and localized Lagrange multipliers

NASA Astrophysics Data System (ADS)

Abbiati, Giuseppe; La Salandra, Vincenzo; Bursi, Oreste S.; Caracoglia, Luca

2018-02-01

Successful online hybrid (numerical/physical) dynamic substructuring simulations have shown their potential in enabling realistic dynamic analysis of almost any type of non-linear structural system (e.g., an as-built/isolated viaduct, a petrochemical piping system subjected to non-stationary seismic loading, etc.). Moreover, owing to faster and more accurate testing equipment, a number of different offline experimental substructuring methods, operating both in time (e.g. the impulse-based substructuring) and frequency domains (i.e. the Lagrange multiplier frequency-based substructuring), have been employed in mechanical engineering to examine dynamic substructure coupling. Numerous studies have dealt with the above-mentioned methods and with consequent uncertainty propagation issues, either associated with experimental errors or modelling assumptions. Nonetheless, a limited number of publications have systematically cross-examined the performance of the various Experimental Dynamic Substructuring (EDS) methods and the possibility of their exploitation in a complementary way to expedite a hybrid experiment/numerical simulation. From this perspective, this paper performs a comparative uncertainty propagation analysis of three EDS algorithms for coupling physical and numerical subdomains with a dual assembly approach based on localized Lagrange multipliers. The main results and comparisons are based on a series of Monte Carlo simulations carried out on a five-DoF linear/non-linear chain-like systems that include typical aleatoric uncertainties emerging from measurement errors and excitation loads. In addition, we propose a new Composite-EDS (C-EDS) method to fuse both online and offline algorithms into a unique simulator. Capitalizing from the results of a more complex case study composed of a coupled isolated tank-piping system, we provide a feasible way to employ the C-EDS method when nonlinearities and multi-point constraints are present in the emulated system.

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.

Numerical taxonomy on data: Experimental results

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

Cohen, J.; Farach, M.

1997-12-01

The numerical taxonomy problems associated with most of the optimization criteria described above are NP - hard [3, 5, 1, 4]. In, the first positive result for numerical taxonomy was presented. They showed that if e is the distance to the closest tree metric under the L{sub {infinity}} norm. i.e., e = min{sub T} [L{sub {infinity}} (T-D)], then it is possible to construct a tree T such that L{sub {infinity}} (T-D) {le} 3e, that is, they gave a 3-approximation algorithm for this problem. We will refer to this algorithm as the Single Pivot (SP) heuristic.

Investigating power capping toward energy-efficient scientific applications: Investigating Power Capping toward Energy-Efficient Scientific Applications

DOE PAGES

Haidar, Azzam; Jagode, Heike; Vaccaro, Phil; ...

2018-03-22

The emergence of power efficiency as a primary constraint in processor and system design poses new challenges concerning power and energy awareness for numerical libraries and scientific applications. Power consumption also plays a major role in the design of data centers, which may house petascale or exascale-level computing systems. At these extreme scales, understanding and improving the energy efficiency of numerical libraries and their related applications becomes a crucial part of the successful implementation and operation of the computing system. In this paper, we study and investigate the practice of controlling a compute system's power usage, and we explore howmore » different power caps affect the performance of numerical algorithms with different computational intensities. Further, we determine the impact, in terms of performance and energy usage, that these caps have on a system running scientific applications. This analysis will enable us to characterize the types of algorithms that benefit most from these power management schemes. Our experiments are performed using a set of representative kernels and several popular scientific benchmarks. Lastly, we quantify a number of power and performance measurements and draw observations and conclusions that can be viewed as a roadmap to achieving energy efficiency in the design and execution of scientific algorithms.« less

Investigating power capping toward energy-efficient scientific applications: Investigating Power Capping toward Energy-Efficient Scientific Applications

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

Haidar, Azzam; Jagode, Heike; Vaccaro, Phil

The emergence of power efficiency as a primary constraint in processor and system design poses new challenges concerning power and energy awareness for numerical libraries and scientific applications. Power consumption also plays a major role in the design of data centers, which may house petascale or exascale-level computing systems. At these extreme scales, understanding and improving the energy efficiency of numerical libraries and their related applications becomes a crucial part of the successful implementation and operation of the computing system. In this paper, we study and investigate the practice of controlling a compute system's power usage, and we explore howmore » different power caps affect the performance of numerical algorithms with different computational intensities. Further, we determine the impact, in terms of performance and energy usage, that these caps have on a system running scientific applications. This analysis will enable us to characterize the types of algorithms that benefit most from these power management schemes. Our experiments are performed using a set of representative kernels and several popular scientific benchmarks. Lastly, we quantify a number of power and performance measurements and draw observations and conclusions that can be viewed as a roadmap to achieving energy efficiency in the design and execution of scientific algorithms.« less

High-order hydrodynamic algorithms for exascale computing

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

Morgan, Nathaniel Ray

Hydrodynamic algorithms are at the core of many laboratory missions ranging from simulating ICF implosions to climate modeling. The hydrodynamic algorithms commonly employed at the laboratory and in industry (1) typically lack requisite accuracy for complex multi- material vortical flows and (2) are not well suited for exascale computing due to poor data locality and poor FLOP/memory ratios. Exascale computing requires advances in both computer science and numerical algorithms. We propose to research the second requirement and create a new high-order hydrodynamic algorithm that has superior accuracy, excellent data locality, and excellent FLOP/memory ratios. This proposal will impact a broadmore » range of research areas including numerical theory, discrete mathematics, vorticity evolution, gas dynamics, interface instability evolution, turbulent flows, fluid dynamics and shock driven flows. If successful, the proposed research has the potential to radically transform simulation capabilities and help position the laboratory for computing at the exascale.« less

Maximum likelihood estimates, from censored data, for mixed-Weibull distributions

NASA Astrophysics Data System (ADS)

Jiang, Siyuan; Kececioglu, Dimitri

1992-06-01

A new algorithm for estimating the parameters of mixed-Weibull distributions from censored data is presented. The algorithm follows the principle of maximum likelihood estimate (MLE) through the expectation and maximization (EM) algorithm, and it is derived for both postmortem and nonpostmortem time-to-failure data. It is concluded that the concept of the EM algorithm is easy to understand and apply (only elementary statistics and calculus are required). The log-likelihood function cannot decrease after an EM sequence; this important feature was observed in all of the numerical calculations. The MLEs of the nonpostmortem data were obtained successfully for mixed-Weibull distributions with up to 14 parameters in a 5-subpopulation, mixed-Weibull distribution. Numerical examples indicate that some of the log-likelihood functions of the mixed-Weibull distributions have multiple local maxima; therefore, the algorithm should start at several initial guesses of the parameter set.

Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field

NASA Astrophysics Data System (ADS)

Zhang, Ruili; Wang, Yulei; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa

2018-02-01

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. The numerical simulation of relativistic dynamics is often multi-scale and requires accurate long-term numerical simulations. Therefore, explicit symplectic algorithms are much more preferable than non-symplectic methods and implicit symplectic algorithms. In this paper, we employ the proper time and express the Hamiltonian as the sum of exactly solvable terms and product-separable terms in space-time coordinates. Then, we give the explicit symplectic algorithms based on the generating functions of orders 2 and 3 for relativistic dynamics of a charged particle. The methodology is not new, which has been applied to non-relativistic dynamics of charged particles, but the algorithm for relativistic dynamics has much significance in practical simulations, such as the secular simulation of runaway electrons in tokamaks.

Physical and numerical studies of a fracture system model

NASA Astrophysics Data System (ADS)

Piggott, Andrew R.; Elsworth, Derek

1989-03-01

Physical and numerical studies of transient flow in a model of discretely fractured rock are presented. The physical model is a thermal analogue to fractured media flow consisting of idealized disc-shaped fractures. The numerical model is used to predict the behavior of the physical model. The use of different insulating materials to encase the physical model allows the effects of differing leakage magnitudes to be examined. A procedure for determining appropriate leakage parameters is documented. These parameters are used in forward analysis to predict the thermal response of the physical model. Knowledge of the leakage parameters and of the temporal variation of boundary conditions are shown to be essential to an accurate prediction. Favorable agreement is illustrated between numerical and physical results. The physical model provides a data source for the benchmarking of alternative numerical algorithms.

Ensemble-type numerical uncertainty information from single model integrations

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

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

A piloted simulator evaluation of a ground-based 4-D descent advisor algorithm

NASA Technical Reports Server (NTRS)

Davis, Thomas J.; Green, Steven M.; Erzberger, Heinz

1990-01-01

A ground-based, four dimensional (4D) descent-advisor algorithm is under development at NASA-Ames. The algorithm combines detailed aerodynamic, propulsive, and atmospheric models with an efficient numerical integration scheme to generate 4D descent advisories. The ability is investigated of the 4D descent advisor algorithm to provide adequate control of arrival time for aircraft not equipped with on-board 4D guidance systems. A piloted simulation was conducted to determine the precision with which the descent advisor could predict the 4D trajectories of typical straight-in descents flown by airline pilots under different wind conditions. The effects of errors in the estimation of wind and initial aircraft weight were also studied. A description of the descent advisor as well as the result of the simulation studies are presented.

The generalization ability of SVM classification based on Markov sampling.

PubMed

Xu, Jie; Tang, Yuan Yan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang; Zhang, Baochang

2015-06-01

The previously known works studying the generalization ability of support vector machine classification (SVMC) algorithm are usually based on the assumption of independent and identically distributed samples. In this paper, we go far beyond this classical framework by studying the generalization ability of SVMC based on uniformly ergodic Markov chain (u.e.M.c.) samples. We analyze the excess misclassification error of SVMC based on u.e.M.c. samples, and obtain the optimal learning rate of SVMC for u.e.M.c. We also introduce a new Markov sampling algorithm for SVMC to generate u.e.M.c. samples from given dataset, and present the numerical studies on the learning performance of SVMC based on Markov sampling for benchmark datasets. The numerical studies show that the SVMC based on Markov sampling not only has better generalization ability as the number of training samples are bigger, but also the classifiers based on Markov sampling are sparsity when the size of dataset is bigger with regard to the input dimension.

PNS predictions for supersonic/hypersonic flows over finned missile configurations

NASA Technical Reports Server (NTRS)

Bhutta, Bilal A.; Lewis, Clark H.

1992-01-01

Finned missile design entails accurate and computationally fast numerical techniques for predicting viscous flows over complex lifting configurations at small to moderate angles of attack and over Mach 3 to 15; these flows are often characterized by strong embedded shocks, so that numerical algorithms are also required to capture embedded shocks. The recent real-gas Flux Vector Splitting technique is here extended to investigate the Mach 3 flow over a typical finned missile configuration with/without side fin deflections. Elliptic grid-generation techniques for Mach 15 flows are shown to be inadequate for Mach 3 flows over finned configurations and need to be modified. Fin-deflection studies indicate that even small amounts of missile fin deflection can substantially modify vehicle aerodynamics. This 3D parabolized Navier-Stokes scheme is also extended into an efficient embedded algorithm for studying small axially separated flow regions due to strong fin and control surface deflections.

Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

NASA Technical Reports Server (NTRS)

Sun, Xian-He

1997-01-01

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

Bulk refrigeration of fruits and vegetables. Part 2: Computer algorithm for heat loads and moisture loss

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

Becker, B.; Misra, A.; Fricke, B.A.

1997-12-31

A computer algorithm was developed that estimates the latent and sensible heat loads due to the bulk refrigeration of fruits and vegetables. The algorithm also predicts the commodity moisture loss and temperature distribution which occurs during refrigeration. Part 1 focused upon the thermophysical properties of commodities and the flowfield parameters which govern the heat and mass transfer from fresh fruits and vegetables. This paper, Part 2, discusses the modeling methodology utilized in the current computer algorithm and describes the development of the heat and mass transfer models. Part 2 also compares the results of the computer algorithm to experimental datamore » taken from the literature and describes a parametric study which was performed with the algorithm. In addition, this paper also reviews existing numerical models for determining the heat and mass transfer in bulk loads of fruits and vegetables.« less

Numerical parametric studies of spray combustion instability

NASA Technical Reports Server (NTRS)

Pindera, M. Z.

1993-01-01

A coupled numerical algorithm has been developed for studies of combustion instabilities in spray-driven liquid rocket engines. The model couples gas and liquid phase physics using the method of fractional steps. Also introduced is a novel, efficient methodology for accounting for spray formation through direct solution of liquid phase equations. Preliminary parametric studies show marked sensitivity of spray penetration and geometry to droplet diameter, considerations of liquid core, and acoustic interactions. Less sensitivity was shown to the combustion model type although more rigorous (multi-step) formulations may be needed for the differences to become apparent.

New Parallel Algorithms for Landscape Evolution Model

NASA Astrophysics Data System (ADS)

Jin, Y.; Zhang, H.; Shi, Y.

2017-12-01

Most landscape evolution models (LEM) developed in the last two decades solve the diffusion equation to simulate the transportation of surface sediments. This numerical approach is difficult to parallelize due to the computation of drainage area for each node, which needs huge amount of communication if run in parallel. In order to overcome this difficulty, we developed two parallel algorithms for LEM with a stream net. One algorithm handles the partition of grid with traditional methods and applies an efficient global reduction algorithm to do the computation of drainage areas and transport rates for the stream net; the other algorithm is based on a new partition algorithm, which partitions the nodes in catchments between processes first, and then partitions the cells according to the partition of nodes. Both methods focus on decreasing communication between processes and take the advantage of massive computing techniques, and numerical experiments show that they are both adequate to handle large scale problems with millions of cells. We implemented the two algorithms in our program based on the widely used finite element library deal.II, so that it can be easily coupled with ASPECT.

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

PubMed

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well and are fairly easy to program. In slices with no continuous symmetries, spectral integral-iteration algorithms and elliptic-PDE algorithms are fast and accurate, but require good initial guesses to converge. In many cases, Schnetter's "pretracking" algorithm can greatly improve an elliptic-PDE algorithm's robustness. Flow algorithms are generally quite slow but can be very robust in their convergence. Minimization methods are slow and relatively inaccurate in the context of a finite differencing simulation, but in a spectral code they can be relatively faster and more robust.

The foamed structures in numerical testing

NASA Astrophysics Data System (ADS)

John, Antoni; John, Małgorzata

2018-01-01

In the paper numerical simulation of the foamed metal structures using numerical homogenization algorithm is prescribed. From the beginning, numerical model of heterogeneous porous simplified structures of typical foamed metal, based on the FEM was built and material parameters (coefficients of elasticity matrix of the considered structure) were determined with use of numerical homogenization algorithm. During the work the different RVE models of structure were created and their properties were compared at different relative density, different numbers and the size and structure of the arrangement of voids. Finally, obtained results were used in modeling of typical elements made from foam metals structures - sandwich structure and profile filled with metal foam. Simulation were performed for different dimensions of cladding and core. Additionally, the test of influence material orientation (arrangement of voids in RVE element) on the maximum stresses and displacement during bending test was performed.

SIMULATION OF DISPERSION OF A POWER PLANT PLUME USING AN ADAPTIVE GRID ALGORITHM

EPA Science Inventory

A new dynamic adaptive grid algorithm has been developed for use in air quality modeling. This algorithm uses a higher order numerical scheme?the piecewise parabolic method (PPM)?for computing advective solution fields; a weight function capable of promoting grid node clustering ...

Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

NASA Astrophysics Data System (ADS)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

Numerical simulation of Bragg scattering of sound by surface roughness for different values of the Rayleigh parameter

NASA Astrophysics Data System (ADS)

Salin, M. B.; Dosaev, A. S.; Konkov, A. I.; Salin, B. M.

2014-07-01

Numerical simulation methods are described for the spectral characteristics of an acoustic signal scattered by multiscale surface waves. The methods include the algorithms for calculating the scattered field by the Kirchhoff method and with the use of an integral equation, as well as the algorithms of surface waves generation with allowance for nonlinear hydrodynamic effects. The paper focuses on studying the spectrum of Bragg scattering caused by surface waves whose frequency exceeds the fundamental low-frequency component of the surface waves by several octaves. The spectrum broadening of the backscattered signal is estimated. The possibility of extending the range of applicability of the computing method developed under small perturbation conditions to cases characterized by a Rayleigh parameter of ≥1 is estimated.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

An efficient impedance method for induced field evaluation based on a stabilized Bi-conjugate gradient algorithm.

PubMed

Wang, Hua; Liu, Feng; Xia, Ling; Crozier, Stuart

2008-11-21

This paper presents a stabilized Bi-conjugate gradient algorithm (BiCGstab) that can significantly improve the performance of the impedance method, which has been widely applied to model low-frequency field induction phenomena in voxel phantoms. The improved impedance method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional, successive over-relaxation (SOR)-based algorithm. The scheme has been validated against other numerical/analytical solutions on a lossy, multilayered sphere phantom excited by an ideal coil loop. To demonstrate the computational performance and application capability of the developed algorithm, the induced fields inside a human phantom due to a low-frequency hyperthermia device is evaluated. The simulation results show the numerical accuracy and superior performance of the method.

A Christoffel function weighted least squares algorithm for collocation approximations

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

Narayan, Akil; Jakeman, John D.; Zhou, Tao

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

Un algorithme efficace d'intégration plastique pour un matériau obéissant au critère anisotrope de Hill

NASA Astrophysics Data System (ADS)

Titeux, Isabelle; Li, Yuming M.; Debray, Karl; Guo, Ying-Qiao

2004-11-01

This Note deals with an efficient algorithm to carry out the plastic integration and compute the stresses due to large strains for materials satisfying the Hill's anisotropic yield criterion. The classical algorithm of plastic integration such as 'Return Mapping Method' is largely used for nonlinear analyses of structures and numerical simulations of forming processes, but it requires an iterative schema and may have convergence problems. A new direct algorithm based on a scalar method is developed which allows us to directly obtain the plastic multiplier without an iteration procedure; thus the computation time is largely reduced and the numerical problems are avoided. To cite this article: I. Titeux et al., C. R. Mecanique 332 (2004).

Conservative algorithms for non-Maxwellian plasma kinetics

DOE PAGES

Le, Hai P.; Cambier, Jean -Luc

2017-12-08

Here, we present a numerical model and a set of conservative algorithms for Non-Maxwellian plasma kinetics with inelastic collisions. These algorithms self-consistently solve for the time evolution of an isotropic electron energy distribution function interacting with an atomic state distribution function of an arbitrary number of levels through collisional excitation, deexcitation, as well as ionization and recombination. Electron-electron collisions, responsible for thermalization of the electron distribution, are also included in the model. The proposed algorithms guarantee mass/charge and energy conservation in a single step, and is applied to the case of non-uniform gridding of the energy axis in the phasemore » space of the electron distribution function. Numerical test cases are shown to demonstrate the accuracy of the method and its conservation properties.« less

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

Narayan, Akil; Jakeman, John D.; Zhou, Tao

2016-11-28

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

Implementation of a partitioned algorithm for simulation of large CSI problems

NASA Technical Reports Server (NTRS)

Alvin, Kenneth F.; Park, K. C.

1991-01-01

The implementation of a partitioned numerical algorithm for determining the dynamic response of coupled structure/controller/estimator finite-dimensional systems is reviewed. The partitioned approach leads to a set of coupled first and second-order linear differential equations which are numerically integrated with extrapolation and implicit step methods. The present software implementation, ACSIS, utilizes parallel processing techniques at various levels to optimize performance on a shared-memory concurrent/vector processing system. A general procedure for the design of controller and filter gains is also implemented, which utilizes the vibration characteristics of the structure to be solved. Also presented are: example problems; a user's guide to the software; the procedures and algorithm scripts; a stability analysis for the algorithm; and the source code for the parallel implementation.

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization.

PubMed

Oran, Omer Faruk; Ider, Yusuf Ziya

2012-08-21

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇²B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇²B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

Interpolation on the manifold of K component GMMs.

PubMed

Kim, Hyunwoo J; Adluru, Nagesh; Banerjee, Monami; Vemuri, Baba C; Singh, Vikas

2015-12-01

Probability density functions (PDFs) are fundamental objects in mathematics with numerous applications in computer vision, machine learning and medical imaging. The feasibility of basic operations such as computing the distance between two PDFs and estimating a mean of a set of PDFs is a direct function of the representation we choose to work with. In this paper, we study the Gaussian mixture model (GMM) representation of the PDFs motivated by its numerous attractive features. (1) GMMs are arguably more interpretable than, say, square root parameterizations (2) the model complexity can be explicitly controlled by the number of components and (3) they are already widely used in many applications. The main contributions of this paper are numerical algorithms to enable basic operations on such objects that strictly respect their underlying geometry. For instance, when operating with a set of K component GMMs, a first order expectation is that the result of simple operations like interpolation and averaging should provide an object that is also a K component GMM. The literature provides very little guidance on enforcing such requirements systematically. It turns out that these tasks are important internal modules for analysis and processing of a field of ensemble average propagators (EAPs), common in diffusion weighted magnetic resonance imaging. We provide proof of principle experiments showing how the proposed algorithms for interpolation can facilitate statistical analysis of such data, essential to many neuroimaging studies. Separately, we also derive interesting connections of our algorithm with functional spaces of Gaussians, that may be of independent interest.

Solving a combinatorial problem via self-organizing process: an application of the Kohonen algorithm to the traveling salesman problem.

PubMed

Fort, J C

1988-01-01

We present an application of the Kohonen algorithm to the traveling salesman problem: Using only this algorithm, without energy function nor any parameter chosen "ad hoc", we found good suboptimal tours. We give a neural model version of this algorithm, closer to classical neural networks. This is illustrated with various numerical examples.

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Differential Cloud Particles Evolution Algorithm Based on Data-Driven Mechanism for Applications of ANN

PubMed Central

2017-01-01

Computational scientists have designed many useful algorithms by exploring a biological process or imitating natural evolution. These algorithms can be used to solve engineering optimization problems. Inspired by the change of matter state, we proposed a novel optimization algorithm called differential cloud particles evolution algorithm based on data-driven mechanism (CPDD). In the proposed algorithm, the optimization process is divided into two stages, namely, fluid stage and solid stage. The algorithm carries out the strategy of integrating global exploration with local exploitation in fluid stage. Furthermore, local exploitation is carried out mainly in solid stage. The quality of the solution and the efficiency of the search are influenced greatly by the control parameters. Therefore, the data-driven mechanism is designed for obtaining better control parameters to ensure good performance on numerical benchmark problems. In order to verify the effectiveness of CPDD, numerical experiments are carried out on all the CEC2014 contest benchmark functions. Finally, two application problems of artificial neural network are examined. The experimental results show that CPDD is competitive with respect to other eight state-of-the-art intelligent optimization algorithms. PMID:28761438

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface.

PubMed

Ingebrigtsen, Trond S; Toxvaerd, Søren; Heilmann, Ole J; Schrøder, Thomas B; Dyre, Jeppe C

2011-09-14

An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid. © 2011 American Institute of Physics

Regularization iteration imaging algorithm for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Tong, Guowei; Liu, Shi; Chen, Hongyan; Wang, Xueyao

2018-03-01

The image reconstruction method plays a crucial role in real-world applications of the electrical capacitance tomography technique. In this study, a new cost function that simultaneously considers the sparsity and low-rank properties of the imaging targets is proposed to improve the quality of the reconstruction images, in which the image reconstruction task is converted into an optimization problem. Within the framework of the split Bregman algorithm, an iterative scheme that splits a complicated optimization problem into several simpler sub-tasks is developed to solve the proposed cost function efficiently, in which the fast-iterative shrinkage thresholding algorithm is introduced to accelerate the convergence. Numerical experiment results verify the effectiveness of the proposed algorithm in improving the reconstruction precision and robustness.

Coverage-maximization in networks under resource constraints.

PubMed

Nandi, Subrata; Brusch, Lutz; Deutsch, Andreas; Ganguly, Niloy

2010-06-01

Efficient coverage algorithms are essential for information search or dispersal in all kinds of networks. We define an extended coverage problem which accounts for constrained resources of consumed bandwidth B and time T . Our solution to the network challenge is here studied for regular grids only. Using methods from statistical mechanics, we develop a coverage algorithm with proliferating message packets and temporally modulated proliferation rate. The algorithm performs as efficiently as a single random walker but O(B(d-2)/d) times faster, resulting in significant service speed-up on a regular grid of dimension d . The algorithm is numerically compared to a class of generalized proliferating random walk strategies and on regular grids shown to perform best in terms of the product metric of speed and efficiency.

A new approach of watermarking technique by means multichannel wavelet functions

NASA Astrophysics Data System (ADS)

Agreste, Santa; Puccio, Luigia

2012-12-01

The digital piracy involving images, music, movies, books, and so on, is a legal problem that has not found a solution. Therefore it becomes crucial to create and to develop methods and numerical algorithms in order to solve the copyright problems. In this paper we focus the attention on a new approach of watermarking technique applied to digital color images. Our aim is to describe the realized watermarking algorithm based on multichannel wavelet functions with multiplicity r = 3, called MCWM 1.0. We report a large experimentation and some important numerical results in order to show the robustness of the proposed algorithm to geometrical attacks.

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.

ALGORITHM TO REDUCE APPROXIMATION ERROR FROM THE COMPLEX-VARIABLE BOUNDARY-ELEMENT METHOD APPLIED TO SOIL FREEZING.

USGS Publications Warehouse

Hromadka, T.V.; Guymon, G.L.

1985-01-01

An algorithm is presented for the numerical solution of the Laplace equation boundary-value problem, which is assumed to apply to soil freezing or thawing. The Laplace equation is numerically approximated by the complex-variable boundary-element method. The algorithm aids in reducing integrated relative error by providing a true measure of modeling error along the solution domain boundary. This measure of error can be used to select locations for adding, removing, or relocating nodal points on the boundary or to provide bounds for the integrated relative error of unknown nodal variable values along the boundary.

Algorithm for loading shot noise microbunching in multi-dimensional, free-electron laser simulation codes

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

Fawley, William M.

We discuss the underlying reasoning behind and the details of the numerical algorithm used in the GINGER free-electron laser(FEL) simulation code to load the initial shot noise microbunching on the electron beam. In particular, we point out that there are some additional subtleties which must be followed for multi-dimensional codes which are not necessary for one-dimensional formulations. Moreover, requiring that the higher harmonics of the microbunching also be properly initialized with the correct statistics leads to additional complexities. We present some numerical results including the predicted incoherent, spontaneous emission as tests of the shot noise algorithm's correctness.

An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems

NASA Technical Reports Server (NTRS)

Farhat, C.; Park, K. C.; Dubois-Pelerin, Y.

1991-01-01

An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.

Electromagnetic Field Effects in Semiconductor Crystal Growth

NASA Technical Reports Server (NTRS)

Dulikravich, George S.

1996-01-01

This proposed two-year research project was to involve development of an analytical model, a numerical algorithm for its integration, and a software for the analysis of a solidification process under the influence of electric and magnetic fields in microgravity. Due to the complexity of the analytical model that was developed and its boundary conditions, only a preliminary version of the numerical algorithm was developed while the development of the software package was not completed.

A numerical algorithm of tooth profile of non-circular cylindrical gear

NASA Astrophysics Data System (ADS)

Wang, Xuan

2017-08-01

Non-circular cylindrical gear (NCCG) is a common form of non-circular gear. Different from the circular gear, the tooth profile equation of NCCG cannot be obtained. So it is necessary to use a numerical algorithm to calculate the tooth profile of NCCG. For this reason, this paper presents a simple and highly efficient numerical algorithm to obtain the tooth profile of NCCG. Firstly, the mathematical model of tooth profile envelope of NCCG is established based on the principle of gear shaping, and the tooth profile envelope of NCCG is obtained. Secondly, the polar radius and polar angle of shaper cutter tooth profile are chosen as the criterions, by which the points of NCCG tooth cogging can be screened out. Finally, the boundary of tooth cogging points is extracted by a distance criterion and correspondingly the tooth profile of NCCG is obtained.

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Yao, Minwu; Walker, Kevin P.

1992-01-01

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

Fast algorithms for Quadrature by Expansion I: Globally valid expansions

NASA Astrophysics Data System (ADS)

Rachh, Manas; Klöckner, Andreas; O'Neil, Michael

2017-09-01

The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.

Parabolized Navier-Stokes Code for Computing Magneto-Hydrodynamic Flowfields

NASA Technical Reports Server (NTRS)

Mehta, Unmeel B. (Technical Monitor); Tannehill, J. C.

2003-01-01

This report consists of two published papers, 'Computation of Magnetohydrodynamic Flows Using an Iterative PNS Algorithm' and 'Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm'.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

PubMed

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

PubMed Central

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

NASA Astrophysics Data System (ADS)

Korepanov, V. V.; Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

2013-07-01

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

Simultaneous and semi-alternating projection algorithms for solving split equality problems.

PubMed

Dong, Qiao-Li; Jiang, Dan

2018-01-01

In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms.

Numerical simulation of a bubble rising in an environment consisting of Xanthan gum

NASA Astrophysics Data System (ADS)

Aguirre, Víctor A.; Castillo, Byron A.; Narvaez, Christian P.

2017-09-01

An improved numerical algorithm for front tracking method is developed to simulate a bubble rising in viscous liquid. In the new numerical algorithm, volume correction is introduced to conserve the bubble volume while tracking the bubble's rising and deforming. Volume flux conservation is adopted to solve the Navier-Stokes equation for fluid flow using finite volume method. Non-Newtonian fluids are widely used in industry such as feed and energy industries. In this research we used Xanthan gum which is a microbiological polysaccharide. In order to obtain the properties of the Xanthan gum, such as viscosity, storage and loss modulus, shear rate, etc., it was necessary to do an amplitude sweep and steady flow test in a rheometer with a concentric cylinder as geometry. Based on the data given and using a numerical regression, the coefficients required by Giesekus model are obtained. With these coefficients, it is possible to simulate the comportment of the fluid by the use of the developed algorithm. Once the data given by OpenFOAM is acquired, it is compared with the experimental data.

Optimization methods and silicon solar cell numerical models

NASA Technical Reports Server (NTRS)

Girardini, K.; Jacobsen, S. E.

1986-01-01

An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

SIMULATION OF DISPERSION OF A POWER PLANT PLUME USING AN ADAPTIVE GRID ALGORITHM. (R827028)

EPA Science Inventory

A new dynamic adaptive grid algorithm has been developed for use in air quality modeling. This algorithm uses a higher order numerical scheme––the piecewise parabolic method (PPM)––for computing advective solution fields; a weight function capable o...

Derivative Free Gradient Projection Algorithms for Rotation

ERIC Educational Resources Information Center

Jennrich, Robert I.

2004-01-01

A simple modification substantially simplifies the use of the gradient projection (GP) rotation algorithms of Jennrich (2001, 2002). These algorithms require subroutines to compute the value and gradient of any specific rotation criterion of interest. The gradient can be difficult to derive and program. It is shown that using numerical gradients…

Alocomotino Control Algorithm for Robotic Linkage Systems

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

Dohner, Jeffrey L.

This dissertation describes the development of a control algorithm that transitions a robotic linkage system between stabilized states producing responsive locomotion. The developed algorithm is demonstrated using a simple robotic construction consisting of a few links with actuation and sensing at each joint. Numerical and experimental validation is presented.

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

Fischetti, Sebastian; Cadonati, Laura; Mohapatra, Satyanarayan R. P.

Recent years have witnessed tremendous progress in numerical relativity and an ever improving performance of ground-based interferometric gravitational wave detectors. In preparation for the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO) and a new era in gravitational wave astronomy, the numerical relativity and gravitational wave data analysis communities are collaborating to ascertain the most useful role for numerical relativity waveforms in the detection and characterization of binary black hole coalescences. In this paper, we explore the detectability of equal mass, merging black hole binaries with precessing spins and total mass M{sub T}(set-membership sign)[80,350]M{sub {center_dot}}, using numerical relativity waveforms andmore » templateless search algorithms designed for gravitational wave bursts. In particular, we present a systematic study using waveforms produced by the MayaKranc code that are added to colored, Gaussian noise and analyzed with the Omega burst search algorithm. Detection efficiency is weighed against the orientation of one of the black-hole's spin axes. We find a strong correlation between the detection efficiency and the radiated energy and angular momentum, and that the inclusion of the l=2, m={+-}1, 0 modes, at a minimum, is necessary to account for the full dynamics of precessing systems.« less

An improved grey wolf optimizer algorithm for the inversion of geoelectrical data

NASA Astrophysics Data System (ADS)

Li, Si-Yu; Wang, Shu-Ming; Wang, Peng-Fei; Su, Xiao-Lu; Zhang, Xin-Song; Dong, Zhi-Hui

2018-05-01

The grey wolf optimizer (GWO) is a novel bionics algorithm inspired by the social rank and prey-seeking behaviors of grey wolves. The GWO algorithm is easy to implement because of its basic concept, simple formula, and small number of parameters. This paper develops a GWO algorithm with a nonlinear convergence factor and an adaptive location updating strategy and applies this improved grey wolf optimizer (improved grey wolf optimizer, IGWO) algorithm to geophysical inversion problems using magnetotelluric (MT), DC resistivity and induced polarization (IP) methods. Numerical tests in MATLAB 2010b for the forward modeling data and the observed data show that the IGWO algorithm can find the global minimum and rarely sinks to the local minima. For further study, inverted results using the IGWO are contrasted with particle swarm optimization (PSO) and the simulated annealing (SA) algorithm. The outcomes of the comparison reveal that the IGWO and PSO similarly perform better in counterpoising exploration and exploitation with a given number of iterations than the SA.

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

NASA Technical Reports Server (NTRS)

Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.

2017-01-01

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

Quantitative imaging technique using the layer-stripping algorithm

NASA Astrophysics Data System (ADS)

Beilina, L.

2017-07-01

We present the layer-stripping algorithm for the solution of the hyperbolic coefficient inverse problem (CIP). Our numerical examples show quantitative reconstruction of small tumor-like inclusions in two-dimensions.

Reconstructing householder vectors from Tall-Skinny QR

DOE PAGES

Ballard, Grey Malone; Demmel, James; Grigori, Laura; ...

2015-08-05

The Tall-Skinny QR (TSQR) algorithm is more communication efficient than the standard Householder algorithm for QR decomposition of matrices with many more rows than columns. However, TSQR produces a different representation of the orthogonal factor and therefore requires more software development to support the new representation. Further, implicitly applying the orthogonal factor to the trailing matrix in the context of factoring a square matrix is more complicated and costly than with the Householder representation. We show how to perform TSQR and then reconstruct the Householder vector representation with the same asymptotic communication efficiency and little extra computational cost. We demonstratemore » the high performance and numerical stability of this algorithm both theoretically and empirically. The new Householder reconstruction algorithm allows us to design more efficient parallel QR algorithms, with significantly lower latency cost compared to Householder QR and lower bandwidth and latency costs compared with Communication-Avoiding QR (CAQR) algorithm. Experiments on supercomputers demonstrate the benefits of the communication cost improvements: in particular, our experiments show substantial improvements over tuned library implementations for tall-and-skinny matrices. Furthermore, we also provide algorithmic improvements to the Householder QR and CAQR algorithms, and we investigate several alternatives to the Householder reconstruction algorithm that sacrifice guarantees on numerical stability in some cases in order to obtain higher performance.« less

Optimization of laminated stacking sequence for buckling load maximization by genetic algorithm

NASA Technical Reports Server (NTRS)

Le Riche, Rodolphe; Haftka, Raphael T.

1992-01-01

The use of a genetic algorithm to optimize the stacking sequence of a composite laminate for buckling load maximization is studied. Various genetic parameters including the population size, the probability of mutation, and the probability of crossover are optimized by numerical experiments. A new genetic operator - permutation - is proposed and shown to be effective in reducing the cost of the genetic search. Results are obtained for a graphite-epoxy plate, first when only the buckling load is considered, and then when constraints on ply contiguity and strain failure are added. The influence on the genetic search of the penalty parameter enforcing the contiguity constraint is studied. The advantage of the genetic algorithm in producing several near-optimal designs is discussed.

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

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

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr; CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex; Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity ofmore » the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less

Shock wave-free interface interaction

NASA Astrophysics Data System (ADS)

Frolov, Roman; Minev, Peter; Krechetnikov, Rouslan

2016-11-01

The problem of shock wave-free interface interaction has been widely studied in the context of compressible two-fluid flows using analytical, experimental, and numerical techniques. While various physical effects and possible interaction patterns for various geometries have been identified in the literature, the effects of viscosity and surface tension are usually neglected in such models. In our study, we apply a novel numerical algorithm for simulation of viscous compressible two-fluid flows with surface tension to investigate the influence of these effects on the shock-interface interaction. The method combines together the ideas from Finite Volume adaptation of invariant domains preserving algorithm for systems of hyperbolic conservation laws by Guermond and Popov and ADI parallel solver for viscous incompressible NSEs by Guermond and Minev. This combination has been further extended to a two-fluid flow case, including surface tension effects. Here we report on a quantitative study of how surface tension and viscosity affect the structure of the shock wave-free interface interaction region.

Domain Decomposition Algorithms for First-Order System Least Squares Methods

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Novel Kalman Filter Algorithm for Statistical Monitoring of Extensive Landscapes with Synoptic Sensor Data

PubMed Central

Czaplewski, Raymond L.

2015-01-01

Wall-to-wall remotely sensed data are increasingly available to monitor landscape dynamics over large geographic areas. However, statistical monitoring programs that use post-stratification cannot fully utilize those sensor data. The Kalman filter (KF) is an alternative statistical estimator. I develop a new KF algorithm that is numerically robust with large numbers of study variables and auxiliary sensor variables. A National Forest Inventory (NFI) illustrates application within an official statistics program. Practical recommendations regarding remote sensing and statistical issues are offered. This algorithm has the potential to increase the value of synoptic sensor data for statistical monitoring of large geographic areas. PMID:26393588

An NN-Based SRD Decomposition Algorithm and Its Application in Nonlinear Compensation

PubMed Central

Yan, Honghang; Deng, Fang; Sun, Jian; Chen, Jie

2014-01-01

In this study, a neural network-based square root of descending (SRD) order decomposition algorithm for compensating for nonlinear data generated by sensors is presented. The study aims at exploring the optimized decomposition of data 1.00,0.00,0.00 and minimizing the computational complexity and memory space of the training process. A linear decomposition algorithm, which automatically finds the optimal decomposition of N subparts and reduces the training time to 1N and memory cost to 1N, has been implemented on nonlinear data obtained from an encoder. Particular focus is given to the theoretical access of estimating the numbers of hidden nodes and the precision of varying the decomposition method. Numerical experiments are designed to evaluate the effect of this algorithm. Moreover, a designed device for angular sensor calibration is presented. We conduct an experiment that samples the data of an encoder and compensates for the nonlinearity of the encoder to testify this novel algorithm. PMID:25232912

PSO-Based Smart Grid Application for Sizing and Optimization of Hybrid Renewable Energy Systems

PubMed Central

Mohamed, Mohamed A.; Eltamaly, Ali M.; Alolah, Abdulrahman I.

2016-01-01

This paper introduces an optimal sizing algorithm for a hybrid renewable energy system using smart grid load management application based on the available generation. This algorithm aims to maximize the system energy production and meet the load demand with minimum cost and highest reliability. This system is formed by photovoltaic array, wind turbines, storage batteries, and diesel generator as a backup source of energy. Demand profile shaping as one of the smart grid applications is introduced in this paper using load shifting-based load priority. Particle swarm optimization is used in this algorithm to determine the optimum size of the system components. The results obtained from this algorithm are compared with those from the iterative optimization technique to assess the adequacy of the proposed algorithm. The study in this paper is performed in some of the remote areas in Saudi Arabia and can be expanded to any similar regions around the world. Numerous valuable results are extracted from this study that could help researchers and decision makers. PMID:27513000

PSO-Based Smart Grid Application for Sizing and Optimization of Hybrid Renewable Energy Systems.

PubMed

Mohamed, Mohamed A; Eltamaly, Ali M; Alolah, Abdulrahman I

2016-01-01

This paper introduces an optimal sizing algorithm for a hybrid renewable energy system using smart grid load management application based on the available generation. This algorithm aims to maximize the system energy production and meet the load demand with minimum cost and highest reliability. This system is formed by photovoltaic array, wind turbines, storage batteries, and diesel generator as a backup source of energy. Demand profile shaping as one of the smart grid applications is introduced in this paper using load shifting-based load priority. Particle swarm optimization is used in this algorithm to determine the optimum size of the system components. The results obtained from this algorithm are compared with those from the iterative optimization technique to assess the adequacy of the proposed algorithm. The study in this paper is performed in some of the remote areas in Saudi Arabia and can be expanded to any similar regions around the world. Numerous valuable results are extracted from this study that could help researchers and decision makers.

Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

NASA Astrophysics Data System (ADS)

Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.

2017-10-01

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.

Computing Evans functions numerically via boundary-value problems

NASA Astrophysics Data System (ADS)

Barker, Blake; Nguyen, Rose; Sandstede, Björn; Ventura, Nathaniel; Wahl, Colin

2018-03-01

The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.

Variational Algorithms for Test Particle Trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. Leland; Finn, John M.; Qin, Hong; Tang, William M.

2015-11-01

The theory of variational integration provides a novel framework for constructing conservative numerical methods for magnetized test particle dynamics. The retention of conservation laws in the numerical time advance captures the correct qualitative behavior of the long time dynamics. For modeling the Lorentz force system, new variational integrators have been developed that are both symplectic and electromagnetically gauge invariant. For guiding center test particle dynamics, discretization of the phase-space action principle yields multistep variational algorithms, in general. Obtaining the desired long-term numerical fidelity requires mitigation of the multistep method's parasitic modes or applying a discretization scheme that possesses a discrete degeneracy to yield a one-step method. Dissipative effects may be modeled using Lagrange-D'Alembert variational principles. Numerical results will be presented using a new numerical platform that interfaces with popular equilibrium codes and utilizes parallel hardware to achieve reduced times to solution. This work was supported by DOE Contract DE-AC02-09CH11466.

Fuzzy multi objective transportation problem – evolutionary algorithm approach

NASA Astrophysics Data System (ADS)

Karthy, T.; Ganesan, K.

2018-04-01

This paper deals with fuzzy multi objective transportation problem. An fuzzy optimal compromise solution is obtained by using Fuzzy Genetic Algorithm. A numerical example is provided to illustrate the methodology.

Fast convergent frequency-domain MIMO equalizer for few-mode fiber communication systems

NASA Astrophysics Data System (ADS)

He, Xuan; Weng, Yi; Wang, Junyi; Pan, Z.

2018-02-01

Space division multiplexing using few-mode fibers has been extensively explored to sustain the continuous traffic growth. In few-mode fiber optical systems, both spatial and polarization modes are exploited to transmit parallel channels, thus increasing the overall capacity. However, signals on spatial channels inevitably suffer from the intrinsic inter-modal coupling and large accumulated differential mode group delay (DMGD), which causes spatial modes de-multiplex even harder. Many research articles have demonstrated that frequency domain adaptive multi-input multi-output (MIMO) equalizer can effectively compensate the DMGD and demultiplex the spatial channels with digital signal processing (DSP). However, the large accumulated DMGD usually requires a large number of training blocks for the initial convergence of adaptive MIMO equalizers, which will decrease the overall system efficiency and even degrade the equalizer performance in fast-changing optical channels. Least mean square (LMS) algorithm is always used in MIMO equalization to dynamically demultiplex the spatial signals. We have proposed to use signal power spectral density (PSD) dependent method and noise PSD directed method to improve the convergence speed of adaptive frequency domain LMS algorithm. We also proposed frequency domain recursive least square (RLS) algorithm to further increase the convergence speed of MIMO equalizer at cost of greater hardware complexity. In this paper, we will compare the hardware complexity and convergence speed of signal PSD dependent and noise power directed algorithms against the conventional frequency domain LMS algorithm. In our numerical study of a three-mode 112 Gbit/s PDM-QPSK optical system with 3000 km transmission, the noise PSD directed and signal PSD dependent methods could improve the convergence speed by 48.3% and 36.1% respectively, at cost of 17.2% and 10.7% higher hardware complexity. We will also compare the frequency domain RLS algorithm against conventional frequency domain LMS algorithm. Our numerical study shows that, in a three-mode 224 Gbit/s PDM-16-QAM system with 3000 km transmission, the RLS algorithm could improve the convergence speed by 53.7% over conventional frequency domain LMS algorithm.

Diagnostic and Remedial Learning Strategy Based on Conceptual Graphs

ERIC Educational Resources Information Center

Jong, BinShyan; Lin, TsongWuu; Wu, YuLung; Chan, Teyi

2004-01-01

Numerous scholars have applied conceptual graphs for explanatory purposes. This study devised the Remedial-Instruction Decisive path (RID path) algorithm for diagnosing individual student learning situation. This study focuses on conceptual graphs. According to the concepts learned by students and the weight values of relations among these…

An algorithm for the automatic synchronization of Omega receivers

NASA Technical Reports Server (NTRS)

Stonestreet, W. M.; Marzetta, T. L.

1977-01-01

The Omega navigation system and the requirement for receiver synchronization are discussed. A description of the synchronization algorithm is provided. The numerical simulation and its associated assumptions were examined and results of the simulation are presented. The suggested form of the synchronization algorithm and the suggested receiver design values were surveyed. A Fortran of the synchronization algorithm used in the simulation was also included.

Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

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

Chen, G., E-mail: gchen@lanl.gov; Chacón, L.; Leibs, C.A.

2014-02-01

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solvemore » is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.« less

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

The Kineticist’s Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

DTIC Science & Technology

1991-06-01

algorithms (for the analysis of mechanisms), traditional numerical simulation methods, and algorithms that examine the (continued on back) 14. SUBJECT TERMS ...7540-01-280.S500 )doo’c -O• 98 (; : 89) 2YB 󈧆 Block 13 continued: simulation results and reinterpret them in qualitative terms . Moreover...simulation results and reinterpret them in qualitative terms . Moreover, the Workbench can use symbolic procedures to help guide or simplify the task

Structure-preserving and rank-revealing QR-factorizations

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

Bischof, C.H.; Hansen, P.C.

1991-11-01

The rank-revealing QR-factorization (RRQR-factorization) is a special QR-factorization that is guaranteed to reveal the numerical rank of the matrix under consideration. This makes the RRQR-factorization a useful tool in the numerical treatment of many rank-deficient problems in numerical linear algebra. In this paper, a framework is presented for the efficient implementation of RRQR algorithms, in particular, for sparse matrices. A sparse RRQR-algorithm should seek to preserve the structure and sparsity of the matrix as much as possible while retaining the ability to capture safely the numerical rank. To this end, the paper proposes to compute an initial QR-factorization using amore » restricted pivoting strategy guarded by incremental condition estimation (ICE), and then applies the algorithm suggested by Chan and Foster to this QR-factorization. The column exchange strategy used in the initial QR factorization will exploit the fact that certain column exchanges do not change the sparsity structure, and compute a sparse QR-factorization that is a good approximation of the sought-after RRQR-factorization. Due to quantities produced by ICE, the Chan/Foster RRQR algorithm can be implemented very cheaply, thus verifying that the sought-after RRQR-factorization has indeed been computed. Experimental results on a model problem show that the initial QR-factorization is indeed very likely to produce RRQR-factorization.« less

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

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

Li, Zhihui; Ma, Qiang; Wu, Junlin

2014-12-09

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinatemore » points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.« less

INTEGRATION OF PARTICLE-GAS SYSTEMS WITH STIFF MUTUAL DRAG INTERACTION

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

Yang, Chao-Chin; Johansen, Anders, E-mail: ccyang@astro.lu.se, E-mail: anders@astro.lu.se

2016-06-01

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff—particularly because of small particles and/or strong local solid concentration—that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct,more » we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.« less

Harmony search method: theory and applications.

PubMed

Gao, X Z; Govindasamy, V; Xu, H; Wang, X; Zenger, K

2015-01-01

The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem.

Research on numerical method for multiple pollution source discharge and optimal reduction program

NASA Astrophysics Data System (ADS)

Li, Mingchang; Dai, Mingxin; Zhou, Bin; Zou, Bin

2018-03-01

In this paper, the optimal method for reduction program is proposed by the nonlinear optimal algorithms named that genetic algorithm. The four main rivers in Jiangsu province, China are selected for reducing the environmental pollution in nearshore district. Dissolved inorganic nitrogen (DIN) is studied as the only pollutant. The environmental status and standard in the nearshore district is used to reduce the discharge of multiple river pollutant. The research results of reduction program are the basis of marine environmental management.

Cone-beam reconstruction for the two-circles-plus-one-line trajectory

NASA Astrophysics Data System (ADS)

Lu, Yanbin; Yang, Jiansheng; Emerson, John W.; Mao, Heng; Zhou, Tie; Si, Yuanzheng; Jiang, Ming

2012-05-01

The Kodak Image Station In-Vivo FX has an x-ray module with cone-beam configuration for radiographic imaging but lacks the functionality of tomography. To introduce x-ray tomography into the system, we choose the two-circles-plus-one-line trajectory by mounting one translation motor and one rotation motor. We establish a reconstruction algorithm by applying the M-line reconstruction method. Numerical studies and preliminary physical phantom experiment demonstrate the feasibility of the proposed design and reconstruction algorithm.

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

Chen, Qiang; Qin, Hong; Liu, Jian

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

A software simulation study of a (255,223) Reed-Solomon encoder-decoder

NASA Technical Reports Server (NTRS)

Pollara, F.

1985-01-01

A set of software programs which simulates a (255,223) Reed-Solomon encoder/decoder pair is described. The transform decoder algorithm uses a modified Euclid algorithm, and closely follows the pipeline architecture proposed for the hardware decoder. Uncorrectable error patterns are detected by a simple test, and the inverse transform is computed by a finite field FFT. Numerical examples of the decoder operation are given for some test codewords, with and without errors. The use of the software package is briefly described.

A Novel Hybrid Classification Model of Genetic Algorithms, Modified k-Nearest Neighbor and Developed Backpropagation Neural Network

PubMed Central

Salari, Nader; Shohaimi, Shamarina; Najafi, Farid; Nallappan, Meenakshii; Karishnarajah, Isthrinayagy

2014-01-01

Among numerous artificial intelligence approaches, k-Nearest Neighbor algorithms, genetic algorithms, and artificial neural networks are considered as the most common and effective methods in classification problems in numerous studies. In the present study, the results of the implementation of a novel hybrid feature selection-classification model using the above mentioned methods are presented. The purpose is benefitting from the synergies obtained from combining these technologies for the development of classification models. Such a combination creates an opportunity to invest in the strength of each algorithm, and is an approach to make up for their deficiencies. To develop proposed model, with the aim of obtaining the best array of features, first, feature ranking techniques such as the Fisher's discriminant ratio and class separability criteria were used to prioritize features. Second, the obtained results that included arrays of the top-ranked features were used as the initial population of a genetic algorithm to produce optimum arrays of features. Third, using a modified k-Nearest Neighbor method as well as an improved method of backpropagation neural networks, the classification process was advanced based on optimum arrays of the features selected by genetic algorithms. The performance of the proposed model was compared with thirteen well-known classification models based on seven datasets. Furthermore, the statistical analysis was performed using the Friedman test followed by post-hoc tests. The experimental findings indicated that the novel proposed hybrid model resulted in significantly better classification performance compared with all 13 classification methods. Finally, the performance results of the proposed model was benchmarked against the best ones reported as the state-of-the-art classifiers in terms of classification accuracy for the same data sets. The substantial findings of the comprehensive comparative study revealed that performance of the proposed model in terms of classification accuracy is desirable, promising, and competitive to the existing state-of-the-art classification models. PMID:25419659

Numerical simulation of three-dimensional transonic turbulent projectile aerodynamics by TVD schemes

NASA Technical Reports Server (NTRS)

Shiau, Nae-Haur; Hsu, Chen-Chi; Chyu, Wei-Jao

1989-01-01

The two-dimensional symmetric TVD scheme proposed by Yee has been extended to and investigated for three-dimensional thin-layer Navier-Stokes simulation of complex aerodynamic problems. An existing three-dimensional Navier-stokes code based on the beam and warming algorithm is modified to provide an option of using the TVD algorithm and the flow problem considered is a transonic turbulent flow past a projectile with sting at ten-degree angle of attack. Numerical experiments conducted for three flow cases, free-stream Mach numbers of 0.91, 0.96 and 1.20 show that the symmetric TVD algorithm can provide surface pressure distribution in excellent agreement with measured data; moreover, the rate of convergence to attain a steady state solution is about two times faster than the original beam and warming algorithm.

Nash equilibrium and multi criterion aerodynamic optimization

NASA Astrophysics Data System (ADS)

Tang, Zhili; Zhang, Lianhe

2016-06-01

Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.

Efficiency Analysis of the Parallel Implementation of the SIMPLE Algorithm on Multiprocessor Computers

NASA Astrophysics Data System (ADS)

Lashkin, S. V.; Kozelkov, A. S.; Yalozo, A. V.; Gerasimov, V. Yu.; Zelensky, D. K.

2017-12-01

This paper describes the details of the parallel implementation of the SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. The iteration schemes for the serial and parallel versions of the SIMPLE algorithm are implemented. In the description of the parallel implementation, special attention is paid to computational data exchange among processors under the condition of the grid model decomposition using fictitious cells. We discuss the specific features for the storage of distributed matrices and implementation of vector-matrix operations in parallel mode. It is shown that the proposed way of matrix storage reduces the number of interprocessor exchanges. A series of numerical experiments illustrates the effect of the multigrid SLAE solver tuning on the general efficiency of the algorithm; the tuning involves the types of the cycles used (V, W, and F), the number of iterations of a smoothing operator, and the number of cells for coarsening. Two ways (direct and indirect) of efficiency evaluation for parallelization of the numerical algorithm are demonstrated. The paper presents the results of solving some internal and external flow problems with the evaluation of parallelization efficiency by two algorithms. It is shown that the proposed parallel implementation enables efficient computations for the problems on a thousand processors. Based on the results obtained, some general recommendations are made for the optimal tuning of the multigrid solver, as well as for selecting the optimal number of cells per processor.

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for a Thin Solenoid with Uniform Current Density

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

Walstrom, Peter Lowell

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for radially thin solenoids with uniform current density is described in this note. An algorithm for computing the vector potential A θ is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. The (apparently) new feature of themore » algorithms described in this note applies to cases where the field point is outside of the bore of the solenoid and the field-point radius approaches the solenoid radius. Since the elliptic integrals of the third kind normally used in computing B z and A θ become infinite in this region of parameter space, fields for points with the axial coordinate z outside of the ends of the solenoid and near the solenoid radius are treated by use of elliptic integrals of the third kind of modified argument, derived by use of an addition theorem. Also, the algorithms also avoid the numerical difficulties the textbook solutions have for points near the axis arising from explicit factors of 1/r or 1/r 2 in the some of the expressions.« less

A comparative study of AGN feedback algorithms

NASA Astrophysics Data System (ADS)

Wurster, J.; Thacker, R. J.

2013-05-01

Modelling active galactic nuclei (AGN) feedback in numerical simulations is both technically and theoretically challenging, with numerous approaches having been published in the literature. We present a study of five distinct approaches to modelling AGN feedback within gravitohydrodynamic simulations of major mergers of Milky Way-sized galaxies. To constrain differences to only be between AGN feedback models, all simulations start from the same initial conditions and use the same star formation algorithm. Most AGN feedback algorithms have five key aspects: the black hole accretion rate, energy feedback rate and method, particle accretion algorithm, black hole advection algorithm and black hole merger algorithm. All models follow different accretion histories, and in some cases, accretion rates differ by up to three orders of magnitude at any given time. We consider models with either thermal or kinetic feedback, with the associated energy deposited locally around the black hole. Each feedback algorithm modifies the region around the black hole to different extents, yielding gas densities and temperatures within r ˜ 200 pc that differ by up to six orders of magnitude at any given time. The particle accretion algorithms usually maintain good agreement between the total mass accreted by dot{M} dt and the total mass of gas particles removed from the simulation, although not all algorithms guarantee this to be true. The black hole advection algorithms dampen inappropriate dragging of the black holes by two-body interactions. Advecting the black hole a limited distance based upon local mass distributions has many desirably properties, such as avoiding large artificial jumps and allowing the possibility of the black hole remaining in a gas void. Lastly, two black holes instantly merge when given criteria are met, and we find a range of merger times for different criteria. This is important since the AGN feedback rate changes across the merger in a way that is dependent on the specific accretion algorithm used. Using the MBH-σ relation as a diagnostic of the remnants yields three models that lie within the one-sigma scatter of the observed relation and two that fall below the expected relation. The wide variation in accretion behaviours of the models reinforces the fact that there remains much to be learnt about the evolution of galactic nuclei.

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

A pheromone-rate-based analysis on the convergence time of ACO algorithm.

PubMed

Huang, Han; Wu, Chun-Guo; Hao, Zhi-Feng

2009-08-01

Ant colony optimization (ACO) has widely been applied to solve combinatorial optimization problems in recent years. There are few studies, however, on its convergence time, which reflects how many iteration times ACO algorithms spend in converging to the optimal solution. Based on the absorbing Markov chain model, we analyze the ACO convergence time in this paper. First, we present a general result for the estimation of convergence time to reveal the relationship between convergence time and pheromone rate. This general result is then extended to a two-step analysis of the convergence time, which includes the following: 1) the iteration time that the pheromone rate spends on reaching the objective value and 2) the convergence time that is calculated with the objective pheromone rate in expectation. Furthermore, four brief ACO algorithms are investigated by using the proposed theoretical results as case studies. Finally, the conclusions of the case studies that the pheromone rate and its deviation determine the expected convergence time are numerically verified with the experiment results of four one-ant ACO algorithms and four ten-ant ACO algorithms.

Adaptive Wavelet Modeling of Geophysical Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H.; Dahmen, W.; Vorloeper, J.

2009-12-01

Despite the ever-increasing power of modern computers, realistic modeling of complex three-dimensional Earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modeling approaches includes either finite difference or non-adaptive finite element algorithms, and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behavior of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modeled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet based approach that is applicable to a large scope of problems, also including nonlinear problems. To the best of our knowledge such algorithms have not yet been applied in geophysics. Adaptive wavelet algorithms offer several attractive features: (i) for a given subsurface model, they allow the forward modeling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient, and (iii) the modeling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving three-dimensional geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best fit subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectrical modeling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with spatially highly variable electrical conductivities. The linear dependency of the modeling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

Methods, Software and Tools for Three Numerical Applications. Final report

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

E. R. Jessup

2000-03-01

This is a report of the results of the authors work supported by DOE contract DE-FG03-97ER25325. They proposed to study three numerical problems. They are: (1) the extension of the PMESC parallel programming library; (2) the development of algorithms and software for certain generalized eigenvalue and singular value (SVD) problems, and (3) the application of techniques of linear algebra to an information retrieval technique known as latent semantic indexing (LSI).

Improved numerical methods for turbulent viscous recirculating flows

NASA Technical Reports Server (NTRS)

Turan, A.

1985-01-01

The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.

Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

PubMed

Zhao, Ying; Shi, Luoyi

2017-01-01

This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.

Electrical conductivity imaging using gradient B, decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT).

PubMed

Park, Chunjae; Kwon, Ohin; Woo, Eung Je; Seo, Jin Keun

2004-03-01

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.

Simulation of 3-D Nonequilibrium Seeded Air Flow in the NASA-Ames MHD Channel

NASA Technical Reports Server (NTRS)

Gupta, Sumeet; Tannehill, John C.; Mehta, Unmeel B.

2004-01-01

The 3-D nonequilibrium seeded air flow in the NASA-Ames experimental MHD channel has been numerically simulated. The channel contains a nozzle section, a center section, and an accelerator section where magnetic and electric fields can be imposed on the flow. In recent tests, velocity increases of up to 40% have been achieved in the accelerator section. The flow in the channel is numerically computed us ing a 3-D parabolized Navier-Stokes (PNS) algorithm that has been developed to efficiently compute MHD flows in the low magnetic Reynolds number regime: The MHD effects are modeled by introducing source terms into the PNS equations which can then be solved in a very efficient manner. The algorithm has been extended in the present study to account for nonequilibrium seeded air flows. The electrical conductivity of the flow is determined using the program of Park. The new algorithm has been used to compute two test cases that match the experimental conditions. In both cases, magnetic and electric fields are applied to the seeded flow. The computed results are in good agreement with the experimental data.

A radiation and energy budget algorithm for forest canopies

NASA Astrophysics Data System (ADS)

Tunick, A.

2006-01-01

Previously, it was shown that a one-dimensional, physics-based (conservation-law) computer model can provide a useful mathematical representation of the wind flow, temperatures, and turbulence inside and above a uniform forest stand. A key element of this calculation was a radiation and energy budget algorithm (implemented to predict the heat source). However, to keep the earlier publication brief, a full description of the radiation and energy budget algorithm was not given. Hence, this paper presents our equation set for calculating the incoming total radiation at the canopy top as well as the transmission, reflection, absorption, and emission of the solar flux through a forest stand. In addition, example model output is presented from three interesting numerical experiments, which were conducted to simulate the canopy microclimate for a forest stand that borders the Blossom Point Field Test Facility (located near La Plata, Maryland along the Potomac River). It is anticipated that the current numerical study will be useful to researchers and experimental planners who will be collecting acoustic and meteorological data at the Blossom Point Facility in the near future.

Design of isolated buildings with S-FBI system subjected to near-fault earthquakes using NSGA-II algorithm

NASA Astrophysics Data System (ADS)

Ozbulut, O. E.; Silwal, B.

2014-04-01

This study investigates the optimum design parameters of a superelastic friction base isolator (S-FBI) system through a multi-objective genetic algorithm and performance-based evaluation approach. The S-FBI system consists of a flat steel- PTFE sliding bearing and a superelastic NiTi shape memory alloy (SMA) device. Sliding bearing limits the transfer of shear across the isolation interface and provides damping from sliding friction. SMA device provides restoring force capability to the isolation system together with additional damping characteristics. A three-story building is modeled with S-FBI isolation system. Multiple-objective numerical optimization that simultaneously minimizes isolation-level displacements and superstructure response is carried out with a genetic algorithm (GA) in order to optimize S-FBI system. Nonlinear time history analyses of the building with S-FBI system are performed. A set of 20 near-field ground motion records are used in numerical simulations. Results show that S-FBI system successfully control response of the buildings against near-fault earthquakes without sacrificing in isolation efficacy and producing large isolation-level deformations.

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions.

PubMed

Wang, Wenlong; Moore, M A; Katzgraber, Helmut G

2018-03-01

The fractal dimension of domain walls produced by changing the boundary conditions from periodic to antiperiodic in one spatial direction is studied using both the strong-disorder renormalization group algorithm and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or fewer space dimensions, the fractal dimension is lower than the space dimension. This means that interfaces are not space filling, thus implying that replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space dimension in six dimensions, indicating that replica symmetry breaking occurs above six dimensions. In two space dimensions, the strong-disorder renormalization group results for the fractal dimension are in good agreement with essentially exact numerical results, but the small difference is significant. We discuss the origin of this close agreement. For the greedy algorithm there is analytical expectation that the fractal dimension is equal to the space dimension in six dimensions and our numerical results are consistent with this expectation.

Numerical Roll Reversal Predictor Corrector Aerocapture and Precision Landing Guidance Algorithms for the Mars Surveyor Program 2001 Missions

NASA Technical Reports Server (NTRS)

Powell, Richard W.

1998-01-01

This paper describes the development and evaluation of a numerical roll reversal predictor-corrector guidance algorithm for the atmospheric flight portion of the Mars Surveyor Program 2001 Orbiter and Lander missions. The Lander mission utilizes direct entry and has a demanding requirement to deploy its parachute within 10 km of the target deployment point. The Orbiter mission utilizes aerocapture to achieve a precise captured orbit with a single atmospheric pass. Detailed descriptions of these predictor-corrector algorithms are given. Also, results of three and six degree-of-freedom Monte Carlo simulations which include navigation, aerodynamics, mass properties and atmospheric density uncertainties are presented.

Parallel language constructs for tensor product computations on loosely coupled architectures

NASA Technical Reports Server (NTRS)

Mehrotra, Piyush; Vanrosendale, John

1989-01-01

Distributed memory architectures offer high levels of performance and flexibility, but have proven awkard to program. Current languages for nonshared memory architectures provide a relatively low level programming environment, and are poorly suited to modular programming, and to the construction of libraries. A set of language primitives designed to allow the specification of parallel numerical algorithms at a higher level is described. Tensor product array computations are focused on along with a simple but important class of numerical algorithms. The problem of programming 1-D kernal routines is focused on first, such as parallel tridiagonal solvers, and then how such parallel kernels can be combined to form parallel tensor product algorithms is examined.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane-Emden type

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Youssri, Y. H.

2013-10-01

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane-Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Reliability enhancement of Navier-Stokes codes through convergence acceleration

NASA Technical Reports Server (NTRS)

Merkle, Charles L.; Dulikravich, George S.

1995-01-01

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

Optimal Detection Range of RFID Tag for RFID-based Positioning System Using the k-NN Algorithm.

PubMed

Han, Soohee; Kim, Junghwan; Park, Choung-Hwan; Yoon, Hee-Cheon; Heo, Joon

2009-01-01

Positioning technology to track a moving object is an important and essential component of ubiquitous computing environments and applications. An RFID-based positioning system using the k-nearest neighbor (k-NN) algorithm can determine the position of a moving reader from observed reference data. In this study, the optimal detection range of an RFID-based positioning system was determined on the principle that tag spacing can be derived from the detection range. It was assumed that reference tags without signal strength information are regularly distributed in 1-, 2- and 3-dimensional spaces. The optimal detection range was determined, through analytical and numerical approaches, to be 125% of the tag-spacing distance in 1-dimensional space. Through numerical approaches, the range was 134% in 2-dimensional space, 143% in 3-dimensional space.

A study on directional resistivity logging-while-drilling based on self-adaptive hp-FEM

NASA Astrophysics Data System (ADS)

Liu, Dejun; Li, Hui; Zhang, Yingying; Zhu, Gengxue; Ai, Qinghui

2014-12-01

Numerical simulation of resistivity logging-while-drilling (LWD) tool response provides guidance for designing novel logging instruments and interpreting real-time logging data. In this paper, based on self-adaptive hp-finite element method (hp-FEM) algorithm, we analyze LWD tool response against model parameters and briefly illustrate geosteering capabilities of directional resistivity LWD. Numerical simulation results indicate that the change of source spacing is of obvious influence on the investigation depth and detecting precision of resistivity LWD tool; the change of frequency can improve the resolution of low-resistivity formation and high-resistivity formation. The simulation results also indicate that the self-adaptive hp-FEM algorithm has good convergence speed and calculation accuracy to guide the geologic steering drilling and it is suitable to simulate the response of resistivity LWD tools.

Modeling of fracture of protective concrete structures under impact loads

NASA Astrophysics Data System (ADS)

Radchenko, P. A.; Batuev, S. P.; Radchenko, A. V.; Plevkov, V. S.

2015-10-01

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Identification of overlapping communities and their hierarchy by locally calculating community-changing resolution levels

NASA Astrophysics Data System (ADS)

Havemann, Frank; Heinz, Michael; Struck, Alexander; Gläser, Jochen

2011-01-01

We propose a new local, deterministic and parameter-free algorithm that detects fuzzy and crisp overlapping communities in a weighted network and simultaneously reveals their hierarchy. Using a local fitness function, the algorithm greedily expands natural communities of seeds until the whole graph is covered. The hierarchy of communities is obtained analytically by calculating resolution levels at which communities grow rather than numerically by testing different resolution levels. This analytic procedure is not only more exact than its numerical alternatives such as LFM and GCE but also much faster. Critical resolution levels can be identified by searching for intervals in which large changes of the resolution do not lead to growth of communities. We tested our algorithm on benchmark graphs and on a network of 492 papers in information science. Combined with a specific post-processing, the algorithm gives much more precise results on LFR benchmarks with high overlap compared to other algorithms and performs very similarly to GCE.

A simple algorithm for beam profile diagnostics using a thermographic camera

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

Katagiri, Ken; Hojo, Satoru; Honma, Toshihiro

2014-03-15

A new algorithm for digital image processing apparatuses is developed to evaluate profiles of high-intensity DC beams from temperature images of irradiated thin foils. Numerical analyses are performed to examine the reliability of the algorithm. To simulate the temperature images acquired by a thermographic camera, temperature distributions are numerically calculated for 20 MeV proton beams with different parameters. Noise in the temperature images which is added by the camera sensor is also simulated to account for its effect. Using the algorithm, beam profiles are evaluated from the simulated temperature images and compared with exact solutions. We find that niobium ismore » an appropriate material for the thin foil used in the diagnostic system. We also confirm that the algorithm is adaptable over a wide beam current range of 0.11–214 μA, even when employing a general-purpose thermographic camera with rather high noise (ΔT{sub NETD} ≃ 0.3 K; NETD: noise equivalent temperature difference)« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE PAGES

Jakeman, John D.; Narayan, Akil; Zhou, Tao

2017-06-22

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Adaptive Load-Balancing Algorithms Using Symmetric Broadcast Networks

NASA Technical Reports Server (NTRS)

Das, Sajal K.; Biswas, Rupak; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

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 Dam 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 novel SBN-based load-balancing algorithms, and implement them on an SP2. A thorough experimental study with Poisson-distributed synthetic loads demonstrates that these algorithms are very effective in balancing system load while minimizing processor idle time. They also compare favorably with several other existing load-balancing techniques. Additional experiments performed with real data demonstrate that the SBN approach is effective in adaptive computational science and engineering applications where dynamic load balancing is extremely crucial.

Adaptive rehabilitation gaming system: on-line individualization of stroke rehabilitation.

PubMed

Nirme, Jens; Duff, Armin; Verschure, Paul F M J

2011-01-01

The effects of stroke differ considerably in degree and symptoms for different patients. It has been shown that specific, individualized and varied therapy favors recovery. The Rehabilitation Gaming System (RGS) is a Virtual Reality (VR) based rehabilitation system designed following these principles. We have developed two algorithms to control the level of task difficulty that a user of the RGS is exposed to, as well as providing controlled variation in the therapy. In this paper, we compare the two algorithms by running numerical simulations and a study with healthy subjects. We show that both algorithms allow for individualization of the challenge level of the task. Further, the results reveal that the algorithm that iteratively learns a user model for each subject also allows a high variation of the task.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

Joint Optimization of Receiver Placement and Illuminator Selection for a Multiband Passive Radar Network.

PubMed

Xie, Rui; Wan, Xianrong; Hong, Sheng; Yi, Jianxin

2017-06-14

The performance of a passive radar network can be greatly improved by an optimal radar network structure. Generally, radar network structure optimization consists of two aspects, namely the placement of receivers in suitable places and selection of appropriate illuminators. The present study investigates issues concerning the joint optimization of receiver placement and illuminator selection for a passive radar network. Firstly, the required radar cross section (RCS) for target detection is chosen as the performance metric, and the joint optimization model boils down to the partition p -center problem (PPCP). The PPCP is then solved by a proposed bisection algorithm. The key of the bisection algorithm lies in solving the partition set covering problem (PSCP), which can be solved by a hybrid algorithm developed by coupling the convex optimization with the greedy dropping algorithm. In the end, the performance of the proposed algorithm is validated via numerical simulations.

Parallel Algorithms for Least Squares and Related Computations.

DTIC Science & Technology

1991-03-22

for dense computations in linear algebra . The work has recently been published in a general reference book on parallel algorithms by SIAM. AFO SR...written his Ph.D. dissertation with the principal investigator. (See publication 6.) • Parallel Algorithms for Dense Linear Algebra Computations. Our...and describe and to put into perspective a selection of the more important parallel algorithms for numerical linear algebra . We give a major new

Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

NASA Astrophysics Data System (ADS)

Li, Xiao; Scaglione, Anna

2013-11-01

The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations

NASA Astrophysics Data System (ADS)

Zhang, Ying; Wu, Ai-Guo; Sun, Hui-Jie

2018-01-01

In this paper, an implicit iterative algorithm is proposed for solving a class of Lyapunov matrix equations arising in Itô stochastic linear systems. A tuning parameter is introduced in this algorithm, and thus the convergence rate of the algorithm can be changed. Some conditions are presented such that the developed algorithm is convergent. In addition, an explicit expression is also derived for the optimal tuning parameter, which guarantees that the obtained algorithm achieves its fastest convergence rate. Finally, numerical examples are employed to illustrate the effectiveness of the given algorithm.

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

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

Priimak, Dmitri

2014-12-01

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

Multi-fidelity stochastic collocation method for computation of statistical moments

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

Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu; Linebarger, Erin M., E-mail: aerinline@sci.utah.edu; Xiu, Dongbin, E-mail: xiu.16@osu.edu

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

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.

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.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Algorithm Estimates Microwave Water-Vapor Delay

NASA Technical Reports Server (NTRS)

Robinson, Steven E.

1989-01-01

Accuracy equals or exceeds conventional linear algorithms. "Profile" algorithm improved algorithm using water-vapor-radiometer data to produce estimates of microwave delays caused by water vapor in troposphere. Does not require site-specific and weather-dependent empirical parameters other than standard meteorological data, latitude, and altitude for use in conjunction with published standard atmospheric data. Basic premise of profile algorithm, wet-path delay approximated closely by solution to simplified version of nonlinear delay problem and generated numerically from each radiometer observation and simultaneous meteorological data.

A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix

NASA Technical Reports Server (NTRS)

Shroff, Gautam

1989-01-01

A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.

An arrhythmia classification algorithm using a dedicated wavelet adapted to different subjects.

PubMed

Kim, Jinkwon; Min, Se Dong; Lee, Myoungho

2011-06-27

Numerous studies have been conducted regarding a heartbeat classification algorithm over the past several decades. However, many algorithms have also been studied to acquire robust performance, as biosignals have a large amount of variation among individuals. Various methods have been proposed to reduce the differences coming from personal characteristics, but these expand the differences caused by arrhythmia. In this paper, an arrhythmia classification algorithm using a dedicated wavelet adapted to individual subjects is proposed. We reduced the performance variation using dedicated wavelets, as in the ECG morphologies of the subjects. The proposed algorithm utilizes morphological filtering and a continuous wavelet transform with a dedicated wavelet. A principal component analysis and linear discriminant analysis were utilized to compress the morphological data transformed by the dedicated wavelets. An extreme learning machine was used as a classifier in the proposed algorithm. A performance evaluation was conducted with the MIT-BIH arrhythmia database. The results showed a high sensitivity of 97.51%, specificity of 85.07%, accuracy of 97.94%, and a positive predictive value of 97.26%. The proposed algorithm achieves better accuracy than other state-of-the-art algorithms with no intrasubject between the training and evaluation datasets. And it significantly reduces the amount of intervention needed by physicians.

An arrhythmia classification algorithm using a dedicated wavelet adapted to different subjects

PubMed Central

2011-01-01

Background Numerous studies have been conducted regarding a heartbeat classification algorithm over the past several decades. However, many algorithms have also been studied to acquire robust performance, as biosignals have a large amount of variation among individuals. Various methods have been proposed to reduce the differences coming from personal characteristics, but these expand the differences caused by arrhythmia. Methods In this paper, an arrhythmia classification algorithm using a dedicated wavelet adapted to individual subjects is proposed. We reduced the performance variation using dedicated wavelets, as in the ECG morphologies of the subjects. The proposed algorithm utilizes morphological filtering and a continuous wavelet transform with a dedicated wavelet. A principal component analysis and linear discriminant analysis were utilized to compress the morphological data transformed by the dedicated wavelets. An extreme learning machine was used as a classifier in the proposed algorithm. Results A performance evaluation was conducted with the MIT-BIH arrhythmia database. The results showed a high sensitivity of 97.51%, specificity of 85.07%, accuracy of 97.94%, and a positive predictive value of 97.26%. Conclusions The proposed algorithm achieves better accuracy than other state-of-the-art algorithms with no intrasubject between the training and evaluation datasets. And it significantly reduces the amount of intervention needed by physicians. PMID:21707989

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Comparison of particle tracking algorithms in commercial CFD packages: sedimentation and diffusion.

PubMed

Robinson, Risa J; Snyder, Pam; Oldham, Michael J

2007-05-01

Computational fluid dynamic modeling software has enabled microdosimetry patterns of inhaled toxins and toxicants to be predicted and visualized, and is being used in inhalation toxicology and risk assessment. These predicted microdosimetry patterns in airway structures are derived from predicted airflow patterns within these airways and particle tracking algorithms used in computational fluid dynamics (CFD) software packages. Although these commercial CFD codes have been tested for accuracy under various conditions, they have not been well tested for respiratory flows in general. Nor has their particle tracking algorithm accuracy been well studied. In this study, three software packages, Fluent Discrete Phase Model (DPM), Fluent Fine Particle Model (FPM), and ANSYS CFX, were evaluated. Sedimentation and diffusion were each isolated in a straight tube geometry and tested for accuracy. A range of flow rates corresponding to adult low activity (minute ventilation = 10 L/min) and to heavy exertion (minute ventilation = 60 L/min) were tested by varying the range of dimensionless diffusion and sedimentation parameters found using the Weibel symmetric 23 generation lung morphology. Numerical results for fully developed parabolic and uniform (slip) profiles were compared respectively, to Pich (1972) and Yu (1977) analytical sedimentation solutions. Schum and Yeh (1980) equations for sedimentation were also compared. Numerical results for diffusional deposition were compared to analytical solutions of Ingham (1975) for parabolic and uniform profiles. Significant differences were found among the various CFD software packages and between numerical and analytical solutions. Therefore, it is prudent to validate CFD predictions against analytical solutions in idealized geometry before tackling the complex geometries of the respiratory tract.

Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Colella, Phillip

2007-11-01

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.

Solution of quadratic matrix equations for free vibration analysis of structures.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

Summary of research in applied mathematics, numerical analysis, and computer sciences

NASA Technical Reports Server (NTRS)

1986-01-01

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

Meshless Method for Simulation of Compressible Flow

NASA Astrophysics Data System (ADS)

Nabizadeh Shahrebabak, Ebrahim

In the present age, rapid development in computing technology and high speed supercomputers has made numerical analysis and computational simulation more practical than ever before for large and complex cases. Numerical simulations have also become an essential means for analyzing the engineering problems and the cases that experimental analysis is not practical. There are so many sophisticated and accurate numerical schemes, which do these simulations. The finite difference method (FDM) has been used to solve differential equation systems for decades. Additional numerical methods based on finite volume and finite element techniques are widely used in solving problems with complex geometry. All of these methods are mesh-based techniques. Mesh generation is an essential preprocessing part to discretize the computation domain for these conventional methods. However, when dealing with mesh-based complex geometries these conventional mesh-based techniques can become troublesome, difficult to implement, and prone to inaccuracies. In this study, a more robust, yet simple numerical approach is used to simulate problems in an easier manner for even complex problem. The meshless, or meshfree, method is one such development that is becoming the focus of much research in the recent years. The biggest advantage of meshfree methods is to circumvent mesh generation. Many algorithms have now been developed to help make this method more popular and understandable for everyone. These algorithms have been employed over a wide range of problems in computational analysis with various levels of success. Since there is no connectivity between the nodes in this method, the challenge was considerable. The most fundamental issue is lack of conservation, which can be a source of unpredictable errors in the solution process. This problem is particularly evident in the presence of steep gradient regions and discontinuities, such as shocks that frequently occur in high speed compressible flow problems. To solve this discontinuity problem, this research study deals with the implementation of a conservative meshless method and its applications in computational fluid dynamics (CFD). One of the most common types of collocating meshless method the RBF-DQ, is used to approximate the spatial derivatives. The issue with meshless methods when dealing with highly convective cases is that they cannot distinguish the influence of fluid flow from upstream or downstream and some methodology is needed to make the scheme stable. Therefore, an upwinding scheme similar to one used in the finite volume method is added to capture steep gradient or shocks. This scheme creates a flexible algorithm within which a wide range of numerical flux schemes, such as those commonly used in the finite volume method, can be employed. In addition, a blended RBF is used to decrease the dissipation ensuing from the use of a low shape parameter. All of these steps are formulated for the Euler equation and a series of test problems used to confirm convergence of the algorithm. The present scheme was first employed on several incompressible benchmarks to validate the framework. The application of this algorithm is illustrated by solving a set of incompressible Navier-Stokes problems. Results from the compressible problem are compared with the exact solution for the flow over a ramp and compared with solutions of finite volume discretization and the discontinuous Galerkin method, both requiring a mesh. The applicability of the algorithm and its robustness are shown to be applied to complex problems.

New Numerical Approaches for Modeling Thermochemical Convection in a Compositionally Stratified Fluid

NASA Astrophysics Data System (ADS)

Puckett, E. G.; Turcotte, D. L.; He, Y.; Lokavarapu, H. V.; Robey, J.; Kellogg, L. H.

2017-12-01

Geochemical observations of mantle-derived rocks favor a nearly homogeneous upper mantle, the source of mid-ocean ridge basalts (MORB), and heterogeneous lower mantle regions.Plumes that generate ocean island basalts are thought to sample the lower mantle regions and exhibit more heterogeneity than MORB.These regions have been associated with lower mantle structures known as large low shear velocity provinces below Africa and the South Pacific.The isolation of these regions is attributed to compositional differences and density stratification that, consequently, have been the subject of computational and laboratory modeling designed to determine the parameter regime in which layering is stable and understanding how layering evolves.Mathematical models of persistent compositional interfaces in the Earth's mantle may be inherently unstable, at least in some regions of the parameter space relevant to the mantle.Computing approximations to solutions of such problems presents severe challenges, even to state-of-the-art numerical methods.Some numerical algorithms for modeling the interface between distinct compositions smear the interface at the boundary between compositions, such as methods that add numerical diffusion or `artificial viscosity' in order to stabilize the algorithm. We present two new algorithms for maintaining high-resolution and sharp computational boundaries in computations of these types of problems: a discontinuous Galerkin method with a bound preserving limiter and a Volume-of-Fluid interface tracking algorithm.We compare these new methods with two approaches widely used for modeling the advection of two distinct thermally driven compositional fields in mantle convection computations: a high-order accurate finite element advection algorithm with entropy viscosity and a particle method.We compare the performance of these four algorithms on three problems, including computing an approximation to the solution of an initially compositionally stratified fluid at Ra = 105 with buoyancy numbers {B} that vary from no stratification at B = 0 to stratified flow at large B.

Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

NASA Technical Reports Server (NTRS)

Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin

2013-01-01

Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.

A De-centralized Scheduling and Load Balancing Algorithm for Heterogeneous Grid Environments

NASA Technical Reports Server (NTRS)

Arora, Manish; Das, Sajal K.; Biswas, Rupak

2002-01-01

In the past two decades, numerous scheduling and load balancing techniques have been proposed for locally distributed multiprocessor systems. However, they all suffer from significant deficiencies when extended to a Grid environment: some use a centralized approach that renders the algorithm unscalable, while others assume the overhead involved in searching for appropriate resources to be negligible. Furthermore, classical scheduling algorithms do not consider a Grid node to be N-resource rich and merely work towards maximizing the utilization of one of the resources. In this paper, we propose a new scheduling and load balancing algorithm for a generalized Grid model of N-resource nodes that not only takes into account the node and network heterogeneity, but also considers the overhead involved in coordinating among the nodes. Our algorithm is decentralized, scalable, and overlaps the node coordination time with that of the actual processing of ready jobs, thus saving valuable clock cycles needed for making decisions. The proposed algorithm is studied by conducting simulations using the Message Passing Interface (MPI) paradigm.

A De-Centralized Scheduling and Load Balancing Algorithm for Heterogeneous Grid Environments

NASA Technical Reports Server (NTRS)

Arora, Manish; Das, Sajal K.; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2002-01-01

In the past two decades, numerous scheduling and load balancing techniques have been proposed for locally distributed multiprocessor systems. However, they all suffer from significant deficiencies when extended to a Grid environment: some use a centralized approach that renders the algorithm unscalable, while others assume the overhead involved in searching for appropriate resources to be negligible. Furthermore, classical scheduling algorithms do not consider a Grid node to be N-resource rich and merely work towards maximizing the utilization of one of the resources. In this paper we propose a new scheduling and load balancing algorithm for a generalized Grid model of N-resource nodes that not only takes into account the node and network heterogeneity, but also considers the overhead involved in coordinating among the nodes. Our algorithm is de-centralized, scalable, and overlaps the node coordination time of the actual processing of ready jobs, thus saving valuable clock cycles needed for making decisions. The proposed algorithm is studied by conducting simulations using the Message Passing Interface (MPI) paradigm.

Optimization model of conventional missile maneuvering route based on improved Floyd algorithm

NASA Astrophysics Data System (ADS)

Wu, Runping; Liu, Weidong

2018-04-01

Missile combat plays a crucial role in the victory of war under high-tech conditions. According to the characteristics of maneuver tasks of conventional missile units in combat operations, the factors influencing road maneuvering are analyzed. Based on road distance, road conflicts, launching device speed, position requirements, launch device deployment, Concealment and so on. The shortest time optimization model was built to discuss the situation of road conflict and the strategy of conflict resolution. The results suggest that in the process of solving road conflict, the effect of node waiting is better than detour to another way. In this study, we analyzed the deficiency of the traditional Floyd algorithm which may limit the optimal way of solving road conflict, and put forward the improved Floyd algorithm, meanwhile, we designed the algorithm flow which would be better than traditional Floyd algorithm. Finally, throgh a numerical example, the model and the algorithm were proved to be reliable and effective.

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Implementation of a state of the art automated system for the production of cloud/water vapor motion winds from geostationary satellites

NASA Technical Reports Server (NTRS)

Velden, Christopher

1995-01-01

The research objectives in this proposal were part of a continuing program at UW-CIMSS to develop and refine an automated geostationary satellite winds processing system which can be utilized in both research and operational environments. The majority of the originally proposed tasks were successfully accomplished, and in some cases the progress exceeded the original goals. Much of the research and development supported by this grant resulted in upgrades and modifications to the existing automated satellite winds tracking algorithm. These modifications were put to the test through case study demonstrations and numerical model impact studies. After being successfully demonstrated, the modifications and upgrades were implemented into the NESDIS algorithms in Washington DC, and have become part of the operational support. A major focus of the research supported under this grant attended to the continued development of water vapor tracked winds from geostationary observations. The fully automated UW-CIMSS tracking algorithm has been tuned to provide complete upper-tropospheric coverage from this data source, with data set quality close to that of operational cloud motion winds. Multispectral water vapor observations were collected and processed from several different geostationary satellites. The tracking and quality control algorithms were tuned and refined based on ground-truth comparisons and case studies involving impact on numerical model analyses and forecasts. The results have shown the water vapor motion winds are of good quality, complement the cloud motion wind data, and can have a positive impact in NWP on many meteorological scales.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

A Study of Multigrid Preconditioners Using Eigensystem Analysis

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Swanson, R. C.

2005-01-01

The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

Algorithm Diversity for Resilent Systems

DTIC Science & Technology

2016-06-27

data structures. 15. SUBJECT TERMS computer security, software diversity, program transformation 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18...systematic method for transforming Datalog rules with general universal and existential quantification into efficient algorithms with precise complexity...worst case in the size of the ground rules. There are numerous choices during the transformation that lead to diverse algorithms and different

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

PubMed

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

A recursive algorithm for Zernike polynomials

NASA Technical Reports Server (NTRS)

Davenport, J. W.

1982-01-01

The analysis of a function defined on a rotationally symmetric system, with either a circular or annular pupil is discussed. In order to numerically analyze such systems it is typical to expand the given function in terms of a class of orthogonal polynomials. Because of their particular properties, the Zernike polynomials are especially suited for numerical calculations. Developed is a recursive algorithm that can be used to generate the Zernike polynomials up to a given order. The algorithm is recursively defined over J where R(J,N) is the Zernike polynomial of degree N obtained by orthogonalizing the sequence R(J), R(J+2), ..., R(J+2N) over (epsilon, 1). The terms in the preceding row - the (J-1) row - up to the N+1 term is needed for generating the (J,N)th term. Thus, the algorith generates an upper left-triangular table. This algorithm was placed in the computer with the necessary support program also included.

A novel algorithm using an orthotropic material model for topology optimization

NASA Astrophysics Data System (ADS)

Tong, Liyong; Luo, Quantian

2017-09-01

This article presents a novel algorithm for topology optimization using an orthotropic material model. Based on the virtual work principle, mathematical formulations for effective orthotropic material properties of an element containing two materials are derived. An algorithm is developed for structural topology optimization using four orthotropic material properties, instead of one density or area ratio, in each element as design variables. As an illustrative example, minimum compliance problems for linear and nonlinear structures are solved using the present algorithm in conjunction with the moving iso-surface threshold method. The present numerical results reveal that: (1) chequerboards and single-node connections are not present even without filtering; (2) final topologies do not contain large grey areas even using a unity penalty factor; and (3) the well-known numerical issues caused by low-density material when considering geometric nonlinearity are resolved by eliminating low-density elements in finite element analyses.

Classification of cardiac rhythm using heart rate dynamical measures: validation in MIT-BIH databases.

PubMed

Carrara, Marta; Carozzi, Luca; Moss, Travis J; de Pasquale, Marco; Cerutti, Sergio; Lake, Douglas E; Moorman, J Randall; Ferrario, Manuela

2015-01-01

Identification of atrial fibrillation (AF) is a clinical imperative. Heartbeat interval time series are increasingly available from personal monitors, allowing new opportunity for AF diagnosis. Previously, we devised numerical algorithms for identification of normal sinus rhythm (NSR), AF, and SR with frequent ectopy using dynamical measures of heart rate. Here, we wished to validate them in the canonical MIT-BIH ECG databases. We tested algorithms on the NSR, AF and arrhythmia databases. When the databases were combined, the positive predictive value of the new algorithms exceeded 95% for NSR and AF, and was 40% for SR with ectopy. Further, dynamical measures did not distinguish atrial from ventricular ectopy. Inspection of individual 24hour records showed good correlation of observed and predicted rhythms. Heart rate dynamical measures are effective ingredients in numerical algorithms to classify cardiac rhythm from the heartbeat intervals time series alone. Copyright © 2015 Elsevier Inc. All rights reserved.

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

DOE PAGES

Regis, Rommel G.; Wild, Stefan M.

2016-09-26

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, amore » chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.« less

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

NASA Astrophysics Data System (ADS)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

Algorithm-Based Fault Tolerance for Numerical Subroutines

NASA Technical Reports Server (NTRS)

Tumon, Michael; Granat, Robert; Lou, John

2007-01-01

A software library implements a new methodology of detecting faults in numerical subroutines, thus enabling application programs that contain the subroutines to recover transparently from single-event upsets. The software library in question is fault-detecting middleware that is wrapped around the numericalsubroutines. Conventional serial versions (based on LAPACK and FFTW) and a parallel version (based on ScaLAPACK) exist. The source code of the application program that contains the numerical subroutines is not modified, and the middleware is transparent to the user. The methodology used is a type of algorithm- based fault tolerance (ABFT). In ABFT, a checksum is computed before a computation and compared with the checksum of the computational result; an error is declared if the difference between the checksums exceeds some threshold. Novel normalization methods are used in the checksum comparison to ensure correct fault detections independent of algorithm inputs. In tests of this software reported in the peer-reviewed literature, this library was shown to enable detection of 99.9 percent of significant faults while generating no false alarms.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Numerical and experimental analysis of a ducted propeller designed by a fully automated optimization process under open water condition

NASA Astrophysics Data System (ADS)

Yu, Long; Druckenbrod, Markus; Greve, Martin; Wang, Ke-qi; Abdel-Maksoud, Moustafa

2015-10-01

A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The developed process allows the direct integration of a RANSE solver in the design stage. A practical ducted propeller design case study is carried out for validation. Numerical simulations and open water tests are fulfilled and proved that the optimum ducted propeller improves hydrodynamic performance as predicted.

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Signal Analysis Algorithms for Optimized Fitting of Nonresonant Laser Induced Thermal Acoustics Damped Sinusoids

NASA Technical Reports Server (NTRS)

Balla, R. Jeffrey; Miller, Corey A.

2008-01-01

This study seeks a numerical algorithm which optimizes frequency precision for the damped sinusoids generated by the nonresonant LITA technique. It compares computed frequencies, frequency errors, and fit errors obtained using five primary signal analysis methods. Using variations on different algorithms within each primary method, results from 73 fits are presented. Best results are obtained using an AutoRegressive method. Compared to previous results using Prony s method, single shot waveform frequencies are reduced approx.0.4% and frequency errors are reduced by a factor of approx.20 at 303K to approx. 0.1%. We explore the advantages of high waveform sample rates and potential for measurements in low density gases.

Equal Area Logistic Estimation for Item Response Theory

NASA Astrophysics Data System (ADS)

Lo, Shih-Ching; Wang, Kuo-Chang; Chang, Hsin-Li

2009-08-01

Item response theory (IRT) models use logistic functions exclusively as item response functions (IRFs). Applications of IRT models require obtaining the set of values for logistic function parameters that best fit an empirical data set. However, success in obtaining such set of values does not guarantee that the constructs they represent actually exist, for the adequacy of a model is not sustained by the possibility of estimating parameters. In this study, an equal area based two-parameter logistic model estimation algorithm is proposed. Two theorems are given to prove that the results of the algorithm are equivalent to the results of fitting data by logistic model. Numerical results are presented to show the stability and accuracy of the algorithm.

Evaluation of Skin Temperatures Retrieved from GOES-8

NASA Technical Reports Server (NTRS)

Suggs, Ronnie, J.; Jedlovec, G. J.; Lapenta, W. M.; Haines, S. L.

2000-01-01

Skin temperatures derived from geostationary satellites have the potential of providing the temporal and spatial resolution needed for model assimilation. To adequately assess the potential improvements in numerical model forecasts that can be made by assimilating satellite data, an estimate of the accuracy of the skin temperature product is necessary. A particular skin temperature algorithm, the Physical Split Window Technique, that uses the longwave infrared channels of the GOES Imager has shown promise in recent model assimilation studies to provide land surface temperatures with reasonable accuracy. A comparison of retrieved GOES-8 skin temperatures from this algorithm with in situ measurements is presented. Various retrieval algorithm issues are addressed including surface emissivity

Numerically robust and efficient nonlocal electron transport in 2D DRACO simulations

NASA Astrophysics Data System (ADS)

Cao, Duc; Chenhall, Jeff; Moses, Greg; Delettrez, Jacques; Collins, Tim

2013-10-01

An improved implicit algorithm based on Schurtz, Nicolai and Busquet (SNB) algorithm for nonlocal electron transport is presented. Validation with direct drive shock timing experiments and verification with the Goncharov nonlocal model in 1D LILAC simulations demonstrate the viability of this efficient algorithm for producing 2D lagrangian radiation hydrodynamics direct drive simulations. Additionally, simulations provide strong incentive to further modify key parameters within the SNB theory, namely the ``mean free path.'' An example 2D polar drive simulation to study 2D effects of the nonlocal flux as well as mean free path modifications will also be presented. This research was supported by the University of Rochester Laboratory for Laser Energetics.

New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

NASA Astrophysics Data System (ADS)

Puckett, Elbridge Gerry; Turcotte, Donald L.; He, Ying; Lokavarapu, Harsha; Robey, Jonathan M.; Kellogg, Louise H.

2018-03-01

Geochemical observations of mantle-derived rocks favor a nearly homogeneous upper mantle, the source of mid-ocean ridge basalts (MORB), and heterogeneous lower mantle regions. Plumes that generate ocean island basalts are thought to sample the lower mantle regions and exhibit more heterogeneity than MORB. These regions have been associated with lower mantle structures known as large low shear velocity provinces (LLSVPS) below Africa and the South Pacific. The isolation of these regions is attributed to compositional differences and density stratification that, consequently, have been the subject of computational and laboratory modeling designed to determine the parameter regime in which layering is stable and understanding how layering evolves. Mathematical models of persistent compositional interfaces in the Earth's mantle may be inherently unstable, at least in some regions of the parameter space relevant to the mantle. Computing approximations to solutions of such problems presents severe challenges, even to state-of-the-art numerical methods. Some numerical algorithms for modeling the interface between distinct compositions smear the interface at the boundary between compositions, such as methods that add numerical diffusion or 'artificial viscosity' in order to stabilize the algorithm. We present two new algorithms for maintaining high-resolution and sharp computational boundaries in computations of these types of problems: a discontinuous Galerkin method with a bound preserving limiter and a Volume-of-Fluid interface tracking algorithm. We compare these new methods with two approaches widely used for modeling the advection of two distinct thermally driven compositional fields in mantle convection computations: a high-order accurate finite element advection algorithm with entropy viscosity and a particle method that carries a scalar quantity representing the location of each compositional field. All four algorithms are implemented in the open source finite element code ASPECT, which we use to compute the velocity, pressure, and temperature associated with the underlying flow field. We compare the performance of these four algorithms on three problems, including computing an approximation to the solution of an initially compositionally stratified fluid at Ra =105 with buoyancy numbers B that vary from no stratification at B = 0 to stratified flow at large B .

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Computational Astrophysical Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Norman, M. L.

1994-05-01

Cosmic magnetic fields have intrigued and vexed astrophysicists seeking to understand their complex dynamics in a wide variety of astronomical settings. Magnetic fields are believed to play an important role in regulating star formation in molecular clouds, providing an effective viscosity in accretion disks, accelerating astrophysical jets, and influencing the large scale structure of the ISM of disk galaxies. Radio observations of supernova remnants and extragalactic radio jets prove that magnetic fields are are fundamentally linked to astrophysical particle acceleration. Magnetic fields exist on cosmological scales as shown by the existence of radio halos in clusters of galaxies. Theoretical investigation of these and other phenomena require numerical simulations due to the inherent complexity of MHD, but until now neither the computer power nor the numerical algorithms existed to mount a serious attack on the most important problems. That has now changed. Advances in parallel computing and numerical algorithms now permit the simulation of fully nonlinear, time-dependent astrophysical MHD in 2D and 3D. In this talk, I will describe the ZEUS codes for astrophysical MHD developed at the Laboratory for Computational Astrophysics (LCA) at the University of Illinois. These codes are now available to the national community. The numerical algorithms and test suite used to validate them are briefly discussed. Several applications of ZEUS to topics listed above are presented. An extension of ZEUS to model ambipolar diffusion in weakly ionized plasmas is illustrated. I discuss how continuing exponential growth in computer power and new numerical algorithms under development will allow us to tackle two grand challenges: compressible MHD turbulence and relativistic MHD. This work is partially supported by grants NSF AST-9201113 and NASA NAG 5-2493.

GENERAL: Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem

NASA Astrophysics Data System (ADS)

Lu, Wei-Tao; Zhang, Hua; Wang, Shun-Jin

2008-07-01

Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge-Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP.

Algorithms for Brownian first-passage-time estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Numerical studies of the thermal design sensitivity calculation for a reaction-diffusion system with discontinuous derivatives

NASA Technical Reports Server (NTRS)

Hou, Jean W.; Sheen, Jeen S.

1987-01-01

The aim of this study is to find a reliable numerical algorithm to calculate thermal design sensitivities of a transient problem with discontinuous derivatives. The thermal system of interest is a transient heat conduction problem related to the curing process of a composite laminate. A logical function which can smoothly approximate the discontinuity is introduced to modify the system equation. Two commonly used methods, the adjoint variable method and the direct differentiation method, are then applied to find the design derivatives of the modified system. The comparisons of numerical results obtained by these two methods demonstrate that the direct differentiation method is a better choice to be used in calculating thermal design sensitivity.

Performance evaluation of Bragg coherent diffraction imaging

NASA Astrophysics Data System (ADS)

Öztürk, H.; Huang, X.; Yan, H.; Robinson, I. K.; Noyan, I. C.; Chu, Y. S.

2017-10-01

In this study, we present a numerical framework for modeling three-dimensional (3D) diffraction data in Bragg coherent diffraction imaging (Bragg CDI) experiments and evaluating the quality of obtained 3D complex-valued real-space images recovered by reconstruction algorithms under controlled conditions. The approach is used to systematically explore the performance and the detection limit of this phase-retrieval-based microscopy tool. The numerical investigation suggests that the superb performance of Bragg CDI is achieved with an oversampling ratio above 30 and a detection dynamic range above 6 orders. The observed performance degradation subject to the data binning processes is also studied. This numerical tool can be used to optimize experimental parameters and has the potential to significantly improve the throughput of Bragg CDI method.

Numerical Simulation of the Flow over a Segment-Conical Body on the Basis of Reynolds Equations

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Palchekovskaya, N. V.

2018-01-01

Numerical simulation was used to study the 3D supersonic flow over a segment-conical body similar in shape to the ExoMars space vehicle. The nonmonotone behavior of the normal force acting on the body placed in a supersonic gas flow was analyzed depending on the angle of attack. The simulation was based on the numerical solution of the unsteady Reynolds-averaged Navier-Stokes equations with a two-parameter differential turbulence model. The solution of the problem was obtained using the in-house solver HSFlow with an efficient parallel algorithm intended for multiprocessor super computers.

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Flowfield computation of entry vehicles

NASA Technical Reports Server (NTRS)

Prabhu, Dinesh K.

1990-01-01

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

A Taylor weak-statement algorithm for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

NASA Technical Reports Server (NTRS)

Bailey, David H.; Ferguson, Helaman R. P.

1988-01-01

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

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

Le, Hai P.; Cambier, Jean -Luc

Here, we present a numerical model and a set of conservative algorithms for Non-Maxwellian plasma kinetics with inelastic collisions. These algorithms self-consistently solve for the time evolution of an isotropic electron energy distribution function interacting with an atomic state distribution function of an arbitrary number of levels through collisional excitation, deexcitation, as well as ionization and recombination. Electron-electron collisions, responsible for thermalization of the electron distribution, are also included in the model. The proposed algorithms guarantee mass/charge and energy conservation in a single step, and is applied to the case of non-uniform gridding of the energy axis in the phasemore » space of the electron distribution function. Numerical test cases are shown to demonstrate the accuracy of the method and its conservation properties.« less

Variational data assimilation for the initial-value dynamo problem.

PubMed

Li, Kuan; Jackson, Andrew; Livermore, Philip W

2011-11-01

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries.

Information filtering via weighted heat conduction algorithm

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Guo, Qiang; Zhang, Yi-Cheng

2011-06-01

In this paper, by taking into account effects of the user and object correlations on a heat conduction (HC) algorithm, a weighted heat conduction (WHC) algorithm is presented. We argue that the edge weight of the user-object bipartite network should be embedded into the HC algorithm to measure the object similarity. The numerical results indicate that both the accuracy and diversity could be improved greatly compared with the standard HC algorithm and the optimal values reached simultaneously. On the Movielens and Netflix datasets, the algorithmic accuracy, measured by the average ranking score, can be improved by 39.7% and 56.1% in the optimal case, respectively, and the diversity could reach 0.9587 and 0.9317 when the recommendation list equals to 5. Further statistical analysis indicates that, in the optimal case, the distributions of the edge weight are changed to the Poisson form, which may be the reason why HC algorithm performance could be improved. This work highlights the effect of edge weight on a personalized recommendation study, which maybe an important factor affecting personalized recommendation performance.

An approach toward the numerical evaluation of multi-loop Feynman diagrams

NASA Astrophysics Data System (ADS)

Passarino, Giampiero

2001-12-01

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model. As a first step an algorithm, proposed by F.V. Tkachov and based on the so-called generalized Bernstein functional relation, is applied to one-loop multi-leg diagrams with particular emphasis to the presence of infrared singularities, to the problem of tensorial reduction and to the classification of all singularities of a given diagram. Successively, the extension of the algorithm to two-loop diagrams is examined. The proposed solution consists in applying the functional relation to the one-loop sub-diagram which has the largest number of internal lines. In this way the integrand can be made smooth, a part from a factor which is a polynomial in xS, the vector of Feynman parameters needed for the complementary sub-diagram with the smallest number of internal lines. Since the procedure does not introduce new singularities one can distort the xS-integration hyper-contour into the complex hyper-plane, thus achieving numerical stability. The algorithm is then modified to deal with numerical evaluation around normal thresholds. Concise and practical formulas are assembled and presented, numerical results and comparisons with the available literature are shown and discussed for the so-called sunset topology.

Data association approaches in bearings-only multi-target tracking

NASA Astrophysics Data System (ADS)

Xu, Benlian; Wang, Zhiquan

2008-03-01

According to requirements of time computation complexity and correctness of data association of the multi-target tracking, two algorithms are suggested in this paper. The proposed Algorithm 1 is developed from the modified version of dual Simplex method, and it has the advantage of direct and explicit form of the optimal solution. The Algorithm 2 is based on the idea of Algorithm 1 and rotational sort method, it combines not only advantages of Algorithm 1, but also reduces the computational burden, whose complexity is only 1/ N times that of Algorithm 1. Finally, numerical analyses are carried out to evaluate the performance of the two data association algorithms.

Studies of the effects of curvature on dilution jet mixing

NASA Technical Reports Server (NTRS)

Holdeman, James D.; Srinivasan, Ram; Reynolds, Robert S.; White, Craig D.

1992-01-01

An analytical program was conducted using both three-dimensional numerical and empirical models to investigate the effects of transition liner curvature on the mixing of jets injected into a confined crossflow. The numerical code is of the TEACH type with hybrid numerics; it uses the power-law and SIMPLER algorithms, an orthogonal curvilinear coordinate system, and an algebraic Reynolds stress turbulence model. From the results of the numerical calculations, an existing empirical model for the temperature field downstream of single and multiple rows of jets injected into a straight rectangular duct was extended to model the effects of curvature. Temperature distributions, calculated with both the numerical and empirical models, are presented to show the effects of radius of curvature and inner and outer wall injection for single and opposed rows of cool dilution jets injected into a hot mainstream flow.

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

A new shock-capturing numerical scheme for ideal hydrodynamics

NASA Astrophysics Data System (ADS)

Fecková, Z.; Tomášik, B.

2015-05-01

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

Belief Propagation Algorithm for Portfolio Optimization Problems

PubMed Central

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462

Explicit Filtering Based Low-Dose Differential Phase Reconstruction Algorithm with the Grating Interferometry.

PubMed

Jiang, Xiaolei; Zhang, Li; Zhang, Ran; Yin, Hongxia; Wang, Zhenchang

2015-01-01

X-ray grating interferometry offers a novel framework for the study of weakly absorbing samples. Three kinds of information, that is, the attenuation, differential phase contrast (DPC), and dark-field images, can be obtained after a single scanning, providing additional and complementary information to the conventional attenuation image. Phase shifts of X-rays are measured by the DPC method; hence, DPC-CT reconstructs refraction indexes rather than attenuation coefficients. In this work, we propose an explicit filtering based low-dose differential phase reconstruction algorithm, which enables reconstruction from reduced scanning without artifacts. The algorithm adopts a differential algebraic reconstruction technique (DART) with the explicit filtering based sparse regularization rather than the commonly used total variation (TV) method. Both the numerical simulation and the biological sample experiment demonstrate the feasibility of the proposed algorithm.

Explicit Filtering Based Low-Dose Differential Phase Reconstruction Algorithm with the Grating Interferometry

PubMed Central

Zhang, Li; Zhang, Ran; Yin, Hongxia; Wang, Zhenchang

2015-01-01

X-ray grating interferometry offers a novel framework for the study of weakly absorbing samples. Three kinds of information, that is, the attenuation, differential phase contrast (DPC), and dark-field images, can be obtained after a single scanning, providing additional and complementary information to the conventional attenuation image. Phase shifts of X-rays are measured by the DPC method; hence, DPC-CT reconstructs refraction indexes rather than attenuation coefficients. In this work, we propose an explicit filtering based low-dose differential phase reconstruction algorithm, which enables reconstruction from reduced scanning without artifacts. The algorithm adopts a differential algebraic reconstruction technique (DART) with the explicit filtering based sparse regularization rather than the commonly used total variation (TV) method. Both the numerical simulation and the biological sample experiment demonstrate the feasibility of the proposed algorithm. PMID:26089971

Belief Propagation Algorithm for Portfolio Optimization Problems.

PubMed

Shinzato, Takashi; Yasuda, Muneki

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

The use of image analysis in evaluation of the fibers orientation in Wood-polymer composites (WPC)

NASA Astrophysics Data System (ADS)

Bednarz, Arkadiusz; Frącz, Wiesław; Janowski, Grzegorz

2016-12-01

In this paper a novel way of a digital analysis of fibers orientation with a five-step algorithmwas presented. In the study, a molded piece with a dumbbell shape prepared from wood-polymer composite was used. The injection molding process was examined in experimental and numerical way. Based on the developed mathematical algorithm, a significant compliance of fiber orientation in different areas of the molded piece was obtained. The main aim of thisworkwas fiber orientation analysis of wood-polymer composites. An additional goal of thiswork was the comparison of the results reached in numerical analysis with results obtained from an experiment. The results of this research were important for the scientific and also from the practical point of view. In future works the prepared algorithm could be used to reach optimal parameters of the injection molding process.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Technical Reports Server (NTRS)

Chitsomboon, Tawit

1992-01-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Astrophysics Data System (ADS)

Chitsomboon, Tawit

1992-02-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Modeling of fracture of protective concrete structures under impact loads

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

Radchenko, P. A., E-mail: radchenko@live.ru; Batuev, S. P.; Radchenko, A. V.

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength propertiesmore » of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.« less

An online input force time history reconstruction algorithm using dynamic principal component analysis

NASA Astrophysics Data System (ADS)

Prawin, J.; Rama Mohan Rao, A.

2018-01-01

The knowledge of dynamic loads acting on a structure is always required for many practical engineering problems, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. In this paper, we present an online input force time history reconstruction algorithm using Dynamic Principal Component Analysis (DPCA) from the acceleration time history response measurements using moving windows. We also present an optimal sensor placement algorithm to place limited sensors at dynamically sensitive spatial locations. The major advantage of the proposed input force identification algorithm is that it does not require finite element idealization of structure unlike the earlier formulations and therefore free from physical modelling errors. We have considered three numerical examples to validate the accuracy of the proposed DPCA based method. Effects of measurement noise, multiple force identification, different kinds of loading, incomplete measurements, and high noise levels are investigated in detail. Parametric studies have been carried out to arrive at optimal window size and also the percentage of window overlap. Studies presented in this paper clearly establish the merits of the proposed algorithm for online load identification.

Aerocapture Guidance Algorithm Comparison Campaign

NASA Technical Reports Server (NTRS)

Rousseau, Stephane; Perot, Etienne; Graves, Claude; Masciarelli, James P.; Queen, Eric

2002-01-01

The aerocapture is a promising technique for the future human interplanetary missions. The Mars Sample Return was initially based on an insertion by aerocapture. A CNES orbiter Mars Premier was developed to demonstrate this concept. Mainly due to budget constraints, the aerocapture was cancelled for the French orbiter. A lot of studies were achieved during the three last years to develop and test different guidance algorithms (APC, EC, TPC, NPC). This work was shared between CNES and NASA, with a fruitful joint working group. To finish this study an evaluation campaign has been performed to test the different algorithms. The objective was to assess the robustness, accuracy, capability to limit the load, and the complexity of each algorithm. A simulation campaign has been specified and performed by CNES, with a similar activity on the NASA side to confirm the CNES results. This evaluation has demonstrated that the numerical guidance principal is not competitive compared to the analytical concepts. All the other algorithms are well adapted to guaranty the success of the aerocapture. The TPC appears to be the more robust, the APC the more accurate, and the EC appears to be a good compromise.

Solving Capacitated Closed Vehicle Routing Problem with Time Windows (CCVRPTW) using BRKGA with local search

NASA Astrophysics Data System (ADS)

Prasetyo, H.; Alfatsani, M. A.; Fauza, G.

2018-05-01

The main issue in vehicle routing problem (VRP) is finding the shortest route of product distribution from the depot to outlets to minimize total cost of distribution. Capacitated Closed Vehicle Routing Problem with Time Windows (CCVRPTW) is one of the variants of VRP that accommodates vehicle capacity and distribution period. Since the main problem of CCVRPTW is considered a non-polynomial hard (NP-hard) problem, it requires an efficient and effective algorithm to solve the problem. This study was aimed to develop Biased Random Key Genetic Algorithm (BRKGA) that is combined with local search to solve the problem of CCVRPTW. The algorithm design was then coded by MATLAB. Using numerical test, optimum algorithm parameters were set and compared with the heuristic method and Standard BRKGA to solve a case study on soft drink distribution. Results showed that BRKGA combined with local search resulted in lower total distribution cost compared with the heuristic method. Moreover, the developed algorithm was found to be successful in increasing the performance of Standard BRKGA.

Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Mass preserving registration for heart MR images.

PubMed

Zhu, Lei; Haker, Steven; Tannenbaum, Allen

2005-01-01

This paper presents a new algorithm for non-rigid registration between two doubly-connected regions. Our algorithm is based on harmonic analysis and the theory of optimal mass transport. It assumes an underlining continuum model, in which the total amount of mass is exactly preserved during the transformation of tissues. We use a finite element approach to numerically implement the algorithm.

Mass Preserving Registration for Heart MR Images

PubMed Central

Zhu, Lei; Haker, Steven; Tannenbaum, Allen

2013-01-01

This paper presents a new algorithm for non-rigid registration between two doubly-connected regions. Our algorithm is based on harmonic analysis and the theory of optimal mass transport. It assumes an underlining continuum model, in which the total amount of mass is exactly preserved during the transformation of tissues. We use a finite element approach to numerically implement the algorithm. PMID:16685954

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

NASA Astrophysics Data System (ADS)

Ivanov, I.; Imsland, Lars; Bogdanova, B.

2017-03-01

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

PubMed

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Harmony Search Method: Theory and Applications

PubMed Central

Gao, X. Z.; Govindasamy, V.; Xu, H.; Wang, X.; Zenger, K.

2015-01-01

The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem. PMID:25945083

Optimal rail container shipment planning problem in multimodal transportation

NASA Astrophysics Data System (ADS)

Cao, Chengxuan; Gao, Ziyou; Li, Keping

2012-09-01

The optimal rail container shipment planning problem in multimodal transportation is studied in this article. The characteristics of the multi-period planning problem is presented and the problem is formulated as a large-scale 0-1 integer programming model, which maximizes the total profit generated by all freight bookings accepted in a multi-period planning horizon subject to the limited capacities. Two heuristic algorithms are proposed to obtain an approximate optimal solution of the problem. Finally, numerical experiments are conducted to demonstrate the proposed formulation and heuristic algorithms.

An algorithm for simulating fracture of cohesive-frictional materials

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

Nukala, Phani K; Sampath, Rahul S; Barai, Pallab

Fracture of disordered frictional granular materials is dominated by interfacial failure response that is characterized by de-cohesion followed by frictional sliding response. To capture such an interfacial failure response, we introduce a cohesive-friction random fuse model (CFRFM), wherein the cohesive response of the interface is represented by a linear stress-strain response until a failure threshold, which is then followed by a constant response at a threshold lower than the initial failure threshold to represent the interfacial frictional sliding mechanism. This paper presents an efficient algorithm for simulating fracture of such disordered frictional granular materials using the CFRFM. We note that,more » when applied to perfectly plastic disordered materials, our algorithm is both theoretically and numerically equivalent to the traditional tangent algorithm (Roux and Hansen 1992 J. Physique II 2 1007) used for such simulations. However, the algorithm is general and is capable of modeling discontinuous interfacial response. Our numerical simulations using the algorithm indicate that the local and global roughness exponents ({zeta}{sub loc} and {zeta}, respectively) of the fracture surface are equal to each other, and the two-dimensional crack roughness exponent is estimated to be {zeta}{sub loc} = {zeta} = 0.69 {+-} 0.03.« less

The Even-Rho and Even-Epsilon Algorithms for Accelerating Convergence of a Numerical Sequence

DTIC Science & Technology

1981-12-01

equal, leading to zero or very small divisors. Computer programs implementing these algorithms are given along with sample output. An appreciable amount...calculation of the array of Shank’s transforms or, -A equivalently, of the related Padd Table. The :other, the even-rho algorithm, is closely related...leading to zero or very small divisors. Computer pro- grams implementing these algorithms are given along with sample output. An appreciable amount or

Describing Texts for Algorithms: How They Prescribe Operations and Integrate Cases. Reflections Based on Ancient Chinese Mathematical Sources

NASA Astrophysics Data System (ADS)

Chemla (林力娜), Karine

The texts of algorithms fall under the general rubric of instructional texts, discussed by J. Virbel in this book. An algorithm has two facets. It has a text—a written text—, which usually appears to be an enumerated list of operations. In addition, whenever an algorithm is applied to a specific set of numerical values, practitioners derive from its text a sequence of actions, or operations, to be carried out. In the execution of the algorithm, these actions generate events that constitute a flow of computations eventually yielding numerical results. This chapter aims mainly to develop some reflections on the relationship between these two facets: the text and the different sequences of actions that practitioners derive from it. I use two tools in my argumentation. Firstly, I use the description of textual enumerations, as developed by Jacques Virbel, to find out how enumerations of operations were carried out in the text of algorithms and how these enumerations were used. Then I focus on the language acts carried out in some of the sentences composing the texts, since, when prescribing operations, the texts of the algorithms differ in that they use distinct ways of carrying out directives. The conclusion highlights different ways in which the text of an algorithm can be general and convey meanings that go beyond simply prescribing operations.

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

An Improved Cuckoo Search Optimization Algorithm for the Problem of Chaotic Systems Parameter Estimation

PubMed Central

Wang, Jun; Zhou, Bihua; Zhou, Shudao

2016-01-01

This paper proposes an improved cuckoo search (ICS) algorithm to establish the parameters of chaotic systems. In order to improve the optimization capability of the basic cuckoo search (CS) algorithm, the orthogonal design and simulated annealing operation are incorporated in the CS algorithm to enhance the exploitation search ability. Then the proposed algorithm is used to establish parameters of the Lorenz chaotic system and Chen chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. Finally, the results are compared with the CS algorithm, genetic algorithm, and particle swarm optimization algorithm, and the compared results demonstrate the method is energy-efficient and superior. PMID:26880874

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

NASA Technical Reports Server (NTRS)

Smith, R. L.; Huang, C.

1986-01-01

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.

Coordinate Systems, Numerical Objects and Algorithmic Operations of Computational Experiment in Fluid Mechanics

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily

2016-02-01

The paper deals with the computer implementation of direct computational experiments in fluid mechanics, constructed on the basis of the approach developed by the authors. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the effciency of the algorithms developed by numerical procedures with natural parallelism. The paper examines the main objects and operations that let you manage computational experiments and monitor the status of the computation process. Special attention is given to a) realization of tensor representations of numerical schemes for direct simulation; b) realization of representation of large particles of a continuous medium motion in two coordinate systems (global and mobile); c) computing operations in the projections of coordinate systems, direct and inverse transformation in these systems. Particular attention is paid to the use of hardware and software of modern computer systems.

Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration.

PubMed

Budak, Vladimir P; Kaloshin, Gennady A; Shagalov, Oleg V; Zheltov, Victor S

2015-07-27

In this paper we propose the fast, but the accurate algorithm for numerical modeling of light fields in the turbid media slab. For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. The solution regular part is determined numerically. A good choice of the method of the solution anisotropic part elimination determines the high convergence of the algorithm in the mean square metric. The method of synthetic iterations can be used to improve the convergence in the uniform metric. A significant increase in the solution accuracy with the use of synthetic iterations allows applying the two-stream approximation for the regular part determination. This approach permits to generalize the proposed method in the case of an arbitrary 3D geometry of the medium.

A Low-Stress Algorithm for Fractions

ERIC Educational Resources Information Center

Ruais, Ronald W.

1978-01-01

An algorithm is given for the addition and subtraction of fractions based on dividing the sum of diagonal numerator and denominator products by the product of the denominators. As an explanation of the teaching method, activities used in teaching are demonstrated. (MN)

Numerical Optimization Algorithms and Software for Systems Biology

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

Saunders, Michael

2013-02-02

The basic aims of this work are: to develop reliable algorithms for solving optimization problems involving large stoi- chiometric matrices; to investigate cyclic dependency between metabolic and macromolecular biosynthetic networks; and to quantify the significance of thermodynamic constraints on prokaryotic metabolism.

Scalable Domain Decomposed Monte Carlo Particle Transport

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

O'Brien, Matthew Joseph

2013-12-05

In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation.

An evaluation of scanpath-comparison and machine-learning classification algorithms used to study the dynamics of analogy making.

PubMed

French, Robert M; Glady, Yannick; Thibaut, Jean-Pierre

2017-08-01

In recent years, eyetracking has begun to be used to study the dynamics of analogy making. Numerous scanpath-comparison algorithms and machine-learning techniques are available that can be applied to the raw eyetracking data. We show how scanpath-comparison algorithms, combined with multidimensional scaling and a classification algorithm, can be used to resolve an outstanding question in analogy making-namely, whether or not children's and adults' strategies in solving analogy problems are different. (They are.) We show which of these scanpath-comparison algorithms is best suited to the kinds of analogy problems that have formed the basis of much analogy-making research over the years. Furthermore, we use machine-learning classification algorithms to examine the item-to-item saccade vectors making up these scanpaths. We show which of these algorithms best predicts, from very early on in a trial, on the basis of the frequency of various item-to-item saccades, whether a child or an adult is doing the problem. This type of analysis can also be used to predict, on the basis of the item-to-item saccade dynamics in the first third of a trial, whether or not a problem will be solved correctly.

The Exact Solution to Rank-1 L1-Norm TUCKER2 Decomposition

NASA Astrophysics Data System (ADS)

Markopoulos, Panos P.; Chachlakis, Dimitris G.; Papalexakis, Evangelos E.

2018-04-01

We study rank-1 {L1-norm-based TUCKER2} (L1-TUCKER2) decomposition of 3-way tensors, treated as a collection of $N$ $D \\times M$ matrices that are to be jointly decomposed. Our contributions are as follows. i) We prove that the problem is equivalent to combinatorial optimization over $N$ antipodal-binary variables. ii) We derive the first two algorithms in the literature for its exact solution. The first algorithm has cost exponential in $N$; the second one has cost polynomial in $N$ (under a mild assumption). Our algorithms are accompanied by formal complexity analysis. iii) We conduct numerical studies to compare the performance of exact L1-TUCKER2 (proposed) with standard HOSVD, HOOI, GLRAM, PCA, L1-PCA, and TPCA-L1. Our studies show that L1-TUCKER2 outperforms (in tensor approximation) all the above counterparts when the processed data are outlier corrupted.

Numerical computation of solar neutrino flux attenuated by the MSW mechanism

NASA Astrophysics Data System (ADS)

Kim, Jai Sam; Chae, Yoon Sang; Kim, Jung Dae

1999-07-01

We compute the survival probability of an electron neutrino in its flight through the solar core experiencing the Mikheyev-Smirnov-Wolfenstein effect with all three neutrino species considered. We adopted a hybrid method that uses an accurate approximation formula in the non-resonance region and numerical integration in the non-adiabatic resonance region. The key of our algorithm is to use the importance sampling method for sampling the neutrino creation energy and position and to find the optimum radii to start and stop numerical integration. We further developed a parallel algorithm for a message passing parallel computer. By using an idea of job token, we have developed a dynamical load balancing mechanism which is effective under any irregular load distributions

A Numerical, Literal, and Converged Perturbation Algorithm

NASA Astrophysics Data System (ADS)

Wiesel, William E.

2017-09-01

The KAM theorem and von Ziepel's method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory.

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.

1990-01-01

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

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

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

NASA Astrophysics Data System (ADS)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

A Model-Free No-arbitrage Price Bound for Variance Options

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

Bonnans, J. Frederic, E-mail: frederic.bonnans@inria.fr; Tan Xiaolu, E-mail: xiaolu.tan@polytechnique.edu

2013-08-01

We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

Methodology of Numerical Optimization for Orbital Parameters of Binary Systems

NASA Astrophysics Data System (ADS)

Araya, I.; Curé, M.

2010-02-01

The use of a numerical method of maximization (or minimization) in optimization processes allows us to obtain a great amount of solutions. Therefore, we can find a global maximum or minimum of the problem, but this is only possible if we used a suitable methodology. To obtain the global optimum values, we use the genetic algorithm called PIKAIA (P. Charbonneau) and other four algorithms implemented in Mathematica. We demonstrate that derived orbital parameters of binary systems published in some papers, based on radial velocity measurements, are local minimum instead of global ones.

A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Park, Taehoon; Park, Won-Kwang

2015-09-01

Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation.

Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H. R.; Vorloeper, J.; Dahmen, W.

2010-08-01

Despite the ever-increasing power of modern computers, realistic modelling of complex 3-D earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modelling approaches includes either finite difference or non-adaptive finite element algorithms and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behaviour of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modelled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet-based approach that is applicable to a large range of problems, also including nonlinear problems. In comparison with earlier applications of adaptive solvers to geophysical problems we employ here a new adaptive scheme whose core ingredients arose from a rigorous analysis of the overall asymptotically optimal computational complexity, including in particular, an optimal work/accuracy rate. Our adaptive wavelet algorithm offers several attractive features: (i) for a given subsurface model, it allows the forward modelling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient and (iii) the modelling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving 3-D geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best-fitting subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectric modelling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with high spatial variability of electrical conductivities. The linear dependence of the modelling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.