Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry.

PubMed

Glynne-Jones, Peter; Mishra, Puja P; Boltryk, Rosemary J; Hill, Martyn

2013-04-01

A finite element based method is presented for calculating the acoustic radiation force on arbitrarily shaped elastic and fluid particles. Importantly for future applications, this development will permit the modeling of acoustic forces on complex structures such as biological cells, and the interactions between them and other bodies. The model is based on a non-viscous approximation, allowing the results from an efficient, numerical, linear scattering model to provide the basis for the second-order forces. Simulation times are of the order of a few seconds for an axi-symmetric structure. The model is verified against a range of existing analytical solutions (typical accuracy better than 0.1%), including those for cylinders, elastic spheres that are of significant size compared to the acoustic wavelength, and spheroidal particles.

Realization of non-linear coherent states by photonic lattices

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

Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn

2015-06-15

In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.

2010-01-01

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

Model checking for linear temporal logic: An efficient implementation

NASA Technical Reports Server (NTRS)

Sherman, Rivi; Pnueli, Amir

1990-01-01

This report provides evidence to support the claim that model checking for linear temporal logic (LTL) is practically efficient. Two implementations of a linear temporal logic model checker is described. One is based on transforming the model checking problem into a satisfiability problem; the other checks an LTL formula for a finite model by computing the cross-product of the finite state transition graph of the program with a structure containing all possible models for the property. An experiment was done with a set of mutual exclusion algorithms and tested safety and liveness under fairness for these algorithms.

Effect of electron-vibration interactions on the thermoelectric efficiency of molecular junctions.

PubMed

Hsu, Bailey C; Chiang, Chi-Wei; Chen, Yu-Chang

2012-07-11

From first-principles approaches, we investigate the thermoelectric efficiency of a molecular junction where a benzene molecule is connected directly to the platinum electrodes. We calculate the thermoelectric figure of merit ZT in the presence of electron-vibration interactions with and without local heating under two scenarios: linear response and finite bias regimes. In the linear response regime, ZT saturates around the electrode temperature T(e) = 25 K in the elastic case, while in the inelastic case we observe a non-saturated and a much larger ZT beyond T(e) = 25 K attributed to the tail of the Fermi-Dirac distribution. In the finite bias regime, the inelastic effects reveal the signatures of the molecular vibrations in the low-temperature regime. The normal modes exhibiting structures in the inelastic profile are characterized by large components of atomic vibrations along the current density direction on top of each individual atom. In all cases, the inclusion of local heating leads to a higher wire temperature T(w) and thus magnifies further the influence of the electron-vibration interactions due to the increased number of local phonons.

CatSim: a new computer assisted tomography simulation environment

NASA Astrophysics Data System (ADS)

De Man, Bruno; Basu, Samit; Chandra, Naveen; Dunham, Bruce; Edic, Peter; Iatrou, Maria; McOlash, Scott; Sainath, Paavana; Shaughnessy, Charlie; Tower, Brendon; Williams, Eugene

2007-03-01

We present a new simulation environment for X-ray computed tomography, called CatSim. CatSim provides a research platform for GE researchers and collaborators to explore new reconstruction algorithms, CT architectures, and X-ray source or detector technologies. The main requirements for this simulator are accurate physics modeling, low computation times, and geometrical flexibility. CatSim allows simulating complex analytic phantoms, such as the FORBILD phantoms, including boxes, ellipsoids, elliptical cylinders, cones, and cut planes. CatSim incorporates polychromaticity, realistic quantum and electronic noise models, finite focal spot size and shape, finite detector cell size, detector cross-talk, detector lag or afterglow, bowtie filtration, finite detector efficiency, non-linear partial volume, scatter (variance-reduced Monte Carlo), and absorbed dose. We present an overview of CatSim along with a number of validation experiments.

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

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

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

A two-stage Monte Carlo approach to the expression of uncertainty with finite sample sizes.

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

Crowder, Stephen Vernon; Moyer, Robert D.

2005-05-01

Proposed supplement I to the GUM outlines a 'propagation of distributions' approach to deriving the distribution of a measurand for any non-linear function and for any set of random inputs. The supplement's proposed Monte Carlo approach assumes that the distributions of the random inputs are known exactly. This implies that the sample sizes are effectively infinite. In this case, the mean of the measurand can be determined precisely using a large number of Monte Carlo simulations. In practice, however, the distributions of the inputs will rarely be known exactly, but must be estimated using possibly small samples. If these approximatedmore » distributions are treated as exact, the uncertainty in estimating the mean is not properly taken into account. In this paper, we propose a two-stage Monte Carlo procedure that explicitly takes into account the finite sample sizes used to estimate parameters of the input distributions. We will illustrate the approach with a case study involving the efficiency of a thermistor mount power sensor. The performance of the proposed approach will be compared to the standard GUM approach for finite samples using simple non-linear measurement equations. We will investigate performance in terms of coverage probabilities of derived confidence intervals.« less

A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains

NASA Astrophysics Data System (ADS)

Lopes, I. A. Rodrigues; Pires, F. M. Andrade; Reis, F. J. P.

2018-02-01

A mixed parallel strategy for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains is proposed. The approach aims to reduce the computational time and memory requirements of non-linear coupled simulations that use finite element discretization at both scales (FE^2). In the first level of the algorithm, a non-conforming domain decomposition technique, based on the FETI method combined with a mortar discretization at the interface of macroscopic subdomains, is employed. A master-slave scheme, which distributes tasks by macroscopic element and adopts dynamic scheduling, is then used for each macroscopic subdomain composing the second level of the algorithm. This strategy allows the parallelization of FE^2 simulations in computers with either shared memory or distributed memory architectures. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton-Raphson scheme. Several examples are presented to demonstrate the robustness and efficiency of the proposed parallel strategy.

Extension of non-linear beam models with deformable cross sections

NASA Astrophysics Data System (ADS)

Sokolov, I.; Krylov, S.; Harari, I.

2015-12-01

Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.

Fully 3D modeling of tokamak vertical displacement events with realistic parameters

NASA Astrophysics Data System (ADS)

Pfefferle, David; Ferraro, Nathaniel; Jardin, Stephen; Bhattacharjee, Amitava

2016-10-01

In this work, we model the complex multi-domain and highly non-linear physics of Vertical Displacement Events (VDEs), one of the most damaging off-normal events in tokamaks, with the implicit 3D extended MHD code M3D-C1. The code has recently acquired the capability to include finite thickness conducting structures within the computational domain. By exploiting the possibility of running a linear 3D calculation on top of a non-linear 2D simulation, we monitor the non-axisymmetric stability and assess the eigen-structure of kink modes as the simulation proceeds. Once a stability boundary is crossed, a fully 3D non-linear calculation is launched for the remainder of the simulation, starting from an earlier time of the 2D run. This procedure, along with adaptive zoning, greatly increases the efficiency of the calculation, and allows to perform VDE simulations with realistic parameters and high resolution. Simulations are being validated with NSTX data where both axisymmetric (toroidally averaged) and non-axisymmetric induced and conductive (halo) currents have been measured. This work is supported by US DOE Grant DE-AC02-09CH11466.

Finite element modeling of reinforced concrete structures strengthened with FRP laminates : final report.

DOT National Transportation Integrated Search

2001-05-01

Linear and non-linear finite element method models were developed for a reinforced concrete bridge that had been strengthened with fiber reinforced polymer composites. ANSYS and SAP2000 modeling software were used; however, most of the development ef...

From Finite Time to Finite Physical Dimensions Thermodynamics: The Carnot Engine and Onsager's Relations Revisited

NASA Astrophysics Data System (ADS)

Feidt, Michel; Costea, Monica

2018-04-01

Many works have been devoted to finite time thermodynamics since the Curzon and Ahlborn [1] contribution, which is generally considered as its origin. Nevertheless, previous works in this domain have been revealed [2], [3], and recently, results of the attempt to correlate Finite Time Thermodynamics with Linear Irreversible Thermodynamics according to Onsager's theory were reported [4]. The aim of the present paper is to extend and improve the approach relative to thermodynamic optimization of generic objective functions of a Carnot engine with linear response regime presented in [4]. The case study of the Carnot engine is revisited within the steady state hypothesis, when non-adiabaticity of the system is considered, and heat loss is accounted for by an overall heat leak between the engine heat reservoirs. The optimization is focused on the main objective functions connected to engineering conditions, namely maximum efficiency or power output, except the one relative to entropy that is more fundamental. Results given in reference [4] relative to the maximum power output and minimum entropy production as objective function are reconsidered and clarified, and the change from finite time to finite physical dimension was shown to be done by the heat flow rate at the source. Our modeling has led to new results of the Carnot engine optimization and proved that the primary interest for an engineer is mainly connected to what we called Finite Physical Dimensions Optimal Thermodynamics.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

PubMed

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

Testing Linear Temporal Logic Formulae on Finite Execution Traces

NASA Technical Reports Server (NTRS)

Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)

2001-01-01

We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model.

PubMed

Gras, Laure-Lise; Mitton, David; Crevier-Denoix, Nathalie; Laporte, Sébastien

2012-01-01

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

Numerical and Experimental Dynamic Characteristics of Thin-Film Membranes

NASA Technical Reports Server (NTRS)

Young, Leyland G.; Ramanathan, Suresh; Hu, Jia-Zhu; Pai, P. Frank

2004-01-01

Presented is a total-Lagrangian displacement-based non-linear finite-element model of thin-film membranes for static and dynamic large-displacement analyses. The membrane theory fully accounts for geometric non-linearities. Fully non-linear static analysis followed by linear modal analysis is performed for an inflated circular cylindrical Kapton membrane tube under different pressures, and for a rectangular membrane under different tension loads at four comers. Finite element results show that shell modes dominate the dynamics of the inflated tube when the inflation pressure is low, and that vibration modes localized along four edges dominate the dynamics of the rectangular membrane. Numerical dynamic characteristics of the two membrane structures were experimentally verified using a Polytec PI PSV-200 scanning laser vibrometer and an EAGLE-500 8-camera motion analysis system.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

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

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Modeling the interactions between a prosthetic socket, polyurethane liners and the residual limb in transtibial amputees using non-linear finite element analysis.

PubMed

Simpson, G; Fisher, C; Wright, D K

2001-01-01

Continuing earlier studies into the relationship between the residual limb, liner and socket in transtibial amputees, we describe a geometrically accurate non-linear model simulating the donning of a liner and then a socket. The socket is rigid and rectified and the liner is a polyurethane geltype which is accurately described using non-linear (Mooney-Rivlin) material properties. The soft tissue of the residual limb is modelled as homogeneous, non-linear and hyperelastic and the bone structure within the residual limb is taken as rigid. The work gives an indication of how the stress induced by the process of donning the rigid socket is redistributed by the liner. Ultimately we hope to understand how the liner design might be modified to reduce discomfort. The ANSYS finite element code, version 5.6 is used.

Non-linear effects in finite amplitude wave propagation through ducts and nozzles

NASA Technical Reports Server (NTRS)

Salikuddin, M.; Brown, W. H.

1986-01-01

In this paper an extensive study of non-linear effects in finite amplitude wave propagation through ducts and nozzles is summarized. Some results from earlier studies are included to illustrate the non-linear effects on the transmission characteristics of duct and nozzle terminations. Investigaiations, both experimental and analytical, were carried out to determine the magnitudes of the effects for high intensity pulse propagation. The results derived from these investigations are presented in this paper. They include the effect of the sound intensity on the acoustic characteristics of duct and nozzle terminations, the extent of the non-linearities in the propagation of high intensity impulsive sound inside the duct and out into free field, the acoustic energy dissipation mechanism at a termination as shown by flow visualizations, and quantitative evaluations by experimental and analytical means of the influence of the intensity of a sound pulse on the dissipation of its acoustic power.

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1986-01-01

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

Axioms of adaptivity

PubMed Central

Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.

2014-01-01

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower bounds, inexact solvers, inhomogeneous boundary data, or the use of equivalent error estimators. Solely four axioms guarantee the optimality in terms of the error estimators. Compared to the state of the art in the temporary literature, the improvements of this article can be summarized as follows: First, a general framework is presented which covers the existing literature on optimality of adaptive schemes. The abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method. Second, efficiency of the error estimator is neither needed to prove convergence nor quasi-optimal convergence behavior of the error estimator. In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant. Third, some general quasi-Galerkin orthogonality is not only sufficient, but also necessary for the R-linear convergence of the error estimator, which is a fundamental ingredient in the current quasi-optimality analysis due to Stevenson 2007. Finally, the general analysis allows for equivalent error estimators and inexact solvers as well as different non-homogeneous and mixed boundary conditions. PMID:25983390

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

NASA Technical Reports Server (NTRS)

Rosu, Grigore; Havelund, Klaus

2001-01-01

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.

PubMed

Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko

2010-06-28

We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime.

PubMed

Yamamoto, Kaoru; Hatano, Naomichi

2015-10-01

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriately in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-Büttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry [Phys. Rev. Lett. 106, 230602 (2011)]. These results demonstrate how quantum mechanics constrains thermodynamics.

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

Benchmark solution of the dynamic response of a spherical shell at finite strain

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

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

Non-linear 3D evaluation of different oral implant-abutment connections.

PubMed

Streckbein, P; Streckbein, R G; Wilbrand, J F; Malik, C Y; Schaaf, H; Howaldt, H P; Flach, M

2012-12-01

Micro-gaps and osseous overload in the implant-abutment connection are the most common causes of peri-implant bone resorption and implant failure. These undesirable events can be visualized on standardized three-dimensional finite element models and by radiographic methods. The present study investigated the influence of 7 available implant systems (Ankylos, Astra, Bego, Brånemark, Camlog, Straumann, and Xive) with different implant-abutment connections on bone overload and the appearance of micro-gaps in vitro. The individual geometries of the implants were transferred to three-dimensional finite element models. In a non-linear analysis considering the pre-loading of the occlusion screw, friction between the implant and abutment, the influence of the cone angle on bone strain, and the appearance of micro-gaps were determined. Increased bone strains were correlated with small (< 15°) cone angles. Conical implant-abutment connections efficiently avoided micro-gaps but had a negative effect on peri-implant bone strain. Bone strain was reduced in implants with greater wall thickness (Ankylos) or a smaller cone angle (Bego). The results of our in silico study provide a solid basis for the reduction of peri-implant bone strain and micro-gaps in the implant-abutment connection to improve long-term stability.

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

Non-Linear Vibroisolation Pads Design, Numerical FEM Analysis and Introductory Experimental Investigations

NASA Astrophysics Data System (ADS)

Zielnica, J.; Ziółkowski, A.; Cempel, C.

2003-03-01

Design and theoretical and experimental investigation of vibroisolation pads with non-linear static and dynamic responses is the objective of the paper. The analytical investigations are based on non-linear finite element analysis where the load-deflection response is traced against the shape and material properties of the analysed model of the vibroisolation pad. A new model of vibroisolation pad of antisymmetrical type was designed and analysed by the finite element method based on the second-order theory (large displacements and strains) with the assumption of material's non-linearities (Mooney-Rivlin model). Stability loss phenomenon was used in the design of the vibroisolators, and it was proved that it would be possible to design a model of vibroisolator in the form of a continuous pad with non-linear static and dynamic response, typical to vibroisolation purposes. The materials used for the vibroisolator are those of rubber, elastomers, and similar ones. The results of theoretical investigations were examined experimentally. A series of models made of soft rubber were designed for the test purposes. The experimental investigations of the vibroisolation models, under static and dynamic loads, confirmed the results of the FEM analysis.

A linear shock cell model for jets of arbitrary exit geometry

NASA Technical Reports Server (NTRS)

Morris, P. J.; Bhat, T. R. S.; Chen, G.

1989-01-01

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

ISPAN (Interactive Stiffened Panel Analysis): A tool for quick concept evaluation and design trade studies

NASA Technical Reports Server (NTRS)

Hairr, John W.; Dorris, William J.; Ingram, J. Edward; Shah, Bharat M.

1993-01-01

Interactive Stiffened Panel Analysis (ISPAN) modules, written in FORTRAN, were developed to provide an easy to use tool for creating finite element models of composite material stiffened panels. The modules allow the user to interactively construct, solve and post-process finite element models of four general types of structural panel configurations using only the panel dimensions and properties as input data. Linear, buckling and post-buckling solution capability is provided. This interactive input allows rapid model generation and solution by non finite element users. The results of a parametric study of a blade stiffened panel are presented to demonstrate the usefulness of the ISPAN modules. Also, a non-linear analysis of a test panel was conducted and the results compared to measured data and previous correlation analysis.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions

DTIC Science & Technology

2007-09-01

C. (2005). Elementary Linear Algebra . New York: John Wiley and Sons. Avitable, Peter (2001, January) Experimental Modal Analysis, A Simple Non...variables under consideration. 3 Frequency sensitivities are the basis for a linear approximation to compute the change in the natural frequencies of a...THEORY The general problem statement for a non- linear constrained optimization problem is: To minimize ( )f x Objective Function Subject to

Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces

NASA Astrophysics Data System (ADS)

Licht, Christian; Tran Thu Ha

2005-02-01

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).

Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime

NASA Astrophysics Data System (ADS)

Yamamoto, Kaoru; Hatano, Naomichi

2015-10-01

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriately in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-Büttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry [Phys. Rev. Lett. 106, 230602 (2011), 10.1103/PhysRevLett.106.230602]. These results demonstrate how quantum mechanics constrains thermodynamics.

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

DTIC Science & Technology

2006-01-01

i.e., data flows of finite size arrive at the system randomly. For such a system , we propose a modified dual scheduling algorithm that stabilizes ...demon. We compute the efficiency of the controller over finite and infinite time intervals, and since the controller is optimal, this yields hard limits...and highly optimized tolerance. PNAS, 102, 2005. 51. G. N. Nair and R. J. Evans. Stabilizability of stochastic linear systems with finite feedback

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.

New Representation of Bearings in LS-DYNA

NASA Technical Reports Server (NTRS)

Carney, Kelly S.; Howard, Samuel A.; Miller, Brad A.; Benson, David J.

2014-01-01

Non-linear, dynamic, finite element analysis is used in various engineering disciplines to evaluate high-speed, dynamic impact and vibration events. Some of these applications require connecting rotating to stationary components. For example, bird impacts on rotating aircraft engine fan blades are a common analysis performed using this type of analysis tool. Traditionally, rotating machines utilize some type of bearing to allow rotation in one degree of freedom while offering constraints in the other degrees of freedom. Most times, bearings are modeled simply as linear springs with rotation. This is a simplification that is not necessarily accurate under the conditions of high-velocity, high-energy, dynamic events such as impact problems. For this reason, it is desirable to utilize a more realistic non-linear force-deflection characteristic of real bearings to model the interaction between rotating and non-rotating components during dynamic events. The present work describes a rolling element bearing model developed for use in non-linear, dynamic finite element analysis. This rolling element bearing model has been implemented in LS-DYNA as a new element, *ELEMENT_BEARING.

A review of developments in the theory of elasto-plastic flow

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1973-01-01

The theory of elasto-plastic flow is developed so that it may accommodate features such as work-hardening, anisotropy, plastic compressibility, non-continuous loading including local or global unloading, and others. A complete theory is given in quasi-linear form; as a result, many useful attributes are accessible. Several integral theorems may be written, finite deformations may be incorporated, and efficient methods for solving problems may be developed; these and other aspects are described in some detail. The theory is reduced to special forms for 2-space, and extensive experience in solving such problems is cited.

Air Vehicles Division Computational Structural Analysis Facilities Policy and Guidelines for Users

DTIC Science & Technology

2005-05-01

34 Thermal " as appropriate and the tolerance set to "default". b) Create the model geometry. c) Create the finite elements. d) Create the...linear, non-linear, dynamic, thermal , acoustic analysis. The modelling of composite materials, creep, fatigue and plasticity are also covered...perform professional, high quality finite element analysis (FEA). FE analysts from many tasks within AVD are using the facilities to conduct FEA with

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data

NASA Astrophysics Data System (ADS)

Key, Kerry

2016-10-01

This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data balancing normalization weights for the joint inversion of two or more data sets encourages the inversion to fit each data type equally well. A synthetic joint inversion of marine CSEM and MT data illustrates the algorithm's performance and parallel scaling on up to 480 processing cores. CSEM inversion of data from the Middle America Trench offshore Nicaragua demonstrates a real world application. The source code and MATLAB interface tools are freely available at http://mare2dem.ucsd.edu.

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

Thermal radiation and mass transfer effects on unsteady MHD free convection flow past a vertical oscillating plate

NASA Astrophysics Data System (ADS)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.

Mid-frequency Band Dynamics of Large Space Structures

NASA Technical Reports Server (NTRS)

Coppolino, Robert N.; Adams, Douglas S.

2004-01-01

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

A high-accuracy optical linear algebra processor for finite element applications

NASA Technical Reports Server (NTRS)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

NASA Technical Reports Server (NTRS)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels

NASA Astrophysics Data System (ADS)

Colera, Manuel; Pérez-Saborid, Miguel

2017-09-01

A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

Parallelization of implicit finite difference schemes in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

1990-01-01

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding

NASA Astrophysics Data System (ADS)

LEWANDOWSKI, R.

2002-05-01

In this paper the non-linear vibrations of beams excited by vortex-shedding are considered. In particular, the steady state responses of beams near the synchronization region are taken into account. The main aerodynamic properties of wind are described by using the semi-empirical model proposed by Hartlen and Currie. The finite element method and the strip method are used to formulate the equation of motion of the system treated. The harmonic balance method is adopted to derive the amplitude equations. These equations are solved with the help of the continuation method which is very convenient to perform the parametric studies of the problem and to determine the response curve in the synchronization region. Moreover, the equations of motion are also integrated using the Newmark method. The results of calculations of several example problems are also shown to confirm the efficiency and accuracy of the presented method. The results obtained by the harmonic balance method and by the Newmark methods are in good agreement with each other.

2D constant-loss taper for mode conversion

NASA Astrophysics Data System (ADS)

Horth, Alexandre; Kashyap, Raman; Quitoriano, Nathaniel J.

2015-03-01

Proposed in this manuscript is a novel taper geometry, the constant-loss taper (CLT). This geometry is derived with 1D slabs of silicon embedded in silicon dioxide using coupled-mode theory (CMT). The efficiency of the CLT is compared to both linear and parabolic tapers using CMT and 2D finite-difference time-domain simulations. It is shown that over a short 2D, 4.45 μm long taper the CLT's mode conversion efficiency is ~90% which is 10% and 18% more efficient than a 2D parabolic or linear taper, respectively.

Finite Element Study on Continuous Rotating versus Reciprocating Nickel-Titanium Instruments.

PubMed

El-Anwar, Mohamed I; Yousief, Salah A; Kataia, Engy M; El-Wahab, Tarek M Abd

2016-01-01

In the present study, GTX and ProTaper as continuous rotating endodontic files were numerically compared with WaveOne reciprocating file using finite element analysis, aiming at having a low cost, accurate/trustworthy comparison as well as finding out the effect of instrument design and manufacturing material on its lifespan. Two 3D finite element models were especially prepared for this comparison. Commercial engineering CAD/CAM package was used to model full detailed flute geometries of the instruments. Multi-linear materials were defined in analysis by using real strain-stress data of NiTi and M-Wire. Non-linear static analysis was performed to simulate the instrument inside root canal at a 45° angle in the apical portion and subjected to 0.3 N.cm torsion. The three simulations in this study showed that M-Wire is slightly more resistant to failure than conventional NiTi. On the other hand, both materials are fairly similar in case of severe locking conditions. For the same instrument geometry, M-Wire instruments may have longer lifespan than the conventional NiTi ones. In case of severe locking conditions both materials will fail similarly. Larger cross sectional area (function of instrument taper) resisted better to failure than the smaller ones, while the cross sectional shape and its cutting angles could affect instrument cutting efficiency.

Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas

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

Hnat, B.

2011-09-22

Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

PubMed Central

Bondell, Howard D.; Stefanski, Leonard A.

2013-01-01

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator’s close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point, and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes, and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real data set with purported outliers. PMID:23976805

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

NASA Astrophysics Data System (ADS)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Finite element modeling of concrete structures strengthened with FRP laminates

DOT National Transportation Integrated Search

2001-05-01

Linear and non-linear method models were developed for a reinforced concrete bridge that had been strengthened with fiber reinforced polymer (FRP) composites. ANSYS and SAP2000 modeling software were used; however, most of the development effort used...

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

MHOST: An efficient finite element program for inelastic analysis of solids and structures

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1988-01-01

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

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.

Architecting the Finite Element Method Pipeline for the GPU.

PubMed

Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T

2014-02-01

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

One-dimensional Numerical Model of Transient Discharges in Air of a Spatial Plasma Ignition Device

NASA Astrophysics Data System (ADS)

Saceleanu, Florin N.

This thesis examines the modes of discharge of a plasma ignition device. Oscilloscope data of the discharge voltage and current are analyzed for various pressures in air at ambient temperature. It is determined that the discharge operates in 2 modes: a glow discharge and a postulated streamer discharge. Subsequently, a 1-dimensional fluid simulation of plasma using the finite volume method (FVM) is developed to gain insight into the particle kinetics. Transient results of the simulation agree with theories of electric discharges; however, quasi-steady state results were not reached due to high diffusion time of ions in air. Next, an ordinary differential equation (ODE) is derived to understand the discharge transition. Simulated results were used to estimate the voltage waveform, which describes the ODE's forcing function; additional simulated results were used to estimate the discharge current and the ODE's non-linearity. It is found that the ODE's non-linearity increases exponentially for capacitive discharges. It is postulated that the non-linearity defines the mode transition observed experimentally. The research is motivated by Spatial Plasma Discharge Ignition (SPDI), an innovative ignition system postulated to increase combustion efficiency in automobile engines for up to 9%. The research thus far can only hypothesize SPDI's benefits on combustion, based on the literature review and the modes of discharge.

Status Report on NEAMS System Analysis Module Development

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

Hu, R.; Fanning, T. H.; Sumner, T.

2015-12-01

Under the Reactor Product Line (RPL) of DOE-NE’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, an advanced SFR System Analysis Module (SAM) is being developed at Argonne National Laboratory. The goal of the SAM development is to provide fast-running, improved-fidelity, whole-plant transient analyses capabilities. SAM utilizes an object-oriented application framework MOOSE), and its underlying meshing and finite-element library libMesh, as well as linear and non-linear solvers PETSc, to leverage modern advanced software environments and numerical methods. It also incorporates advances in physical and empirical models and seeks closure models based on information from high-fidelity simulations and experiments. This reportmore » provides an update on the SAM development, and summarizes the activities performed in FY15 and the first quarter of FY16. The tasks include: (1) implement the support of 2nd-order finite elements in SAM components for improved accuracy and computational efficiency; (2) improve the conjugate heat transfer modeling and develop pseudo 3-D full-core reactor heat transfer capabilities; (3) perform verification and validation tests as well as demonstration simulations; (4) develop the coupling requirements for SAS4A/SASSYS-1 and SAM integration.« less

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

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

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Computer-aided design studies of the homopolar linear synchronous motor

NASA Astrophysics Data System (ADS)

Dawson, G. E.; Eastham, A. R.; Ong, R.

1984-09-01

The linear induction motor (LIM), as an urban transit drive, can provide good grade-climbing capabilities and propulsion/braking performance that is independent of steel wheel-rail adhesion. In view of its 10-12 mm airgap, the LIM is characterized by a low power factor-efficiency product of order 0.4. A synchronous machine offers high efficiency and controllable power factor. An assessment of the linear homopolar configuration of this machine is presented as an alternative to the LIM. Computer-aided design studies using the finite element technique have been conducted to identify a suitable machine design for urban transit propulsion.

A combined dislocation fan-finite element (DF-FE) method for stress field simulation of dislocations emerging at the free surfaces of 3D elastically anisotropic crystals

NASA Astrophysics Data System (ADS)

Balusu, K.; Huang, H.

2017-04-01

A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.

A three dimensional finite element formulation for thermoviscoelastic orthotropic media

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

Zocher, M.A.

1997-12-31

A numerical algorithm for the efficient solution of the uncoupled quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation is briefly outlined.

Cost Considerations in Nonlinear Finite-Element Computing

NASA Technical Reports Server (NTRS)

Utku, S.; Melosh, R. J.; Islam, M.; Salama, M.

1985-01-01

Conference paper discusses computational requirements for finiteelement analysis using quasi-linear approach to nonlinear problems. Paper evaluates computational efficiency of different computer architecturtural types in terms of relative cost and computing time.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Numerical modelling and experimental analysis of acoustic emission

NASA Astrophysics Data System (ADS)

Gerasimov, S. I.; Sych, T. V.

2018-05-01

In the present paper, the authors report on the application of non-destructive acoustic waves technologies to determine the structural integrity of engineering components. In particular, a finite element (FE) system COSMOS/M is used to investigate propagation characteristics of ultrasonic waves in linear, plane and three-dimensional structures without and with geometric concentrators. In addition, the FE results obtained are compared to the analytical and experimental ones. The study illustrates the efficient use of the FE method to model guided wave propagation problems and demonstrates the FE method’s potential to solve problems when an analytical solution is not possible due to “complicated” geometry.

LOOPREF: A Fluid Code for the Simulation of Coronal Loops

NASA Technical Reports Server (NTRS)

deFainchtein, Rosalinda; Antiochos, Spiro; Spicer, Daniel

1998-01-01

This report documents the code LOOPREF. LOOPREF is a semi-one dimensional finite element code that is especially well suited to simulate coronal-loop phenomena. It has a full implementation of adaptive mesh refinement (AMR), which is crucial for this type of simulation. The AMR routines are an improved version of AMR1D. LOOPREF's versatility makes is suitable to simulate a wide variety of problems. In addition to efficiently providing very high resolution in rapidly changing regions of the domain, it is equipped to treat loops of variable cross section, any non-linear form of heat conduction, shocks, gravitational effects, and radiative loss.

New generation of one-dimensional photonic crystal cavities as robust high-efficient frequency converter

NASA Astrophysics Data System (ADS)

Parvini, T. S.; Tehranchi, M. M.; Hamidi, S. M.

2017-07-01

An effective method is proposed to design finite one-dimensional photonic crystal cavities (PhCCs) as robust high-efficient frequency converter. For this purpose, we consider two groups of PhCCs which are constructed by stacking m nonlinear (LiNbO3) and n linear (air) layers with variable thicknesses. In the first group, the number of linear layers is less than the nonlinear layers by one and in the second group by two. The conversion efficiency is calculated as a function of the arrangement and thicknesses of the linear and nonlinear layers by benefiting from nonlinear transfer matrix method. Our numerical simulations show that for each group of PhCCs, there is a structural formula by which the configurations with the highest efficiency can be constructed for any values of m and n (i.e. any number of layers). The efficient configurations are equivalent to Fabry-Pérot cavities that depend on the relationship between m and n and the mirrors in two sides of these cavities can be periodic or nonperiodic. The conversion efficiencies of these designed PhCCs are more than 5 orders of magnitude higher than the perfect ones which satisfy photonic bandgap edge and quasi-phase matching. Moreover, the results reveal that conversion efficiencies of Fabry-Pérot cavities with non-periodic mirrors are one order of magnitude higher than those with periodic mirrors. The major physical mechanisms of the enhancement are quasi-phase matching effect, cavity effect induced by dispersive mirrors, and double resonance for the pump and the harmonic fields in defect state. We believe that this method is very beneficial to the design of high-efficient compact optical frequency converters.

M-step preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

Adams, L.

1983-01-01

Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

Calculation of cogging force in a novel slotted linear tubular brushless permanent magnet motor

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

Zhu, Z.Q.; Hor, P.J.; Howe, D.

1997-09-01

There is an increasing requirement for controlled linear motion over short and long strokes, in the factory automation and packaging industries, for example. Linear brushless PM motors could offer significant advantages over conventional actuation technologies, such as motor driven cams and linkages and pneumatic rams--in terms of efficiency, operating bandwidth, speed and thrust control, stroke and positional accuracy, and indeed over other linear motor technologies, such as induction motors. Here, a finite element/analytical based technique for the prediction of cogging force in a novel topology of slotted linear brushless permanent magnet motor has been developed and validated. The various forcemore » components, which influence cogging are pre-calculated by the finite element analysis of some basic magnetic structures, facilitate the analytical synthesis of the resultant cogging force. The technique can be used to aid design for the minimization of cogging.« less

Edge effect modeling of small tool polishing in planetary movement

NASA Astrophysics Data System (ADS)

Li, Qi-xin; Ma, Zhen; Jiang, Bo; Yao, Yong-sheng

2018-03-01

As one of the most challenging problems in Computer Controlled Optical Surfacing (CCOS), the edge effect greatly affects the polishing accuracy and efficiency. CCOS rely on stable tool influence function (TIF), however, at the edge of the mirror surface,with the grinding head out of the mirror ,the contact area and pressure distribution changes, which resulting in a non-linear change of TIF, and leads to tilting or sagging at the edge of the mirror. In order reduce the adverse effects and improve the polishing accuracy and efficiency. In this paper, we used the finite element simulation to analyze the pressure distribution at the mirror edge and combined with the improved traditional method to establish a new model. The new method fully considered the non-uniformity of pressure distribution. After modeling the TIFs in different locations, the description and prediction of the edge effects are realized, which has a positive significance on the control and suppression of edge effects

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

NASA Astrophysics Data System (ADS)

Al-Mayah, Adil; Moseley, Joanne; Velec, Mike; Brock, Kristy

2011-08-01

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

Finite-horizon differential games for missile-target interception system using adaptive dynamic programming with input constraints

NASA Astrophysics Data System (ADS)

Sun, Jingliang; Liu, Chunsheng

2018-01-01

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.

A proof of the Woodward-Lawson sampling method for a finite linear array

NASA Technical Reports Server (NTRS)

Somers, Gary A.

1993-01-01

An extension of the continuous aperture Woodward-Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Non-Linear Acoustic Concealed Weapons Detector

DTIC Science & Technology

2006-05-01

signature analysis 8 the interactions of the beams with concealed objects. The Khokhlov- Zabolotskaya-Kuznetsov ( KZK ) equation is the most widely used...Hamilton developed a finite difference method based on the KZK equation to model pulsed acoustic emissions from axial symmetric sources. Using a...College of William & Mary, we have developed a simulation code using the KZK equation to model non-linear acoustic beams and visualize beam patterns

Existence of entire solutions of some non-linear differential-difference equations.

PubMed

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

Adaptive Importance Sampling for Control and Inference

NASA Astrophysics Data System (ADS)

Kappen, H. J.; Ruiz, H. C.

2016-03-01

Path integral (PI) control problems are a restricted class of non-linear control problems that can be solved formally as a Feynman-Kac PI and can be estimated using Monte Carlo sampling. In this contribution we review PI control theory in the finite horizon case. We subsequently focus on the problem how to compute and represent control solutions. We review the most commonly used methods in robotics and control. Within the PI theory, the question of how to compute becomes the question of importance sampling. Efficient importance samplers are state feedback controllers and the use of these requires an efficient representation. Learning and representing effective state-feedback controllers for non-linear stochastic control problems is a very challenging, and largely unsolved, problem. We show how to learn and represent such controllers using ideas from the cross entropy method. We derive a gradient descent method that allows to learn feed-back controllers using an arbitrary parametrisation. We refer to this method as the path integral cross entropy method or PICE. We illustrate this method for some simple examples. The PI control methods can be used to estimate the posterior distribution in latent state models. In neuroscience these problems arise when estimating connectivity from neural recording data using EM. We demonstrate the PI control method as an accurate alternative to particle filtering.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Instability, finite amplitude pulsation and mass-loss in models of massive OB-type stars

NASA Astrophysics Data System (ADS)

Yadav, Abhay Pratap; Glatzel, Wolfgang

2017-11-01

Variability and mass-loss are common phenomena in massive OB-type stars. It is argued that they are caused by violent strange mode instabilities identified in corresponding stellar models. We present a systematic linear stability analysis with respect to radial perturbations of massive OB-type stars with solar chemical composition and masses between 23 and 100 M⊙. For selected unstable stellar models, we perform non-linear simulations of the evolution of the instabilities into the non-linear regime. Finite amplitude pulsations with periods in the range between hours and 100 d are found to be the final result of the instabilities. The pulsations are associated with a mean acoustic luminosity which can be the origin of a pulsationally driven wind. Corresponding mass-loss rates lie in the range between 10-9 and 10-4 M⊙ yr-1 and may thus affect the evolution of massive stars.

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Design of a transverse-flux permanent-magnet linear generator and controller for use with a free-piston stirling engine

NASA Astrophysics Data System (ADS)

Zheng, Jigui; Huang, Yuping; Wu, Hongxing; Zheng, Ping

2016-07-01

Transverse-flux with high efficiency has been applied in Stirling engine and permanent magnet synchronous linear generator system, however it is restricted for large application because of low and complex process. A novel type of cylindrical, non-overlapping, transverse-flux, and permanent-magnet linear motor(TFPLM) is investigated, furthermore, a high power factor and less process complexity structure research is developed. The impact of magnetic leakage factor on power factor is discussed, by using the Finite Element Analysis(FEA) model of stirling engine and TFPLM, an optimization method for electro-magnetic design of TFPLM is proposed based on magnetic leakage factor. The relation between power factor and structure parameter is investigated, and a structure parameter optimization method is proposed taking power factor maximum as a goal. At last, the test bench is founded, starting experimental and generating experimental are performed, and a good agreement of simulation and experimental is achieved. The power factor is improved and the process complexity is decreased. This research provides the instruction to design high-power factor permanent-magnet linear generator.

Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators

NASA Astrophysics Data System (ADS)

Siudzińska, Katarzyna; Chruściński, Dariusz

2018-03-01

In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

Numerical simulation of transient, incongruent vaporization induced by high power laser

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

Tsai, C.H.

1981-01-01

A mathematical model and numerical calculations were developed to solve the heat and mass transfer problems specifically for uranum oxide subject to laser irradiation. It can easily be modified for other heat sources or/and other materials. In the uranium-oxygen system, oxygen is the preferentially vaporizing component, and as a result of the finite mobility of oxygen in the solid, an oxygen deficiency is set up near the surface. Because of the bivariant behavior of uranium oxide, the heat transfer problem and the oxygen diffusion problem are coupled and a numerical method of simultaneously solving the two boundary value problems ismore » studied. The temperature dependence of the thermal properties and oxygen diffusivity, as well as the highly ablative effect on the surface, leads to considerable non-linearities in both the governing differential equations and the boundary conditions. Based on the earlier work done in this laboratory by Olstad and Olander on Iron and on Zirconium hydride, the generality of the problem is expanded and the efficiency of the numerical scheme is improved. The finite difference method, along with some advanced numerical techniques, is found to be an efficient way to solve this problem.« less

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

PubMed

Townsend, Molly T; Sarigul-Klijn, Nesrin

2016-01-01

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

Model of the non-linear stress-strain behavior of a 2D-SiC/SiC ceramic matrix composite (CMC)

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

Guillaumat, L; Lamon, J.

The non-linear stress-strain behaviour of a 2D-SiC/SiC composite reinforced with fabrics of fiber bundles was predicted from properties of major constituents. A finite element analysis was employed for stress computation. The different steps of matrix damage identified experimentally were duplicated in the mesh. Predictions compared satisfactorily with experimental data.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

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

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

NASA Astrophysics Data System (ADS)

Wienkers, A. F.; Ogilvie, G. I.

2018-07-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalizes the often-used Cartesian shearing box model. The numerical method is an overall second-order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localize the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of 'bursty' dynamics such as the superhump phenomenon.

A Technique of Treating Negative Weights in WENO Schemes

NASA Technical Reports Server (NTRS)

Shi, Jing; Hu, Changqing; Shu, Chi-Wang

2000-01-01

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

Arnold, Steve M. (Technical Monitor); Bednarcyk, Brett A.; Yarrington, Phillip W.

2004-01-01

The Higher Order Theory - Structural/Micro Analysis Code (HOT-SMAC) software package is applied to analyze the linearly elastic and elasto-plastic response of adhesively bonded tee joints. Joints of this type are finding an increasing number of applications with the increased use of composite materials within advanced aerospace vehicles, and improved tools for the design and analysis of these joints are needed. The linearly elastic results of the code are validated vs. finite element analysis results from the literature under different loading and boundary conditions, and new results are generated to investigate the inelastic behavior of the tee joint. The comparison with the finite element results indicates that HOT-SMAC is an efficient and accurate alternative to the finite element method and has a great deal of potential as an analysis tool for a wide range of bonded joints.

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

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

Hager, Robert, E-mail: rhager@pppl.gov; Yoon, E.S., E-mail: yoone@rpi.edu; Ku, S., E-mail: sku@pppl.gov

2016-06-15

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable onmore » high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.« less

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

DOE PAGES

Hager, Robert; Yoon, E. S.; Ku, S.; ...

2016-04-04

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less

Stress Induced in Periodontal Ligament under Orthodontic Loading (Part II): A Comparison of Linear Versus Non-Linear Fem Study.

PubMed

Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B

2015-09-01

Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. This shows that the force level required for non-linear analysis is lesser than that of linear analysis.

A General Formulation for Robust and Efficient Integration of Finite Differences and Phase Unwrapping on Sparse Multidimensional Domains

NASA Astrophysics Data System (ADS)

Costantini, Mario; Malvarosa, Fabio; Minati, Federico

2010-03-01

Phase unwrapping and integration of finite differences are key problems in several technical fields. In SAR interferometry and differential and persistent scatterers interferometry digital elevation models and displacement measurements can be obtained after unambiguously determining the phase values and reconstructing the mean velocities and elevations of the observed targets, which can be performed by integrating differential estimates of these quantities (finite differences between neighboring points).In this paper we propose a general formulation for robust and efficient integration of finite differences and phase unwrapping, which includes standard techniques methods as sub-cases. The proposed approach allows obtaining more reliable and accurate solutions by exploiting redundant differential estimates (not only between nearest neighboring points) and multi-dimensional information (e.g. multi-temporal, multi-frequency, multi-baseline observations), or external data (e.g. GPS measurements). The proposed approach requires the solution of linear or quadratic programming problems, for which computationally efficient algorithms exist.The validation tests obtained on real SAR data confirm the validity of the method, which was integrated in our production chain and successfully used also in massive productions.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Superlinear variant of the dual affine scaling algorithm

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

Luz, C.; Cardosa, D.

1994-12-31

The affine scaling methods introduced by Dikin are generally considered the most efficient interior point algorithms from a computational point of view. However, it is actually an open question to know whether there is a polynomial affine scaling algorithm. This fact has motivated many investigations efforts and led to several convergence results. This is the case of the recently obtained results by Tsuchiya, Tseng and Luo and Tsuchiya and Muramatsu which, unlike the pioneering Dikin`s convergence result, do not require any non degeneracy assumption. This paper presents a new variant of the dual affine scaling algorithm for Linear Programming that,more » in a finite number of iterations, determines a primal-dual pair of optimal solutions. It is also shown the superlinear convergence of that variant without requiring any non degeneracy assumption.« less

A Linear Electromagnetic Piston Pump

NASA Astrophysics Data System (ADS)

Hogan, Paul H.

Advancements in mobile hydraulics for human-scale applications have increased demand for a compact hydraulic power supply. Conventional designs couple a rotating electric motor to a hydraulic pump, which increases the package volume and requires several energy conversions. This thesis investigates the use of a free piston as the moving element in a linear motor to eliminate multiple energy conversions and decrease the overall package volume. A coupled model used a quasi-static magnetic equivalent circuit to calculate the motor inductance and the electromagnetic force acting on the piston. The force was an input to a time domain model to evaluate the mechanical and pressure dynamics. The magnetic circuit model was validated with finite element analysis and an experimental prototype linear motor. The coupled model was optimized using a multi-objective genetic algorithm to explore the parameter space and maximize power density and efficiency. An experimental prototype linear pump coupled pistons to an off-the-shelf linear motor to validate the mechanical and pressure dynamics models. The magnetic circuit force calculation agreed within 3% of finite element analysis, and within 8% of experimental data from the unoptimized prototype linear motor. The optimized motor geometry also had good agreement with FEA; at zero piston displacement, the magnetic circuit calculates optimized motor force within 10% of FEA in less than 1/1000 the computational time. This makes it well suited to genetic optimization algorithms. The mechanical model agrees very well with the experimental piston pump position data when tuned for additional unmodeled mechanical friction. Optimized results suggest that an improvement of 400% of the state of the art power density is attainable with as high as 85% net efficiency. This demonstrates that a linear electromagnetic piston pump has potential to serve as a more compact and efficient supply of fluid power for the human scale.

Blind identification of nonlinear models with non-Gaussian inputs

NASA Astrophysics Data System (ADS)

Prakriya, Shankar; Pasupathy, Subbarayan; Hatzinakos, Dimitrios

1995-12-01

Some methods are proposed for the blind identification of finite-order discrete-time nonlinear models with non-Gaussian circular inputs. The nonlinear models consist of two finite memory linear time invariant (LTI) filters separated by a zero-memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI models). The linear subsystems are allowed to be of non-minimum phase (NMP). The methods base their estimates of the impulse responses on slices of the N plus 1th order polyspectra of the output sequence. It is shown that the identification of LTI-ZMNL systems requires only a 1-D moment or polyspectral slice. The coefficients of the ZMNL are not estimated, and need not be known. The order of the nonlinearity can, in theory, be estimated from the received signal. These methods possess several noise and interference suppression characteristics, and have applications in modeling nonlinearly amplified QAM/QPSK signals in digital satellite and microwave communications.

Formulation of Efficient Finite Element Prediction Models.

DTIC Science & Technology

1980-01-01

vorticity-divergence FEM formulation. This paper will compare these FEM formulations by considering the Vgeostrophic adjustment process with the linearized...by Fourier transforming the terms that are independent of t in (2.12)-(2.14) or (2.19)-(2.21). However, in this paper the final state will be...filtering in a baroclinic primitive equation model. 17 L . , 5. Conclusions The objective of this paper is to determine the response of various finite

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

NASA Astrophysics Data System (ADS)

Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent

2016-04-01

Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

NASA Technical Reports Server (NTRS)

Carlson, F. M.; Chin, L.-Y.; Fripp, A. L.; Crouch, R. K.

1982-01-01

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

Linearized propulsion theory of flapping airfoils revisited

NASA Astrophysics Data System (ADS)

Fernandez-Feria, Ramon

2016-11-01

A vortical impulse theory is used to compute the thrust of a plunging and pitching airfoil in forward flight within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick that considered the leading-edge suction and the projection in the flight direction of the pressure force. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains a new term that generalizes the leading-edge suction term and depends on Theodorsen function C (k) and on a new complex function C1 (k) of the reduced frequency k. The main qualitative difference with Garrick's theory is that the propulsive efficiency tends to zero as the reduced frequency increases to infinity (as 1 / k), in contrast to Garrick's efficiency that tends to a constant (1 / 2). Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as k -> ∞ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining non-dimensional parameters. The present analytical results are in good agreement with experimental data and numerical results for small amplitude oscillations. Supported by the Ministerio de Economia y Competitividad of Spain Grant No. DPI2013-40479-P.

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.

Efficiency at maximum power of a chemical engine.

PubMed

Hooyberghs, Hans; Cleuren, Bart; Salazar, Alberto; Indekeu, Joseph O; Van den Broeck, Christian

2013-10-07

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power η(mp) [corrected] takes the form 1/2+cΔμ+O(Δμ(2)), with 1∕2 a universal constant and Δμ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in η(mp) [corrected] is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model, we obtain η(mp) = 1/(θ + 1) [corrected], with θ > 0 the power of Δμ in the transport equation.

Linear finite-difference bond graph model of an ionic polymer actuator

NASA Astrophysics Data System (ADS)

Bentefrit, M.; Grondel, S.; Soyer, C.; Fannir, A.; Cattan, E.; Madden, J. D.; Nguyen, T. M. G.; Plesse, C.; Vidal, F.

2017-09-01

With the recent growing interest for soft actuation, many new types of ionic polymers working in air have been developed. Due to the interrelated mechanical, electrical, and chemical properties which greatly influence the characteristics of such actuators, their behavior is complex and difficult to understand, predict and optimize. In light of this challenge, an original linear multiphysics finite difference bond graph model was derived to characterize this ionic actuation. This finite difference scheme was divided into two coupled subparts, each related to a specific physical, electrochemical or mechanical domain, and then converted into a bond graph model as this language is particularly suited for systems from multiple energy domains. Simulations were then conducted and a good agreement with the experimental results was obtained. Furthermore, an analysis of the power efficiency of such actuators as a function of space and time was proposed and allowed to evaluate their performance.

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.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

An Integrated Approach to Characterizing Bypassed Oil in Heterogeneous and Fractured Reservoirs Using Partitioning Tracers

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

Akhil Datta-Gupta

2006-12-31

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have investigated the relative merits of the traditional history matching ('amplitude inversion') and a novel travel time inversion in terms of robustness of the method and convergence behavior of the solution. We show that the traditional amplitude inversion is orders of magnitudemore » more non-linear and the solution here is likely to get trapped in local minimum, leading to inadequate history match. The proposed travel time inversion is shown to be extremely efficient and robust for practical field applications. The streamline approach is generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. A detailed comparison with a commercial finite difference simulator shows very good agreement. Furthermore, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications. We also propose a novel approach to history matching finite-difference models that combines the advantage of the streamline models with the versatility of finite-difference simulation. In our approach, we utilize the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. The use of finite-difference model allows us to account for detailed process physics and compressibility effects. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, we discuss several alternative ways of using partitioning interwell tracer tests (PITTs) in oil fields for the calculation of oil saturation, swept pore volume and sweep efficiency, and assess the accuracy of such tests under a variety of reservoir conditions.« less

Advanced composites structural concepts and materials technologies for primary aircraft structures: Structural response and failure analysis

NASA Technical Reports Server (NTRS)

Dorris, William J.; Hairr, John W.; Huang, Jui-Tien; Ingram, J. Edward; Shah, Bharat M.

1992-01-01

Non-linear analysis methods were adapted and incorporated in a finite element based DIAL code. These methods are necessary to evaluate the global response of a stiffened structure under combined in-plane and out-of-plane loading. These methods include the Arc Length method and target point analysis procedure. A new interface material model was implemented that can model elastic-plastic behavior of the bond adhesive. Direct application of this method is in skin/stiffener interface failure assessment. Addition of the AML (angle minus longitudinal or load) failure procedure and Hasin's failure criteria provides added capability in the failure predictions. Interactive Stiffened Panel Analysis modules were developed as interactive pre-and post-processors. Each module provides the means of performing self-initiated finite elements based analysis of primary structures such as a flat or curved stiffened panel; a corrugated flat sandwich panel; and a curved geodesic fuselage panel. This module brings finite element analysis into the design of composite structures without the requirement for the user to know much about the techniques and procedures needed to actually perform a finite element analysis from scratch. An interactive finite element code was developed to predict bolted joint strength considering material and geometrical non-linearity. The developed method conducts an ultimate strength failure analysis using a set of material degradation models.

Towards a Highly Efficient Meshfree Simulation of Non-Newtonian Free Surface Ice Flow: Application to the Haut Glacier d'Arolla

NASA Astrophysics Data System (ADS)

Shcherbakov, V.; Ahlkrona, J.

2016-12-01

In this work we develop a highly efficient meshfree approach to ice sheet modeling. Traditionally mesh based methods such as finite element methods are employed to simulate glacier and ice sheet dynamics. These methods are mature and well developed. However, despite of numerous advantages these methods suffer from some drawbacks such as necessity to remesh the computational domain every time it changes its shape, which significantly complicates the implementation on moving domains, or a costly assembly procedure for nonlinear problems. We introduce a novel meshfree approach that frees us from all these issues. The approach is built upon a radial basis function (RBF) method that, thanks to its meshfree nature, allows for an efficient handling of moving margins and free ice surface. RBF methods are also accurate and easy to implement. Since the formulation is stated in strong form it allows for a substantial reduction of the computational cost associated with the linear system assembly inside the nonlinear solver. We implement a global RBF method that defines an approximation on the entire computational domain. This method exhibits high accuracy properties. However, it suffers from a disadvantage that the coefficient matrix is dense, and therefore the computational efficiency decreases. In order to overcome this issue we also implement a localized RBF method that rests upon a partition of unity approach to subdivide the domain into several smaller subdomains. The radial basis function partition of unity method (RBF-PUM) inherits high approximation characteristics form the global RBF method while resulting in a sparse system of equations, which essentially increases the computational efficiency. To demonstrate the usefulness of the RBF methods we model the velocity field of ice flow in the Haut Glacier d'Arolla. We assume that the flow is governed by the nonlinear Blatter-Pattyn equations. We test the methods for different basal conditions and for a free moving surface. Both RBF methods are compared with a classical finite element method in terms of accuracy and efficiency. We find that the RBF methods are more efficient than the finite element method and well suited for ice dynamics modeling, especially the partition of unity approach.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Wang, Jun; Luo, Ray

2009-01-01

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

Improvements in mode-based waveform modeling and application to Eurasian velocity structure

NASA Astrophysics Data System (ADS)

Panning, M. P.; Marone, F.; Kim, A.; Capdeville, Y.; Cupillard, P.; Gung, Y.; Romanowicz, B.

2006-12-01

We introduce several recent improvements to mode-based 3D and asymptotic waveform modeling and examine how to integrate them with numerical approaches for an improved model of upper-mantle structure under eastern Eurasia. The first step in our approach is to create a large-scale starting model including shear anisotropy using Nonlinear Asymptotic Coupling Theory (NACT; Li and Romanowicz, 1995), which models the 2D sensitivity of the waveform to the great-circle path between source and receiver. We have recently improved this approach by implementing new crustal corrections which include a non-linear correction for the difference between the average structure of several large regions from the global model with further linear corrections to account for the local structure along the path between source and receiver (Marone and Romanowicz, 2006; Panning and Romanowicz, 2006). This model is further refined using a 3D implementation of Born scattering (Capdeville, 2005). We have made several recent improvements to this method, in particular introducing the ability to represent perturbations to discontinuities. While the approach treats all sensitivity as linear perturbations to the waveform, we have also experimented with a non-linear modification analogous to that used in the development of NACT. This allows us to treat large accumulated phase delays determined from a path-average approximation non-linearly, while still using the full 3D sensitivity of the Born approximation. Further refinement of shallow regions of the model is obtained using broadband forward finite-difference waveform modeling. We are also integrating a regional Spectral Element Method code into our tomographic modeling, allowing us to move beyond many assumptions inherent in the analytic mode-based approaches, while still taking advantage of their computational efficiency. Illustrations of the effects of these increasingly sophisticated steps will be presented.

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

NASA Astrophysics Data System (ADS)

Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

2016-09-01

In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

YAP Version 4.0

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

Nelson, Eric M.

2004-05-20

The YAP software library computes (1) electromagnetic modes, (2) electrostatic fields, (3) magnetostatic fields and (4) particle trajectories in 2d and 3d models. The code employs finite element methods on unstructured grids of tetrahedral, hexahedral, prism and pyramid elements, with linear through cubic element shapes and basis functions to provide high accuracy. The novel particle tracker is robust, accurate and efficient, even on unstructured grids with discontinuous fields. This software library is a component of the MICHELLE 3d finite element gun code.

Development of non-linear finite element computer code

NASA Technical Reports Server (NTRS)

Becker, E. B.; Miller, T.

1985-01-01

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

Finite element methods in a simulation code for offshore wind turbines

NASA Astrophysics Data System (ADS)

Kurz, Wolfgang

1994-06-01

Offshore installation of wind turbines will become important for electricity supply in future. Wind conditions above sea are more favorable than on land and appropriate locations on land are limited and restricted. The dynamic behavior of advanced wind turbines is investigated with digital simulations to reduce time and cost in development and design phase. A wind turbine can be described and simulated as a multi-body system containing rigid and flexible bodies. Simulation of the non-linear motion of such a mechanical system using a multi-body system code is much faster than using a finite element code. However, a modal representation of the deformation field has to be incorporated in the multi-body system approach. The equations of motion of flexible bodies due to deformation are generated by finite element calculations. At Delft University of Technology the simulation code DUWECS has been developed which simulates the non-linear behavior of wind turbines in time domain. The wind turbine is divided in subcomponents which are represented by modules (e.g. rotor, tower etc.).

Influence of a Levelness Defect in a Thrust Bearing on the Dynamic Behaviour of AN Elastic Shaft

NASA Astrophysics Data System (ADS)

BERGER, S.; BONNEAU, O.; FRÊNE, J.

2002-01-01

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.

Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles

NASA Astrophysics Data System (ADS)

Tzirtzilakis, E. E.

2015-06-01

In this study, the fundamental problem of biomagnetic fluid flow in an aneurysmal geometry under the influence of a steady localized magnetic field is numerically investigated. The mathematical model used to formulate the problem is consistent with the principles of ferrohydrodynamics. Blood is considered to be an electrically non-conducting, homogeneous, non-isothermal Newtonian magnetic fluid. For the numerical solution of the problem, which is described by a coupled, non-linear system of Partial Differential Equations (PDEs), with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by applying an efficient pseudotransient numerical methodology using finite differences. This methodology is based on the application of a semi-implicit numerical technique, transformations, stretching of the grid, and construction of the boundary conditions for the vorticity. The results regarding the velocity and temperature field, skin friction, and rate of heat transfer indicate that the presence of a magnetic field considerably influences the flow field, particularly in the region of the aneurysm.

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.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Energetics and optimum motion of oscillating lifting surfaces of finite span

NASA Technical Reports Server (NTRS)

Ahmadi, A. R.; Widnall, S. E.

1986-01-01

In certain modes of animal propulsion in nature, such as bird flight and fish swimming, the efficiency compared to man-made vehicles is very high. In such cases, wing and tail motions are typically associated with relatively high Reynolds numbers, where viscous effects are confined to a thin boundary layer at the surface and a thin trailing wake. The propulsive forces, which are generated primarily by the inertial forces, can be calculated from potential-flow theory using linearized unsteady-wing theory (for small-amplitude oscillations). In the present study, a recently developed linearized, low-frequency, unsteady lifting-line theory is employed to calculate the (sectional and total) energetic quantities and optimum motion of an oscillating wing of finite span.

Modelling of deformation of underground tunnel lining, interacting with water-saturated soil

NASA Astrophysics Data System (ADS)

Berezhnoi, D. V.; Balafendieva, I. S.; Sachenkov, A. A.; Sekaeva, L. R.

2016-11-01

Built finite element method of calculating the deformation of underground tunnel lining, interacting with dry and water-saturated soils. To simulate the interaction between the lining and soils environments, including physical and non-linear, a special "contact" finite element, which allows to consider all cases of interaction between the contacting surfaces. It solved a number of problems of deformation with the ground subway tunnel lining rings.

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2000-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

Vascular mechanics of the coronary artery

NASA Technical Reports Server (NTRS)

Veress, A. I.; Vince, D. G.; Anderson, P. M.; Cornhill, J. F.; Herderick, E. E.; Klingensmith, J. D.; Kuban, B. D.; Greenberg, N. L.; Thomas, J. D.

2000-01-01

This paper describes our research into the vascular mechanics of the coronary artery and plaque. The three sections describe the determination of arterial mechanical properties using intravascular ultrasound (IVUS), a constitutive relation for the arterial wall, and finite element method (FEM) models of the arterial wall and atheroma. METHODS: Inflation testing of porcine left anterior descending coronary arteries was conducted. The changes in the vessel geometry were monitored using IVUS, and intracoronary pressure was recorded using a pressure transducer. The creep and quasistatic stress/strain responses were determined. A Standard Linear Solid (SLS) was modified to reproduce the non-linear elastic behavior of the arterial wall. This Standard Non-linear Solid (SNS) was implemented into an axisymetric thick-walled cylinder numerical model. Finite element analysis models were created for five age groups and four levels of stenosis using the Pathobiological Determinants of Atherosclerosis Youth (PDAY) database. RESULTS: The arteries exhibited non-linear elastic behavior. The total tissue creep strain was epsilon creep = 0.082 +/- 0.018 mm/mm. The numerical model could reproduce both the non-linearity of the porcine data and time dependent behavior of the arterial wall found in the literature with a correlation coefficient of 0.985. Increasing age had a strong positive correlation with the shoulder stress level, (r = 0.95). The 30% stenosis had the highest shoulder stress due to the combination of a fully formed lipid pool and a thin cap. CONCLUSIONS: Studying the solid mechanics of the arterial wall and the atheroma provide important insights into the mechanisms involved in plaque rupture.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

NASA Astrophysics Data System (ADS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers.

PubMed

Li, Jing; Wu, Xiaoping

2011-10-10

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam.

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers

PubMed Central

Li, Jing; Wu, Xiaoping

2011-01-01

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam. PMID:21997083

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

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

Palaniswamy, Hariharasudhan; Mondalek, Pamela; Wronski, Maciek

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

On the mechanics of growing thin biological membranes

NASA Astrophysics Data System (ADS)

Rausch, Manuel K.; Kuhl, Ellen

2014-02-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

On the mechanics of growing thin biological membranes

PubMed Central

Rausch, Manuel K.; Kuhl, Ellen

2013-01-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression. PMID:24563551

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: Non-nearest-neighbor effects

NASA Astrophysics Data System (ADS)

Bentz, Jonathan L.; Kozak, John J.; Nicolis, Gregoire

2005-08-01

The influence of non-nearest-neighbor displacements on the efficiency of diffusion-reaction processes involving one and two mobile diffusing reactants is studied. An exact analytic result is given for dimension d=1 from which, for large lattices, one can recover the asymptotic estimate reported 30 years ago by Lakatos-Lindenberg and Shuler. For dimensions d=2,3 we present numerically exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via the theory of finite Markov processes and supported by Monte Carlo simulations. Qualitatively different results are found between processes occurring on d=1 versus d>1 lattices, and between results obtained assuming nearest-neighbor (only) versus non-nearest-neighbor displacements.

Implicit filtered P{sub N} for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

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

Laboure, Vincent M., E-mail: vincent.laboure@tamu.edu; McClarren, Ryan G., E-mail: rgm@tamu.edu; Hauck, Cory D., E-mail: hauckc@ornl.gov

2016-09-15

In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP{sub N}) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

An adjoint-based simultaneous estimation method of the asthenosphere's viscosity and afterslip using a fast and scalable finite-element adjoint solver

NASA Astrophysics Data System (ADS)

Agata, Ryoichiro; Ichimura, Tsuyoshi; Hori, Takane; Hirahara, Kazuro; Hashimoto, Chihiro; Hori, Muneo

2018-04-01

The simultaneous estimation of the asthenosphere's viscosity and coseismic slip/afterslip is expected to improve largely the consistency of the estimation results to observation data of crustal deformation collected in widely spread observation points, compared to estimations of slips only. Such an estimate can be formulated as a non-linear inverse problem of material properties of viscosity and input force that is equivalent to fault slips based on large-scale finite-element (FE) modeling of crustal deformation, in which the degree of freedom is in the order of 109. We formulated and developed a computationally efficient adjoint-based estimation method for this inverse problem, together with a fast and scalable FE solver for the associated forward and adjoint problems. In a numerical experiment that imitates the 2011 Tohoku-Oki earthquake, the advantage of the proposed method is confirmed by comparing the estimated results with those obtained using simplified estimation methods. The computational cost required for the optimization shows that the proposed method enabled the targeted estimation to be completed with moderate amount of computational resources.

Analysis of the Efficiency of an A-Posteriori Error Estimator for Linear Triangular Finite Elements

DTIC Science & Technology

1991-06-01

Release 1.0, NOETIC Tech. Corp., St. Louis, Missouri, 1985. [28] R. VERFURTH, FEMFLOW-user guide. Version 1, Report, Universitiit Zirich, 1989. [29] R... study and research for foreign students in numerical mathematics who are supported by foreign governments or exchange agencies (Fulbright, etc

Linearization instability for generic gravity in AdS spacetime

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Robustness of controllability and observability of linear time-varying systems with application to the emergency control of power systems

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

Sastry, S. S.; Desoer, C. A.

1980-01-01

Fixed point methods from nonlinear anaysis are used to establish conditions under which the uniform complete controllability of linear time-varying systems is preserved under non-linear perturbations in the state dynamics and the zero-input uniform complete observability of linear time-varying systems is preserved under non-linear perturbation in the state dynamics and output read out map. Algorithms for computing the specific input to steer the perturbed systems from a given initial state to a given final state are also presented. As an application, a very specific emergency control of an interconnected power system is formulated as a steering problem and it ismore » shown that this emergency control is indeed possible in finite time.« less

Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, Carl M.; Tanner, John A.

1987-01-01

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

ADAPTION OF NONSTANDARD PIPING COMPONENTS INTO PRESENT DAY SEISMIC CODES

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

D. T. Clark; M. J. Russell; R. E. Spears

2009-07-01

With spiraling energy demand and flat energy supply, there is a need to extend the life of older nuclear reactors. This sometimes requires that existing systems be evaluated to present day seismic codes. Older reactors built in the 1960s and early 1970s often used fabricated piping components that were code compliant during their initial construction time period, but are outside the standard parameters of present-day piping codes. There are several approaches available to the analyst in evaluating these non-standard components to modern codes. The simplest approach is to use the flexibility factors and stress indices for similar standard components withmore » the assumption that the non-standard component’s flexibility factors and stress indices will be very similar. This approach can require significant engineering judgment. A more rational approach available in Section III of the ASME Boiler and Pressure Vessel Code, which is the subject of this paper, involves calculation of flexibility factors using finite element analysis of the non-standard component. Such analysis allows modeling of geometric and material nonlinearities. Flexibility factors based on these analyses are sensitive to the load magnitudes used in their calculation, load magnitudes that need to be consistent with those produced by the linear system analyses where the flexibility factors are applied. This can lead to iteration, since the magnitude of the loads produced by the linear system analysis depend on the magnitude of the flexibility factors. After the loading applied to the nonstandard component finite element model has been matched to loads produced by the associated linear system model, the component finite element model can then be used to evaluate the performance of the component under the loads with the nonlinear analysis provisions of the Code, should the load levels lead to calculated stresses in excess of Allowable stresses. This paper details the application of component-level finite element modeling to account for geometric and material nonlinear component behavior in a linear elastic piping system model. Note that this technique can be applied to the analysis of B31 piping systems.« less

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

NASA Astrophysics Data System (ADS)

Polstyanko, Sergey V.; Lee, Jin-Fa

1998-03-01

In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss-Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.

A new parallel-vector finite element analysis software on distributed-memory computers

NASA Technical Reports Server (NTRS)

Qin, Jiangning; Nguyen, Duc T.

1993-01-01

A new parallel-vector finite element analysis software package MPFEA (Massively Parallel-vector Finite Element Analysis) is developed for large-scale structural analysis on massively parallel computers with distributed-memory. MPFEA is designed for parallel generation and assembly of the global finite element stiffness matrices as well as parallel solution of the simultaneous linear equations, since these are often the major time-consuming parts of a finite element analysis. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results on the Intel iPSC/860 computers (such as the Intel Gamma with 128 processors and the Intel Touchstone Delta with 512 processors) are presented, including an aircraft structure and some very large truss structures, to demonstrate the efficiency and accuracy of MPFEA.

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, G. H.

1985-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90 percent for sufficiently large problems.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, B. H.

1984-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Shape and Stress Sensing of Multilayered Composite and Sandwich Structures Using an Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Cerracchio, Priscilla; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander

2013-01-01

The marked increase in the use of composite and sandwich material systems in aerospace, civil, and marine structures leads to the need for integrated Structural Health Management systems. A key capability to enable such systems is the real-time reconstruction of structural deformations, stresses, and failure criteria that are inferred from in-situ, discrete-location strain measurements. This technology is commonly referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. A three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains, stresses, and failure criteria that are in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.

A Spectral Finite Element Approach to Modeling Soft Solids Excited with High-Frequency Harmonic Loads

PubMed Central

Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.

2010-01-01

An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402

New approaches for cement-based prophylactic augmentation of the osteoporotic proximal femur provide enhanced reinforcement as predicted by non-linear finite element simulations.

PubMed

Varga, Peter; Inzana, Jason A; Schwiedrzik, Jakob; Zysset, Philippe K; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus

2017-05-01

High incidence and increased mortality related to secondary, contralateral proximal femoral fractures may justify invasive prophylactic augmentation that reinforces the osteoporotic proximal femur to reduce fracture risk. Bone cement-based approaches (femoroplasty) may deliver the required strengthening effect; however, the significant variation in the results of previous studies calls for a systematic analysis and optimization of this method. Our hypothesis was that efficient generalized augmentation strategies can be identified via computational optimization. This study investigated, by means of finite element analysis, the effect of cement location and volume on the biomechanical properties of fifteen proximal femora in sideways fall. Novel cement cloud locations were developed using the principles of bone remodeling and compared to the "single central" location that was previously reported to be optimal. The new augmentation strategies provided significantly greater biomechanical benefits compared to the "single central" cement location. Augmenting with approximately 12ml of cement in the newly identified location achieved increases of 11% in stiffness, 64% in yield force, 156% in yield energy and 59% in maximum force, on average, compared to the non-augmented state. The weaker bones experienced a greater biomechanical benefit from augmentation than stronger bones. The effect of cement volume on the biomechanical properties was approximately linear. Results of the "single central" model showed good agreement with previous experimental studies. These findings indicate enhanced potential of cement-based prophylactic augmentation using the newly developed cementing strategy. Future studies should determine the required level of strengthening and confirm these numerical results experimentally. Copyright © 2017 Elsevier Ltd. All rights reserved.

Development and validation of a subject-specific finite element model of the functional spinal unit to predict vertebral strength.

PubMed

Lee, Chu-Hee; Landham, Priyan R; Eastell, Richard; Adams, Michael A; Dolan, Patricia; Yang, Lang

2017-09-01

Finite element models of an isolated vertebral body cannot accurately predict compressive strength of the spinal column because, in life, compressive load is variably distributed across the vertebral body and neural arch. The purpose of this study was to develop and validate a patient-specific finite element model of a functional spinal unit, and then use the model to predict vertebral strength from medical images. A total of 16 cadaveric functional spinal units were scanned and then tested mechanically in bending and compression to generate a vertebral wedge fracture. Before testing, an image processing and finite element analysis framework (SpineVox-Pro), developed previously in MATLAB using ANSYS APDL, was used to generate a subject-specific finite element model with eight-node hexahedral elements. Transversely isotropic linear-elastic material properties were assigned to vertebrae, and simple homogeneous linear-elastic properties were assigned to the intervertebral disc. Forward bending loading conditions were applied to simulate manual handling. Results showed that vertebral strengths measured by experiment were positively correlated with strengths predicted by the functional spinal unit finite element model with von Mises or Drucker-Prager failure criteria ( R 2  = 0.80-0.87), with areal bone mineral density measured by dual-energy X-ray absorptiometry ( R 2  = 0.54) and with volumetric bone mineral density from quantitative computed tomography ( R 2  = 0.79). Large-displacement non-linear analyses on all specimens did not improve predictions. We conclude that subject-specific finite element models of a functional spinal unit have potential to estimate the vertebral strength better than bone mineral density alone.

A permanent magnet tubular linear generator for wave energy conversion

NASA Astrophysics Data System (ADS)

Yu, Haitao; Liu, Chunyuan; Yuan, Bang; Hu, Minqiang; Huang, Lei; Zhou, Shigui

2012-04-01

A novel three-phase permanent magnet tubular linear generator (PMTLG) with Halbach array is proposed for the sea wave energy conversion. Non-linear axi-symmetrical finite element method (FEM) is implemented to calculate the magnetic fields along air-gap for different Halbach arrays of PMTLGs. The PMTLG characteristics are analyzed and the simulation results are validated by the experiment. An assistant tooth is implemented to greatly minimize the end and cogging effects which cause the oscillatory detent force.

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

PubMed

Chronopoulos, D

2017-01-01

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

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

PubMed

Kong, Shengchun; Nan, Bin

2014-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

PubMed Central

Kong, Shengchun; Nan, Bin

2013-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses. PMID:24516328

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

Duality in non-linear programming

NASA Astrophysics Data System (ADS)

Jeyalakshmi, K.

2018-04-01

In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.

Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats

NASA Astrophysics Data System (ADS)

Stalter, S.; Yelash, L.; Emamy, N.; Statt, A.; Hanke, M.; Lukáčová-Medvid'ová, M.; Virnau, P.

2018-03-01

Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation boxes. We also argue that if colloidal systems are considered as opposed to atomistic systems, the gap between microscopic and macroscopic simulations regarding time and length scales is significantly smaller. We propose a novel reduced-order technique for the coupling to the macroscopic solver, which allows us to approximate a non-linear stress-strain relation efficiently and thus further reduce computational effort of microscopic simulations.

Simulation of crash tests for high impact levels of a new bridge safety barrier

NASA Astrophysics Data System (ADS)

Drozda, Jiří; Rotter, Tomáš

2017-09-01

The purpose is to show the opportunity of a non-linear dynamic impact simulation and to explain the possibility of using finite element method (FEM) for developing new designs of safety barriers. The main challenge is to determine the means to create and validate the finite element (FE) model. The results of accurate impact simulations can help to reduce necessary costs for developing of a new safety barrier. The introductory part deals with the creation of the FE model, which includes the newly-designed safety barrier and focuses on the application of an experimental modal analysis (EMA). The FE model has been created in ANSYS Workbench and is formed from shell and solid elements. The experimental modal analysis, which was performed on a real pattern, was employed for measuring the modal frequencies and shapes. After performing the EMA, the FE mesh was calibrated after comparing the measured modal frequencies with the calculated ones. The last part describes the process of the numerical non-linear dynamic impact simulation in LS-DYNA. This simulation was validated after comparing the measured ASI index with the calculated ones. The aim of the study is to improve professional public knowledge about dynamic non-linear impact simulations. This should ideally lead to safer, more accurate and profitable designs.

The power of a critical heat engine

PubMed Central

Campisi, Michele; Fazio, Rosario

2016-01-01

Since its inception about two centuries ago thermodynamics has sparkled continuous interest and fundamental questions. According to the second law no heat engine can have an efficiency larger than Carnot's efficiency. The latter can be achieved by the Carnot engine, which however ideally operates in infinite time, hence delivers null power. A currently open question is whether the Carnot efficiency can be achieved at finite power. Most of the previous works addressed this question within the Onsager matrix formalism of linear response theory. Here we pursue a different route based on finite-size-scaling theory. We focus on quantum Otto engines and show that when the working substance is at the verge of a second order phase transition diverging energy fluctuations can enable approaching the Carnot point without sacrificing power. The rate of such approach is dictated by the critical indices, thus showing the universal character of our analysis. PMID:27320127

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Numerical calculations of two dimensional, unsteady transonic flows with circulation

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1974-01-01

The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

Optimal Transient Growth of Submesoscale Baroclinic Instabilities

NASA Astrophysics Data System (ADS)

White, Brian; Zemskova, Varvara; Passaggia, Pierre-Yves

2016-11-01

Submesoscale instabilities are analyzed using a transient growth approach to determine the optimal perturbation for a rotating Boussinesq fluid subject to baroclinic instabilities. We consider a base flow with uniform shear and stratification and consider the non-normal evolution over finite-time horizons of linear perturbations in an ageostrophic, non-hydrostatic regime. Stone (1966, 1971) showed that the stability of the base flow to normal modes depends on the Rossby and Richardson numbers, with instabilities ranging from geostrophic (Ro -> 0) and ageostrophic (finite Ro) baroclinic modes to symmetric (Ri < 1 , Ro > 1) and Kelvin-Helmholtz (Ri < 1 / 4) modes. Non-normal transient growth, initiated by localized optimal wave packets, represents a faster mechanism for the growth of perturbations and may provide an energetic link between large-scale flows in geostrophic balance and dissipation scales via submesoscale instabilities. Here we consider two- and three-dimensional optimal perturbations by means of direct-adjoint iterations of the linearized Boussinesq Navier-Stokes equations to determine the form of the optimal perturbation, the optimal energy gain, and the characteristics of the most unstable perturbation.

Generalization of mixed multiscale finite element methods with applications

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

Lee, C S

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixedmore » multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii« less

Monitoring Programs Using Rewriting

NASA Technical Reports Server (NTRS)

Havelund, Klaus; Rosu, Grigore; Lan, Sonie (Technical Monitor)

2001-01-01

We present a rewriting algorithm for efficiently testing future time Linear Temporal Logic (LTL) formulae on finite execution traces, The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive in most past applications of LTL, theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications, corresponding to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property end then suggest an optimized algorithm based on transforming LTL formulae. We use the Maude rewriting logic, which turns out to be a good notation and being supported by an efficient rewriting engine for performing these experiments. The work constitutes part of the Java PathExplorer (JPAX) project, the purpose of which is to develop a flexible tool for monitoring Java program executions.

EAGLE can do Efficient LTL Monitoring

NASA Technical Reports Server (NTRS)

Barringer, Howard; Goldberg, Allen; Havelund, Klaus; Sen, Koushik

2003-01-01

We briefly present a rule-based framework, called EAGLE, that has been shown to be capable of defining and implementing finite trace monitoring logics, including future and past time temporal logic, extended regular expressions, real-time logics, interval logics, forms of quantified temporal logics, and so on. In this paper we show how EAGLE can do linear temporal logic (LTL) monitoring in an efficient way. We give an upper bound on the space and time complexity of this monitoring.

Performance and limitations of p-version finite element method for problems containing singularities

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

Wong, K.K.; Surana, K.S.

1996-10-01

In this paper, the authors investigate the performance of p-version Least Squares Finite Element Formulation (LSFEF) for a hyperbolic system of equations describing a one-dimensional radial flow of an upper-convected Maxwell fluid. This problem has r{sup 2} singularity in stress and r{sup {minus}1} singularity in velocity at r = 0. By carefully controlling the inner radius r{sub j}, Deborah number DE and Reynolds number Re, this problem can be used to simulate the following four classes of problems: (a) smooth linear problems, (b) smooth non-linear problems, (c) singular linear problems and (d) singular non-linear problems. They demonstrate that in casesmore » (a) and (b) the p-version method, in particular p-version LSFEF is meritorious. However, for cases (c) and (d) p-version LSFEF, even with extreme mesh refinement and very high p-levels, either produces wrong solutions, or results in the failure of the iterative solution procedure. Even though in the numerical studies they have considered p-version LSFEF for the radial flow of the upper-convected Maxwell fluid, the findings and conclusions are equally valid for other smooth and singular problems as well, regardless of the formulation strategy chosen and element approximation functions employed.« less

Postprocessing techniques for 3D non-linear structures

NASA Technical Reports Server (NTRS)

Gallagher, Richard S.

1987-01-01

How graphics postprocessing techniques are currently used to examine the results of 3-D nonlinear analyses, some new techniques which take advantage of recent technology, and how these results relate to both the finite element model and its geometric parent are reviewed.

Transient Non Lin Deformation in Fractured Rock

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

Sartori, Enrico

1998-10-14

MATLOC is a nonlinear, transient, two-dimensional (planer and axisymmetric), thermal stress, finite-element code designed to determine the deformation within a fractured rock mass. The mass is modeled as a nonlinear anistropic elastic material which can exhibit stress-dependent bi-linear locking behavior.

Jupyter Notebooks for Earth Sciences: An Interactive Training Platform for Seismology

NASA Astrophysics Data System (ADS)

Igel, H.; Chow, B.; Donner, S.; Krischer, L.; van Driel, M.; Tape, C.

2017-12-01

We have initiated a community platform (http://www.seismo-live.org) where Python-based Jupyter notebooks (https://jupyter.org) can be accessed and run without necessary downloads or local software installations. The increasingly popular Jupyter notebooks allow the combination of markup language, graphics, and equations with interactive, executable Python code examples. Jupyter notebooks are a powerful and easy-to-grasp tool for students to develop entire projects, scientists to collaborate and efficiently interchange evolving workflows, and trainers to develop efficient practical material. Utilizing the tmpnb project (https://github.com/jupyter/tmpnb), we link the power of Jupyter notebooks with an underlying server, such that notebooks can be run from anywhere, even on smart phones. We demonstrate the potential with notebooks for 1) learning the programming language Python, 2) basic signal processing, 3) an introduction to the ObsPy library (https://obspy.org) for seismology, 4) seismic noise analysis, 5) an entire suite of notebooks for computational seismology (the finite-difference method, pseudospectral methods, finite/spectral element methods, the finite-volume and the discontinuous Galerkin methods, Instaseis), 6) rotational seismology, 7) making results in papers fully reproducible, 8) a rate-and-state friction toolkit, 9) glacial seismology. The platform is run as a community project using Github. Submission of complementary Jupyter notebooks is encouraged. Extension in the near future include linear(-ized) and nonlinear inverse problems.

Analysis, Design and Optimization of Non-Cylindrical Fuselage for Blended-Wing-Body (BWB) Vehicle

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Sobieszczanski-Sobieski, J.; Kosaka, I.; Quinn, G.; Charpentier, C.

2002-01-01

Initial results of an investigation towards finding an efficient non-cylindrical fuselage configuration for a conceptual blended-wing-body flight vehicle were presented. A simplified 2-D beam column analysis and optimization was performed first. Then a set of detailed finite element models of deep sandwich panel and ribbed shell construction concepts were analyzed and optimized. Generally these concepts with flat surfaces were found to be structurally inefficient to withstand internal pressure and resultant compressive loads simultaneously. Alternatively, a set of multi-bubble fuselage configuration concepts were developed for balancing internal cabin pressure load efficiently, through membrane stress in inner-stiffened shell and inter-cabin walls. An outer-ribbed shell was designed to prevent buckling due to external resultant compressive loads. Initial results from finite element analysis appear to be promising. These concepts should be developed further to exploit their inherent structurally efficiency.

Finite Element Analysis of Tube Hydroforming in Non-Symmetrical Dies

NASA Astrophysics Data System (ADS)

Nulkar, Abhishek V.; Gu, Randy; Murty, Pilaka

2011-08-01

Tube hydroforming has been studied intensively using commercial finite element programs. A great deal of the investigations dealt with models with symmetric cross-sections. It is known that additional constraints due to symmetry may be imposed on the model so that it is properly supported. For a non-symmetric model, these constraints become invalid and the model does not have sufficient support resulting in a singular finite element system. Majority of commercial codes have a limited capability in solving models with insufficient supports. Recently, new algorithms using penalty variable and air-like contact element (ALCE) have been developed to solve positive semi-definite finite element systems such as those in contact mechanics. In this study the ALCE algorithm is first validated by comparing its result against a commercial code using a symmetric model in which a circular tube is formed to polygonal dies with symmetric shapes. Then, the study investigates the accuracy and efficiency of using ALCE in analyzing hydroforming of tubes with various cross-sections in non-symmetrical dies in 2-D finite element settings.

Dynamics in atomic signaling games.

PubMed

Fox, Michael J; Touri, Behrouz; Shamma, Jeff S

2015-07-07

We study an atomic signaling game under stochastic evolutionary dynamics. There are a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss. Copyright © 2015 Elsevier Ltd. All rights reserved.

The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Norrie, D. H.; De Vries, G.

1979-01-01

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

A Non-Linear Finite Element Model for the Determination of Elastic and Thermal Properties of Nanocomposites

DTIC Science & Technology

2009-04-01

individuals who helped me in many ways throughout my research and thesis writing process. First and foremost, my sincere thanks go to my advisor, Dr... go to Professor John Akin who helped me in the technical areas of Finite Element programming. Thank you for your time and efforts beyond the...classroom. Thank you to Dr. Enrique Barrera and Dr. Jun Lou for serving on my thesis committee. Many thanks go to Dr. Jan Hewitt as well for volunteering

Properties of finite difference models of non-linear conservative oscillators

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1988-01-01

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

The entrainment matrix of a superfluid nucleon mixture at finite temperatures

NASA Astrophysics Data System (ADS)

Leinson, Lev B.

2018-06-01

It is considered a closed system of non-linear equations for the entrainment matrix of a non-relativistic mixture of superfluid nucleons at arbitrary temperatures below the onset of neutron superfluidity, which takes into account the essential dependence of the superfluid energy gap in the nucleon spectra on the velocities of superfluid flows. It is assumed that the protons condense into the isotropic 1S0 state, and the neutrons are paired into the spin-triplet 3P2 state. It is derived an analytic solution to the non-linear equations for the entrainment matrix under temperatures just below the critical value for the neutron superfluidity onset. In general case of an arbitrary temperature of the superfluid mixture the non-linear equations are solved numerically and fitted by simple formulas convenient for a practical use with an arbitrary set of the Landau parameters.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

PubMed

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms.

PubMed

Ye, Zhuolin; Hu, Yingying; He, Jizhou; Wang, Jianhui

2017-07-24

We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T h and T c (

A novel framework to simulating non-stationary, non-linear, non-Normal hydrological time series using Markov Switching Autoregressive Models

NASA Astrophysics Data System (ADS)

Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.

2012-12-01

In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by non-stationarity either of the system input (climatic variability) and/or the complexity of catchment storage characteristics. The statistical model is also capable of reproducing short (event) and longer-term (inter-event) and wet and dry dynamical "hydrological states". These reflect the non-linear transport mechanisms of flow pathways induced by transient climatic and hydrological variables and modified by catchment characteristics. We conclude that MSARMs are a powerful tool to analyze the temporal dynamics of hydrological data, allowing for explicit integration of non-stationary, non-linear and non-Normal characteristics.

A 3/D finite element approach for metal matrix composites based on micromechanical models

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

Svobodnik, A.J.; Boehm, H.J.; Rammerstorfer, F.G.

Based on analytical considerations by Dvorak and Bahel-El-Din, a 3/D finite element material law has been developed for the elastic-plastic analysis of unidirectional fiber-reinforced metal matrix composites. The material law described in this paper has been implemented in the finite element code ABAQUS via the user subroutine UMAT. A constitutive law is described under the assumption that the fibers are linear-elastic and the matrix is of a von Mises-type with a Prager-Ziegler kinematic hardening rule. The uniaxial effective stress-strain relationship of the matrix in the plastic range is approximated by a Ramberg-Osgood law, a linear hardening rule or a nonhardeningmore » rule. Initial yield surface of the matrix material and for the fiber reinforced composite are compared to show the effect of reinforcement. Implementation of this material law in a finite element program is shown. Furthermore, the efficiency of substepping schemes and stress corrections for the numerical integration of the elastic-plastic stress-strain relations for anisotropic materials are investigated. The results of uniaxial monotonic tests of a boron/aluminum composite are compared to some finite element analyses based on micromechanical considerations. Furthermore a complete 3/D analysis of a tensile test specimen made of a silicon-carbide/aluminum MMC and the analysis of an MMC inlet inserted in a homogenous material are shown. 12 refs.« less

Fluid-structure interaction simulations of deformable structures with non-linear thin shell elements

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Hedayat, Mohammadali; Borazjani, Iman; Scientific Computing; Biofluids Laboratory Team

2017-11-01

Large deformation of structures in a fluid is simulated using a strongly coupled partitioned fluid-structure interaction (FSI) approach which is stabilized with under-relaxation and the Aitken acceleration technique. The fluid is simulated using a recently developed implicit Newton-Krylov method with a novel analytical Jacobian. Structures are simulated using a triangular thin-shell finite element formulation, which considers only translational degrees of freedom. The thin-shell method is developed on the top of a previously implemented membrane finite element formulation. A sharp interface immersed boundary method is used to handle structures in the fluid domain. The developed FSI framework is validated against two three-dimensional experiments: (1) a flexible aquatic vegetation in the fluid and (2) a heaving flexible panel in fluid. Furthermore, the developed FSI framework is used to simulate tissue heart valves, which involve large deformations and non-linear material properties. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.

Efficient Computation Of Behavior Of Aircraft Tires

NASA Technical Reports Server (NTRS)

Tanner, John A.; Noor, Ahmed K.; Andersen, Carl M.

1989-01-01

NASA technical paper discusses challenging application of computational structural mechanics to numerical simulation of responses of aircraft tires during taxing, takeoff, and landing. Presents details of three main elements of computational strategy: use of special three-field, mixed-finite-element models; use of operator splitting; and application of technique reducing substantially number of degrees of freedom. Proposed computational strategy applied to two quasi-symmetric problems: linear analysis of anisotropic tires through use of two-dimensional-shell finite elements and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry and combinations exhibited by response of tire identified.

Weighted cubic and biharmonic splines

NASA Astrophysics Data System (ADS)

Kvasov, Boris; Kim, Tae-Wan

2017-01-01

In this paper we discuss the design of algorithms for interpolating discrete data by using weighted cubic and biharmonic splines in such a way that the monotonicity and convexity of the data are preserved. We formulate the problem as a differential multipoint boundary value problem and consider its finite-difference approximation. Two algorithms for automatic selection of shape control parameters (weights) are presented. For weighted biharmonic splines the resulting system of linear equations can be efficiently solved by combining Gaussian elimination with successive over-relaxation method or finite-difference schemes in fractional steps. We consider basic computational aspects and illustrate main features of this original approach.

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Multivariable optimization of liquid rocket engines using particle swarm algorithms

NASA Astrophysics Data System (ADS)

Jones, Daniel Ray

Liquid rocket engines are highly reliable, controllable, and efficient compared to other conventional forms of rocket propulsion. As such, they have seen wide use in the space industry and have become the standard propulsion system for launch vehicles, orbit insertion, and orbital maneuvering. Though these systems are well understood, historical optimization techniques are often inadequate due to the highly non-linear nature of the engine performance problem. In this thesis, a Particle Swarm Optimization (PSO) variant was applied to maximize the specific impulse of a finite-area combustion chamber (FAC) equilibrium flow rocket performance model by controlling the engine's oxidizer-to-fuel ratio and de Laval nozzle expansion and contraction ratios. In addition to the PSO-controlled parameters, engine performance was calculated based on propellant chemistry, combustion chamber pressure, and ambient pressure, which are provided as inputs to the program. The performance code was validated by comparison with NASA's Chemical Equilibrium with Applications (CEA) and the commercially available Rocket Propulsion Analysis (RPA) tool. Similarly, the PSO algorithm was validated by comparison with brute-force optimization, which calculates all possible solutions and subsequently determines which is the optimum. Particle Swarm Optimization was shown to be an effective optimizer capable of quick and reliable convergence for complex functions of multiple non-linear variables.

Proceedings of the Annual Symposium on Frequency Control (34th), Held 28-30 May 1980 Philadelphia, Pennsylvania

DTIC Science & Technology

1980-01-01

change between 2 x 10- 2 torr PRESSURE (to-r) and I atmosphere was measured (in a non -temper- ature controlled environment) to be less than FIGURE 8...microstrip, how- non -resonant and non -propagating. Losses due to ever, are less desirable. To control radiation finite substrate thickness werE determined .y...Temperature dependence of the stabilized oscillator. 254 Proc. 34th Ann. Freq. Control Symposium, USAERADCOM, Ft. Monmouth. NJ 07703. May 1980 NON -LINEAR

Efficient distance calculation using the spherically-extended polytope (s-tope) model

NASA Technical Reports Server (NTRS)

Hamlin, Gregory J.; Kelley, Robert B.; Tornero, Josep

1991-01-01

An object representation scheme which allows for Euclidean distance calculation is presented. The object model extends the polytope model by representing objects as the convex hull of a finite set of spheres. An algorithm for calculating distances between objects is developed which is linear in the total number of spheres specifying the two objects.

Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.

PubMed

Brihaye, Yves; Radu, Eugen; Tchrakian, D H

2011-02-18

We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

Efficient Controls for Finitely Convergent Sequential Algorithms

PubMed Central

Chen, Wei; Herman, Gabor T.

2010-01-01

Finding a feasible point that satisfies a set of constraints is a common task in scientific computing: examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for solving such problems; an example of such an algorithm is ART3, which is defined in such a way that its control is cyclic in the sense that during its execution it repeatedly cycles through the given constraints. Previously we found a variant of ART3 whose control is no longer cyclic, but which is still finitely convergent and in practice it usually converges faster than ART3 does. In this paper we propose a general methodology for automatic transformation of finitely convergent sequential algorithms in such a way that (i) finite convergence is retained and (ii) the speed of convergence is improved. The first of these two properties is proven by mathematical theorems, the second is illustrated by applying the algorithms to a practical problem. PMID:20953327

An extension of the finite cell method using boolean operations

NASA Astrophysics Data System (ADS)

Abedian, Alireza; Düster, Alexander

2017-05-01

In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Slave finite element for non-linear analysis of engine structures. Volume 2: Programmer's manual and user's manual

NASA Technical Reports Server (NTRS)

Witkop, D. L.; Dale, B. J.; Gellin, S.

1991-01-01

The programming aspects of SFENES are described in the User's Manual. The information presented is provided for the installation programmer. It is sufficient to fully describe the general program logic and required peripheral storage. All element generated data is stored externally to reduce required memory allocation. A separate section is devoted to the description of these files thereby permitting the optimization of Input/Output (I/O) time through efficient buffer descriptions. Individual subroutine descriptions are presented along with the complete Fortran source listings. A short description of the major control, computation, and I/O phases is included to aid in obtaining an overall familiarity with the program's components. Finally, a discussion of the suggested overlay structure which allows the program to execute with a reasonable amount of memory allocation is presented.

Relativistic cosmic-ray spectra in the fully nonlinear theory of shock acceleration

NASA Technical Reports Server (NTRS)

Ellison, D. C.; Eichler, D.

1985-01-01

The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite wave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72 percent, (2) 44 percent, and (3) 26 percent (this includes the energy loss at the upper energy cutoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.

Acceleration of incremental-pressure-correction incompressible flow computations using a coarse-grid projection method

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne

2016-11-01

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping functions transfer data between the two grids. Here we propose a version of CGP for incompressible flow computations using incremental pressure correction methods, called IFEi-CGP (implicit-time-integration, finite-element, incremental coarse grid projection). Incremental pressure correction schemes solve Poisson's equation for an intermediate variable and not the pressure itself. This fact contributes to IFEi-CGP's efficiency in two ways. First, IFEi-CGP preserves the velocity field accuracy even for a high level of pressure field grid coarsening and thus significant speedup is achieved. Second, because incremental schemes reduce the errors that arise from boundaries with artificial homogenous Neumann conditions, CGP generates undamped flows for simulations with velocity Dirichlet boundary conditions. Comparisons of the data accuracy and CPU times for the incremental-CGP versus non-incremental-CGP computations are presented.

Data Combination and Instrumental Variables in Linear Models

ERIC Educational Resources Information Center

Khawand, Christopher

2012-01-01

Instrumental variables (IV) methods allow for consistent estimation of causal effects, but suffer from poor finite-sample properties and data availability constraints. IV estimates also tend to have relatively large standard errors, often inhibiting the interpretability of differences between IV and non-IV point estimates. Lastly, instrumental…

Finite element code development for modeling detonation of HMX composites

NASA Astrophysics Data System (ADS)

Duran, Adam V.; Sundararaghavan, Veera

2017-01-01

In this work, we present a hydrodynamics code for modeling shock and detonation waves in HMX. A stable efficient solution strategy based on a Taylor-Galerkin finite element (FE) discretization was developed to solve the reactive Euler equations. In our code, well calibrated equations of state for the solid unreacted material and gaseous reaction products have been implemented, along with a chemical reaction scheme and a mixing rule to define the properties of partially reacted states. A linear Gruneisen equation of state was employed for the unreacted HMX calibrated from experiments. The JWL form was used to model the EOS of gaseous reaction products. It is assumed that the unreacted explosive and reaction products are in both pressure and temperature equilibrium. The overall specific volume and internal energy was computed using the rule of mixtures. Arrhenius kinetics scheme was integrated to model the chemical reactions. A locally controlled dissipation was introduced that induces a non-oscillatory stabilized scheme for the shock front. The FE model was validated using analytical solutions for SOD shock and ZND strong detonation models. Benchmark problems are presented for geometries in which a single HMX crystal is subjected to a shock condition.

Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite-element model and experimental data.

PubMed

Lundström, T; Jonas, T; Volkwein, A

2008-01-01

Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.

Localization in finite vibroimpact chains: Discrete breathers and multibreathers.

PubMed

Grinberg, Itay; Gendelman, Oleg V

2016-09-01

We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

NASA Astrophysics Data System (ADS)

Feng, Qinggao; Wen, Zhang

2016-08-01

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index ( n), the length of well screen ( w), the apparent radial hydraulic conductivity of the formation zone ( K r2), and the specific storage of the formation zone ( S s2) at early times, and it is very sensitive to the parameters n, w and K r2 at late times, especially to n, while it is not sensitive to the skin thickness ( r s).

Optimal design of FIR triplet halfband filter bank and application in image coding.

PubMed

Kha, H H; Tuan, H D; Nguyen, T Q

2011-02-01

This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semi-infinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented.

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

A combined experimental and finite element study to predict the failure mechanisms in SiC coated carbon/carbon composites at room and elevated temperatures under flexural loading

NASA Technical Reports Server (NTRS)

Mahfuz, Hassan; Das, Partha S.; Xue, Dongwei; Krishnagopalan, Jaya; Jeelani, Shaik

1993-01-01

Response of quasi-isotropic laminates of SiC coated Carbon/Carbon (C/C) composites have been investigated under flexural loading at various temperatures. Variation of load-deflection behavior with temperatures are studied. Increase in flexural strength and stiffness are observed with the rise in temperature. Extensive analyses through Optical Microscope (OM) and Non-Destructive Evaluation (NDE) have been performed to understand the failure mechanisms. Damage zone is found only within the neighborhood of the loading plane. Isoparametric layered shell elements developed on the basis of the first order shear deformation theory have been used to model the thin laminates of C/C under flexural loading. Large deformation behavior has been considered in the finite element analysis to account for the non-linearities encountered during the actual test. Data generated using finite element analysis are presented to corroborate the experimental findings, and a comparison in respect of displacement and stress-strain behavior are given to check the accuracy of the finite element analysis. Reasonable correlation between the experimental and finite element results have been established.

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents

PubMed Central

Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro

2015-01-01

Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena. PMID:26184329

Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

2014-01-01

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

Angular motion equations for a satellite with hinged flexible solar panel

NASA Astrophysics Data System (ADS)

Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

2016-11-01

Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

Deep Neural Network Emulation of a High-Order, WENO-Limited, Space-Time Reconstruction

NASA Astrophysics Data System (ADS)

Norman, M. R.; Hall, D. M.

2017-12-01

Deep Neural Networks (DNNs) have been used to emulate a number of processes in atmospheric models, including radiation and even so-called super-parameterization of moist convection. In each scenario, the DNN provides a good representation of the process even for inputs that have not been encountered before. More notably, they provide an emulation at a fraction of the cost of the original routine, giving speed-ups of 30× and even up to 200× compared to the runtime costs of the original routines. However, to our knowledge there has not been an investigation into using DNNs to emulate the dynamics. The most likely reason for this is that dynamics operators are typically both linear and low cost, meaning they cannot be sped up by a non-linear DNN emulation. However, there exist high-cost non-linear space-time dynamics operators that significantly reduce the number of parallel data transfers necessary to complete an atmospheric simulation. The WENO-limited Finite-Volume method with ADER-DT time integration is a prime example of this - needing only two parallel communications per large, fully limited time step. However, it comes at a high cost in terms of computation, which is why many would hesitate to use it. This talk investigates DNN emulation of the WENO-limited space-time finite-volume reconstruction procedure - the most expensive portion of this method, which densely clusters a large amount of non-linear computation. Different training techniques and network architectures are tested, and the accuracy and speed-up of each is given.

Finite difference modelling of the temperature rise in non-linear medical ultrasound fields.

PubMed

Divall, S A; Humphrey, V F

2000-03-01

Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.

Analysis of Fluid Gauge Sensor for Zero or Microgravity Conditions using Finite Element Method

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.; Doiron, Terence a.

2007-01-01

In this paper the Finite Element Method (FEM) is presented for mass/volume gauging of a fluid in a tank subjected to zero or microgravity conditions. In this approach first mutual capacitances between electrodes embedded inside the tank are measured. Assuming the medium properties the mutual capacitances are also estimated using FEM approach. Using proper non-linear optimization the assumed properties are updated by minimizing the mean square error between estimated and measured capacitances values. Numerical results are presented to validate the present approach.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Improving finite element results in modeling heart valve mechanics.

PubMed

Earl, Emily; Mohammadi, Hadi

2018-06-01

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

NASA Astrophysics Data System (ADS)

EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

2000-01-01

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Numerical Analysis of Stress Concentration in Isotropic and Laminated Plates with Inclined Elliptical Holes

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Belarbi, Mohamed Ouejdi; Guettala, Abdelhamid

2018-03-01

The design of high-performance composite structures frequently includes discontinuities to reduce the weight and fastener holes for joining. Understanding the behavior of perforated laminates is necessary for structural design. In the current work, stress concentrations taking place in laminated and isotropic plates subjected to tensile load are investigated. The stress concentrations are obtained using a recent quadrilateral finite element of four nodes with 32 DOFs. The present finite element (PE) is a combination of two finite elements. The first finite element is a linear isoparametric membrane element and the second is a high precision Hermitian element. One of the essential objectives of the current investigation is to confirm the capability and efficiency of the PE for stress determination in perforated laminates. Different geometric parameters, such as the cutout form, sizes and cutout orientations, which have a considerable effect on the stress values, are studied. Using the present finite element formulation, the obtained results are found to be in good agreement with the analytical findings, which validates the capability and the efficiency of the proposed formulation. Finally, to understand the material parameters effect such as the orientation of fibers and degree of orthotropy ratio on the stress values, many figures are presented using different ellipse major to minor axis ratio. The stress concentration values are considerably affected by increasing the orientation angle of the fibers and degree of orthotropy.

Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

PubMed

Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

2017-12-27

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

Quantum criticality of the two-channel pseudogap Anderson model: universal scaling in linear and non-linear conductance.

PubMed

Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou

2016-05-05

The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, ρc(ω) proportional |ω − μF|(r) (0 < r < 1) near the Fermi energy μF. At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r = rc < 1. Surprisingly, in the 2CK phase, different power-law scalings from the well-known [Formula: see text] or [Formula: see text] form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.

Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Chacon, Luis

2015-09-01

We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, which allows efficient use of large timesteps, O(√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.

Efficient robust doubly adaptive regularized regression with applications.

PubMed

Karunamuni, Rohana J; Kong, Linglong; Tu, Wei

2018-01-01

We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robustness. Furthermore, the proposed procedure satisfies the oracle properties. The new procedure is designed to achieve sparse and robust solutions by imposing adaptive weights on both the decision loss and the penalty function. The proposed method of estimation and variable selection attains full efficiency when the model is correct and, at the same time, achieves maximum robustness when outliers are present. We examine the robustness properties using the finite-sample breakdown point and an influence function. We show that the proposed estimator attains the maximum breakdown point. Furthermore, there is no loss in efficiency when there are no outliers or the error distribution is normal. For practical implementation of the proposed method, we present a computational algorithm. We examine the finite-sample and robustness properties using Monte Carlo studies. Two datasets are also analyzed.

Rigorous theory of graded thermoelectric converters including finite heat transfer coefficients

NASA Astrophysics Data System (ADS)

Gerstenmaier, York Christian; Wachutka, Gerhard

2017-11-01

Maximization of thermoelectric (TE) converter performance with an inhomogeneous material and electric current distribution has been investigated in previous literature neglecting thermal contact resistances to the heat reservoirs. The heat transfer coefficients (HTCs), defined as inverse thermal contact resistances per unit area, are thus infinite, whereas in reality, always parasitic thermal resistances, i.e., finite HTCs, are present. Maximization of the generated electric power and of cooling power in the refrigerator mode with respect to Seebeck coefficients and heat conductivity for a given profile of the material's TE figure of merit Z are mathematically ill-posed problems in the presence of infinite HTCs. As will be shown in this work, a fully self consistent solution is possible for finite HTCs, and in many respects, the results are fundamentally different. A previous theory for 3D devices will be extended to include finite HTCs and is applied to 1D devices. For the heat conductivity profile, an infinite number of solutions exist leading to the same device performance. Cooling power maximization for finite HTCs in 1D will lead to a strongly enhanced corresponding efficiency (coefficient of performance), whereas results with infinite HTCs lead to a non-monotonous temperature profile and coefficient of performance tending to zero for the prescribed heat conductivities. For maximized generated electric power, the corresponding generator efficiency is nearly a constant independent from the finite HTC values. The maximized efficiencies in the generator and cooling mode are equal to the efficiencies for the infinite HTC, provided that the corresponding powers approach zero. These and more findings are condensed in 4 theorems in the conclusions.

The Mixed Finite Element Multigrid Method for Stokes Equations

PubMed Central

Muzhinji, K.; Shateyi, S.; Motsa, S. S.

2015-01-01

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

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

Huang, Chen, E-mail: chuang3@fsu.edu

A key element in the density functional embedding theory (DFET) is the embedding potential. We discuss two major issues related to the embedding potential: (1) its non-uniqueness and (2) the numerical difficulty for solving for it, especially for the spin-polarized systems. To resolve the first issue, we extend DFET to finite temperature: all quantities, such as the subsystem densities and the total system’s density, are calculated at a finite temperature. This is a physical extension since materials work at finite temperatures. We show that the embedding potential is strictly unique at T > 0. To resolve the second issue, wemore » introduce an efficient iterative embedding potential solver. We discuss how to relax the magnetic moments in subsystems and how to equilibrate the chemical potentials across subsystems. The solver is robust and efficient for several non-trivial examples, in all of which good quality spin-polarized embedding potentials were obtained. We also demonstrate the solver on an extended periodic system: iron body-centered cubic (110) surface, which is related to the modeling of the heterogeneous catalysis involving iron, such as the Fischer-Tropsch and the Haber processes. This work would make it efficient and accurate to perform embedding simulations of some challenging material problems, such as the heterogeneous catalysis and the defects of complicated spin configurations in electronic materials.« less

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

NASA Technical Reports Server (NTRS)

Douglas, C. C.; Douglas, J., Jr.; Fyfe, D. E.

1996-01-01

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

The effect of acetabular cup size on the short-term stability of revision hip arthroplasty: a finite element investigation.

PubMed

Phillips, A T M; Pankaj; Usmani, A S; Howie, C R

2004-01-01

The study uses idealized two-dimensional finite element models to examine the behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff-Ling impaction grafting technique. The behaviour of bone graft was considered in detail, with non-linear elasticity and non-associated plasticity being adopted. Load was applied to the acetabular construct through a femoral head using smooth sliding surfaces. In particular, four models were subjected to two idealized cyclic load cases to investigate the effect of acetabular cup size on the short-term stability of the acetabular construct. The study suggests that benefits may be gained by using the largest practical size of acetabular cup.

The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1976-01-01

The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.

Linear and nonlinear interpretation of the direct strike lightning response of the NASA F106B thunderstorm research aircraft

NASA Technical Reports Server (NTRS)

Rudolph, T. H.; Perala, R. A.

1983-01-01

The objective of the work reported here is to develop a methodology by which electromagnetic measurements of inflight lightning strike data can be understood and extended to other aircraft. A linear and time invariant approach based on a combination of Fourier transform and three dimensional finite difference techniques is demonstrated. This approach can obtain the lightning channel current in the absence of the aircraft for given channel characteristic impedance and resistive loading. The model is applied to several measurements from the NASA F106B lightning research program. A non-linear three dimensional finite difference code has also been developed to study the response of the F106B to a lightning leader attachment. This model includes three species air chemistry and fluid continuity equations and can incorporate an experimentally based streamer formulation. Calculated responses are presented for various attachment locations and leader parameters. The results are compared qualitatively with measured inflight data.

Advanced analysis technique for the evaluation of linear alternators and linear motors

NASA Technical Reports Server (NTRS)

Holliday, Jeffrey C.

1995-01-01

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

High speed finite element simulations on the graphics card

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

Huthwaite, P.; Lowe, M. J. S.

A software package is developed to perform explicit time domain finite element simulations of ultrasonic propagation on the graphical processing unit, using Nvidia’s CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The technique is compared to a commercial CPU equivalent,more » demonstrating an overall speedup of at least 100 for a non-destructive testing weld model.« less

Networked dynamical systems with linear coupling: synchronisation patterns, coherence and other behaviours.

PubMed

Judd, Kevin

2013-12-01

Many physical and biochemical systems are well modelled as a network of identical non-linear dynamical elements with linear coupling between them. An important question is how network structure affects chaotic dynamics, for example, by patterns of synchronisation and coherence. It is shown that small networks can be characterised precisely into patterns of exact synchronisation and large networks characterised by partial synchronisation at the local and global scale. Exact synchronisation modes are explained using tools of symmetry groups and invariance, and partial synchronisation is explained by finite-time shadowing of exact synchronisation modes.

Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays

NASA Technical Reports Server (NTRS)

Wrigley, Chris J.; Hancock, Bruce R.; Newton, Kenneth W.; Cunningham, Thomas J.

2013-01-01

Single-slope analog-to-digital converters (ADCs) are particularly useful for onchip digitization in focal plane arrays (FPAs) because of their inherent monotonicity, relative simplicity, and efficiency for column-parallel applications, but they are comparatively slow. Squareroot encoding can allow the number of code values to be reduced without loss of signal-to-noise ratio (SNR) by keeping the quantization noise just below the signal shot noise. This encoding can be implemented directly by using a quadratic ramp. The reduction in the number of code values can substantially increase the quantization speed. However, in an FPA, the fixed pattern noise (FPN) limits the use of small quantization steps at low signal levels. If the zero-point is adjusted so that the lowest column is onscale, the other columns, including those at the center of the distribution, will be pushed up the ramp where the quantization noise is higher. Additionally, the finite frequency response of the ramp buffer amplifier and the comparator distort the shape of the ramp, so that the effective ramp value at the time the comparator trips differs from the intended value, resulting in errors. Allowing increased settling time decreases the quantization speed, while increasing the bandwidth increases the noise. The FPN problem is solved by breaking the ramp into two portions, with some fraction of the available code values allocated to a linear ramp and the remainder to a quadratic ramp. To avoid large transients, both the value and the slope of the linear and quadratic portions should be equal where they join. The span of the linear portion must cover the minimum offset, but not necessarily the maximum, since the fraction of the pixels above the upper limit will still be correctly quantized, albeit with increased quantization noise. The required linear span, maximum signal and ratio of quantization noise to shot noise at high signal, along with the continuity requirement, determines the number of code values that must be allocated to each portion. The distortion problem is solved by using a lookup table to convert captured code values back to signal levels. The values in this table will be similar to the intended ramp value, but with a correction for the finite bandwidth effects. Continuous-time comparators are used, and their bandwidth is set below the step rate, which smoothes the ramp and reduces the noise. No settling time is needed, as would be the case for clocked comparators, but the low bandwidth enhances the distortion of the non-linear portion. This is corrected by use of a return lookup table, which differs from the one used to generate the ramp. The return lookup table is obtained by calibrating against a stepped precision DC reference. This results in a residual non-linearity well below the quantization noise. This method can also compensate for differential non-linearity (DNL) in the DAC used to generate the ramp. The use of a ramp with a combination of linear and quadratic portions for a single-slope ADC is novel. The number of steps is minimized by keeping the step size just below the photon shot noise. This in turn maximizes the speed of the conversion. High resolution is maintained by keeping small quantization steps at low signals, and noise is minimized by allowing the lowest analog bandwidth, all without increasing the quantization noise. A calibrated return lookup table allows the system to maintain excellent linearity.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

High-frequency ground motion amplification during the 2011 Tohoku earthquake explained by soil dilatancy

NASA Astrophysics Data System (ADS)

Roten, D.; Fäh, D.; Bonilla, L. F.

2013-05-01

Ground motions of the 2011 Tohoku earthquake recorded at Onahama port (Iwaki, Fukushima prefecture) rank among the highest accelerations ever observed, with the peak amplitude of the 3-D acceleration vector approaching 2g. The response of the site was distinctively non-linear, as indicated by the presence of horizontal acceleration spikes which have been linked to cyclic mobility during similar observations. Compared to records of weak ground motions, the response of the site during the Mw 9.1 earthquake was characterized by increased amplification at frequencies above 10 Hz and in peak ground acceleration. This behaviour contrasts with the more common non-linear response encountered at non-liquefiable sites, which results in deamplification at higher frequencies. We simulate propagation of SH waves through the dense sand deposit using a non-linear finite difference code that is capable of modelling the development of excess pore water pressure. Dynamic soil parameters are calibrated using a direct search method that minimizes the difference between observed and simulated acceleration envelopes and response spectra. The finite difference simulations yield surface acceleration time-series that are consistent with the observations in shape and amplitude, pointing towards soil dilatancy as a likely explanation for the high-frequency pulses recorded at Onahama port. The simulations also suggest that the occurrence of high-frequency spikes coincided with a rapid increase in pore water pressure in the upper part of the sand deposit between 145 and 170 s. This sudden increase is possibly linked to a burst of high-frequency energy from a large slip patch below the Iwaki region.

Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

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

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

The effect of nonlinear propagation on heating of tissue: A numerical model of diagnostic ultrasound beams

NASA Astrophysics Data System (ADS)

Cahill, Mark D.; Humphrey, Victor F.; Doody, Claire

2000-07-01

Thermal safety indices for diagnostic ultrasound beams are calculated under the assumption that the sound propagates under linear conditions. A non-axisymmetric finite difference model is used to solve the KZK equation, and so to model the beam of a diagnostic scanner in pulsed Doppler mode. Beams from both a uniform focused rectangular source and a linear array are considered. Calculations are performed in water, and in attenuating media with tissue-like characteristics. Attenuating media are found to exhibit significant nonlinear effects for finite-amplitude beams. The resulting loss of intensity by the beam is then used as the source term in a model of tissue heating to estimate the maximum temperature rises. These are compared with the thermal indices, derived from the properties of the water-propagated beams.

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

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

A. T. Till; M. Hanuš; J. Lou

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basismore » function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.« less

Consequences of converting graded to action potentials upon neural information coding and energy efficiency.

PubMed

Sengupta, Biswa; Laughlin, Simon Barry; Niven, Jeremy Edward

2014-01-01

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na(+) and K(+) channels, with generator potential and graded potential models lacking voltage-gated Na(+) channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na(+) channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a 'footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

PubMed Central

Sengupta, Biswa; Laughlin, Simon Barry; Niven, Jeremy Edward

2014-01-01

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation. PMID:24465197

Turbine blade forced response prediction using FREPS

NASA Technical Reports Server (NTRS)

Murthy, Durbha, V.; Morel, Michael R.

1993-01-01

This paper describes a software system called FREPS (Forced REsponse Prediction System) that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced response dynamic stresses in axial flow turbomachinery blades due to aerodynamic and mechanical excitations. A flutter analysis capability is also incorporated into the system. The FREPS system performs aeroelastic analysis by modeling the motion of the blade in terms of its normal modes. The structural dynamic analysis is performed by a finite element code such as MSC/NASTRAN. The steady aerodynamic analysis is based on nonlinear potential theory and the unsteady aerodynamic analyses is based on the linearization of the non-uniform potential flow mean. The program description and presentation of the capabilities are reported herein. The effectiveness of the FREPS package is demonstrated on the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine. Both flutter and forced response analyses are performed and typical results are illustrated.

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

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

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

Improved sonic-box computer program for calculating transonic aerodynamic loads on oscillating wings with thickness

NASA Technical Reports Server (NTRS)

Ruo, S. Y.

1978-01-01

A computer program was developed to account approximately for the effects of finite wing thickness in transonic potential flow over an oscillation wing of finite span. The program is based on the original sonic box computer program for planar wing which was extended to account for the effect of wing thickness. Computational efficiency and accuracy were improved and swept trailing edges were accounted for. Account for the nonuniform flow caused by finite thickness was made by application of the local linearization concept with appropriate coordinate transformation. A brief description of each computer routine and the applications of cubic spline and spline surface data fitting techniques used in the program are given, and the method of input was shown in detail. Sample calculations as well as a complete listing of the computer program listing are presented.

Resource allocation in shared spectrum access communications for operators with diverse service requirements

NASA Astrophysics Data System (ADS)

Kibria, Mirza Golam; Villardi, Gabriel Porto; Ishizu, Kentaro; Kojima, Fumihide; Yano, Hiroyuki

2016-12-01

In this paper, we study inter-operator spectrum sharing and intra-operator resource allocation in shared spectrum access communication systems and propose efficient dynamic solutions to address both inter-operator and intra-operator resource allocation optimization problems. For inter-operator spectrum sharing, we present two competent approaches, namely the subcarrier gain-based sharing and fragmentation-based sharing, which carry out fair and flexible allocation of the available shareable spectrum among the operators subject to certain well-defined sharing rules, traffic demands, and channel propagation characteristics. The subcarrier gain-based spectrum sharing scheme has been found to be more efficient in terms of achieved throughput. However, the fragmentation-based sharing is more attractive in terms of computational complexity. For intra-operator resource allocation, we consider resource allocation problem with users' dissimilar service requirements, where the operator supports users with delay constraint and non-delay constraint service requirements, simultaneously. This optimization problem is a mixed-integer non-linear programming problem and non-convex, which is computationally very expensive, and the complexity grows exponentially with the number of integer variables. We propose less-complex and efficient suboptimal solution based on formulating exact linearization, linear approximation, and convexification techniques for the non-linear and/or non-convex objective functions and constraints. Extensive simulation performance analysis has been carried out that validates the efficiency of the proposed solution.

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

An experimental study of miscible viscous fingering of annular ring

NASA Astrophysics Data System (ADS)

Nagatsu, Yuichiro; Othman, Hamirul Bin; Mishra, Manoranjan

2017-11-01

Understanding the viscous fingering (VF) dynamics of finite width sample is important in the fields especially such as liquid chromatography and groundwater contamination and mixing in microfluidics. In this paper, we experimentally investigate such hydrodynamical morphology of VF using a Hele-Shaw flow system in which a miscible annular ring of fluid is displaced radially. Experiments are performed to investigate the effects of the sample volume, the effects of dispersion and log mobility ratio R on the dynamics of VF pattern and onset of such instability. Depending whether the finite width ring is more or less viscous than the carrier fluid, the log mobility ratio R becomes positive or negative respectively. The experiments are successfully conducted to obtain the VF patterns for R>0 and R<0, of the finite annular ring at the inner and outer radial interfaces, respectively. It is found that in the radial displacement, the inward finger moves slower than the outward finger. The experimental results are found to be qualitatively in good agreement with the corresponding linear stability analysis and non-linear simulations results available in the literature.

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

NASA Technical Reports Server (NTRS)

Zingg, David W.

1996-01-01

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

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

Zhang, H.; Betti, R.; Gopalaswamy, V.

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble densitymore » increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.« less

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

DOE PAGES

Zhang, H.; Betti, R.; Gopalaswamy, V.; ...

2018-01-16

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble densitymore » increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.« less

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Non-linear interaction of a detonation/vorticity wave

NASA Technical Reports Server (NTRS)

Lasseigne, D. G.; Jackson, T. L.; Hussaini, M. Y.

1991-01-01

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multi-domain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient encounter with a disturbance, the effects of exothermicity are more pronounced than predicted by linear theory. Finally, it is found that linear theory correctly determines the critical angle.

Finite Element Analysis of the Effect of Epidural Adhesions.

PubMed

Lee, Nam; Ji, Gyu Yeul; Yi, Seong; Yoon, Do Heum; Shin, Dong Ah; Kim, Keung Nyun; Ha, Yoon; Oh, Chang Hyun

2016-07-01

It is well documented that epidural adhesion is associated with spinal pain. However, the underlying mechanism of spinal pain generation by epidural adhesion has not yet been elucidated. To elucidate the underlying mechanism of spinal pain generation by epidural adhesion using a two-dimensional (2D) non-linear finite element (FE) analysis. A finite element analysis. A two-dimensional nonlinear FE model of the herniated lumbar disc on L4/5 with epidural adhesion. A two-dimensional nonlinear FE model of the lumbar spine was developed, consisting of intervertebral discs, dura, spinal nerve, and lamina. The annulus fibrosus and nucleus pulpous were modeled as hyperelastic using the Mooney-Rivlin equation. The FE mesh was generated and analyzed using Abaqus (ABAQUS 6.13.; Hibbitt, Karlsson & Sorenson, Inc., Providence, RI, USA). Epidural adhesion was simulated as rough contact, in which no slip occurred once two surfaces were in contact, between the dura mater and posterior annulus fibrosus. The FE model of adhesion showed significant stress concentration in the spinal nerves, especially on the dorsal root ganglion (DRG). The stress concentration was caused by the lack of adaptive displacement between the dura mater and posterior annulus fibrosus. The peak von Mises stress was higher in the epidural adhesion model (Adhesion, 0.67 vs. Control, 0.46). In the control model, adaptive displacement was observed with decreased stress in the spinal nerve and DRG (with adhesion, 2.59 vs. without adhesion, 3.58, P < 0.00). This study used a 2D non-linear FE model, which simplifies the 3D nature of the human intervertebral disc. In addition, this 2D non-linear FE model has not yet been validated. The current study clearly demonstrated that epidural adhesion causes significantly increased stress in the spinal nerves, especially at the DRG. We believe that the increased stress on the spinal nerve might elicit more pain under similar magnitudes of lumbar disc protrusion.

On the minimum quantum requirement of photosynthesis.

PubMed

Zeinalov, Yuzeir

2009-01-01

An analysis of the shape of photosynthetic light curves is presented and the existence of the initial non-linear part is shown as a consequence of the operation of the non-cooperative (Kok's) mechanism of oxygen evolution or the effect of dark respiration. The effect of nonlinearity on the quantum efficiency (yield) and quantum requirement is reconsidered. The essential conclusions are: 1) The non-linearity of the light curves cannot be compensated using suspensions of algae or chloroplasts with high (>1.0) optical density or absorbance. 2) The values of the maxima of the quantum efficiency curves or the values of the minima of the quantum requirement curves cannot be used for estimation of the exact value of the maximum quantum efficiency and the minimum quantum requirement. The estimation of the maximum quantum efficiency or the minimum quantum requirement should be performed only after extrapolation of the linear part at higher light intensities of the quantum requirement curves to "0" light intensity.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-01-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Astrophysics Data System (ADS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-08-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1987-01-01

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

The p-version of the finite element method in incremental elasto-plastic analysis

NASA Technical Reports Server (NTRS)

Holzer, Stefan M.; Yosibash, Zohar

1993-01-01

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

Boundary Closures for Fourth-order Energy Stable Weighted Essentially Non-Oscillatory Finite Difference Schemes

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.

2009-01-01

A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.

Non-Axisymmetric Inflatable Pressure Structure (NAIPS) Full-Scale Pressure Test

NASA Technical Reports Server (NTRS)

Jones, Thomas C.; Doggett, William R.; Warren, Jerry E.; Watson, Judith J.; Shariff, Khadijah; Makino, Alberto; Yount, Bryan C.

2017-01-01

Inflatable space structures have the potential to significantly reduce the required launch volume for large pressure vessels required for exploration applications including habitats, airlocks and tankage. In addition, mass savings can be achieved via the use of high specific strength softgoods materials, and the reduced design penalty from launching the structure in a densely packaged state. Large inclusions however, such as hatches, induce a high mass penalty at the interfaces with the softgoods and in the added rigid structure while reducing the packaging efficiency. A novel, Non-Axisymmetric Inflatable Pressure Structure (NAIPS) was designed and recently tested at NASA Langley Research Center to demonstrate an elongated inflatable architecture that could provide areas of low stress along a principal axis in the surface. These low stress zones will allow the integration of a flexible linear seal that substantially reduces the added mass and volume of a heritage rigid hatch structure. This paper describes the test of the first full-scale engineering demonstration unit (EDU) of the NAIPS geometry and a comparison of the results to finite element analysis.

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

NASA Astrophysics Data System (ADS)

von Kleist, Max; Schütte, Christof; Zhang, Wei

2018-02-01

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

Engineering Overview of a Multidisciplinary HSCT Design Framework Using Medium-Fidelity Analysis Codes

NASA Technical Reports Server (NTRS)

Weston, R. P.; Green, L. L.; Salas, A. O.; Samareh, J. A.; Townsend, J. C.; Walsh, J. L.

1999-01-01

An objective of the HPCC Program at NASA Langley has been to promote the use of advanced computing techniques to more rapidly solve the problem of multidisciplinary optimization of a supersonic transport configuration. As a result, a software system has been designed and is being implemented to integrate a set of existing discipline analysis codes, some of them CPU-intensive, into a distributed computational framework for the design of a High Speed Civil Transport (HSCT) configuration. The proposed paper will describe the engineering aspects of integrating these analysis codes and additional interface codes into an automated design system. The objective of the design problem is to optimize the aircraft weight for given mission conditions, range, and payload requirements, subject to aerodynamic, structural, and performance constraints. The design variables include both thicknesses of structural elements and geometric parameters that define the external aircraft shape. An optimization model has been adopted that uses the multidisciplinary analysis results and the derivatives of the solution with respect to the design variables to formulate a linearized model that provides input to the CONMIN optimization code, which outputs new values for the design variables. The analysis process begins by deriving the updated geometries and grids from the baseline geometries and grids using the new values for the design variables. This free-form deformation approach provides internal FEM (finite element method) grids that are consistent with aerodynamic surface grids. The next step involves using the derived FEM and section properties in a weights process to calculate detailed weights and the center of gravity location for specified flight conditions. The weights process computes the as-built weight, weight distribution, and weight sensitivities for given aircraft configurations at various mass cases. Currently, two mass cases are considered: cruise and gross take-off weight (GTOW). Weights information is obtained from correlations of data from three sources: 1) as-built initial structural and non-structural weights from an existing database, 2) theoretical FEM structural weights and sensitivities from Genesis, and 3) empirical as-built weight increments, non-structural weights, and weight sensitivities from FLOPS. For the aeroelastic analysis, a variable-fidelity aerodynamic analysis has been adopted. This approach uses infrequent CPU-intensive non-linear CFD to calculate a non-linear correction relative to a linear aero calculation for the same aerodynamic surface at an angle of attack that results in the same configuration lift. For efficiency, this nonlinear correction is applied after each subsequent linear aero solution during the iterations between the aerodynamic and structural analyses. Convergence is achieved when the vehicle shape being used for the aerodynamic calculations is consistent with the structural deformations caused by the aerodynamic loads. To make the structural analyses more efficient, a linearized structural deformation model has been adopted, in which a single stiffness matrix can be used to solve for the deformations under all the load conditions. Using the converged aerodynamic loads, a final set of structural analyses are performed to determine the stress distributions and the buckling conditions for constraint calculation. Performance constraints are obtained by running FLOPS using drag polars that are computed using results from non-linear corrections to the linear aero code plus several codes to provide drag increments due to skin friction, wave drag, and other miscellaneous drag contributions. The status of the integration effort will be presented in the proposed paper, and results will be provided that illustrate the degree of accuracy in the linearizations that have been employed.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

Finite element model for brittle fracture and fragmentation

DOE PAGES

Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; ...

2016-06-01

A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.

Finite element model for brittle fracture and fragmentation

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

Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin

A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

NASA Technical Reports Server (NTRS)

Lebiedzik, Catherine

1995-01-01

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

Exact finite volume expectation values of \\overline{Ψ}Ψ in the massive Thirring model from light-cone lattice correlators

NASA Astrophysics Data System (ADS)

Hegedűs, Árpád

2018-03-01

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

NASA Astrophysics Data System (ADS)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.

Finite element modeling of temperature load effects on the vibration of local modes in multi-cable structures

NASA Astrophysics Data System (ADS)

Treyssède, Fabien

2018-01-01

Understanding thermal effects on the vibration of local (cable-dominant) modes in multi-cable structures is a complicated task. The main difficulty lies in the modification by temperature change of cable tensions, which are then undetermined. This paper applies a finite element procedure to investigate the effects of thermal loads on the linear dynamics of prestressed self-weighted multi-cable structures. Provided that boundary conditions are carefully handled, the discretization of cables with nonlinear curved beam elements can properly represent the thermoelastic behavior of cables as well as their linearized dynamics. A three-step procedure that aims to replace applied pretension forces with displacement continuity conditions is used. Despite an increase in the computational cost related to beam rotational degrees of freedom, such an approach has several advantages. Nonlinear beam finite elements are usually available in commercial codes. The overall method follows a thermoelastic geometrically non-linear analysis and hereby includes the main sources of non-linearities in multi-cable structures. The effects of cable bending stiffness, which can be significant, are also naturally accounted for. The accuracy of the numerical approach is assessed thanks to an analytical model for the vibration of a single inclined cable under temperature change. Then, the effects of thermal loads are investigated for two cable bridges, highlighting how natural frequencies can be affected by temperature. Although counterintuitive, a reverse relative change of natural frequency may occur for certain local modes. This phenomenon can be explained by two distinct mechanisms, one related to the physics intrinsic to cables and the other related to the thermal deflection of the superstructure. Numerical results show that cables cannot be isolated from the rest of the structure and the importance of modeling the whole structure for a quantitative analysis of temperature effects on the dynamics of cable bridges.

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

NASA Astrophysics Data System (ADS)

Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

2017-04-01

In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

NASA Astrophysics Data System (ADS)

Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.

2013-12-01

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Sonnad, Vijay

1991-01-01

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

Linear regression analysis of survival data with missing censoring indicators.

PubMed

Wang, Qihua; Dinse, Gregg E

2011-04-01

Linear regression analysis has been studied extensively in a random censorship setting, but typically all of the censoring indicators are assumed to be observed. In this paper, we develop synthetic data methods for estimating regression parameters in a linear model when some censoring indicators are missing. We define estimators based on regression calibration, imputation, and inverse probability weighting techniques, and we prove all three estimators are asymptotically normal. The finite-sample performance of each estimator is evaluated via simulation. We illustrate our methods by assessing the effects of sex and age on the time to non-ambulatory progression for patients in a brain cancer clinical trial.

Non-linear vacuum polarization in strong fields

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

Gyulassy, M.

1981-07-01

The Wichmann-Kroll formalism for calculating the vacuum polarization density to first order in ..cap alpha.. but to all orders in Z..cap alpha.. is derived. The most essential quantity is shown to be the electrons Green's function in these calculations. The method of constructing that Green's function in the field of finite radius nuclei is then presented.

A three-dimensional finite element evaluation of magnetic attachment attractive force and the influence of the magnetic circuit.

PubMed

Kumano, Hirokazu; Nakamura, Yoshinori; Kanbara, Ryo; Takada, Yukyo; Ochiai, Kent T; Tanaka, Yoshinobu

2014-01-01

The finite element method has been considered to be excellent evaluative technique to study magnetic circuit optimization. The present study analyzed and quantitatively evaluated the different effects of magnetic circuit on attractive force and magnetic flux density using a three-dimensional finite element method for comparative evaluation. The diameter of a non-magnetic material in the shield disk of a magnetic assembly was variably increased by 0.1 mm to a maximum 2.0 mm in this study design. The analysis results demonstrate that attractive force increases until the diameter of the non-magnetic spacing material reaches a diameter of 0.5 mm where it peaks and then decreases as the overall diameter increases over 0.5 mm. The present analysis suggested that the attractive force for a magnetic attachment is optimized with an appropriate magnetic assembly shield disk diameter using a non-magnetic material to effectively change the magnetic circuit efficiency and resulting retention.

A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multi-Axial Loading

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; OBrien, T. Kevin

1999-01-01

Three simple procedures were developed to determine strain energy release rates, G, in composite skin/stringer specimens for various combinations of unaxial and biaxial (in-plane/out-of-plane) loading conditions. These procedures may be used for parametric design studies in such a way that only a few finite element computations will be necessary for a study of many load combinations. The results were compared with mixed mode strain energy release rates calculated directly from nonlinear two-dimensional plane-strain finite element analyses using the virtual crack closure technique. The first procedure involved solving three unknown parameters needed to determine the energy release rates. Good agreement was obtained when the external loads were used in the expression derived. This superposition technique was only applicable if the structure exhibits a linear load/deflection behavior. Consequently, a second technique was derived which was applicable in the case of nonlinear load/deformation behavior. The technique involved calculating six unknown parameters from a set of six simultaneous linear equations with data from six nonlinear analyses to determine the energy release rates. This procedure was not time efficient, and hence, less appealing. A third procedure was developed to calculate mixed mode energy release rates as a function of delamination lengths. This procedure required only one nonlinear finite element analysis of the specimen with a single delamination length to obtain a reference solution for the energy release rates and the scale factors. The delamination was extended in three separate linear models of the local area in the vicinity of the delamination subjected to unit loads to obtain the distribution of G with delamination lengths. This set of sub-problems was Although additional modeling effort is required to create the sub- models, this local technique is efficient for parametric studies.

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Minimum stiffness criteria for ring frame stiffeners of space launch vehicles

NASA Astrophysics Data System (ADS)

Friedrich, Linus; Schröder, Kai-Uwe

2016-12-01

Frame stringer-stiffened shell structures show high load carrying capacity in conjunction with low structural mass and are for this reason frequently used as primary structures of aerospace applications. Due to the great number of design variables, deriving suitable stiffening configurations is a demanding task and needs to be realized using efficient analysis methods. The structural design of ring frame stringer-stiffened shells can be subdivided into two steps. One, the design of a shell section between two ring frames. Two, the structural design of the ring frames such that a general instability mode is avoided. For sizing stringer-stiffened shell sections, several methods were recently developed, but existing ring frame sizing methods are mainly based on empirical relations or on smeared models. These methods do not mandatorily lead to reliable designs and in some cases the lightweight design potential of stiffened shell structures can thus not be exploited. In this paper, the explicit physical behaviour of ring frame stiffeners of space launch vehicles at the onset of panel instability is described using mechanical substitute models. Ring frame stiffeners of a stiffened shell structure are sized applying existing methods and the method suggested in this paper. To verify the suggested method and to demonstrate its potential, geometrically non-linear finite element analyses are performed using detailed finite element models.

Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2017-12-01

Travel time computation is of major interest for a large range of geophysical applications, among which source localization and characterization, phase identification, data windowing and tomography, from decametric scale up to global Earth scale.Ray-tracing tools, being essentially 1D Lagrangian integration along a path, have been used for their efficiency but present some drawbacks, such as a rather difficult control of the medium sampling. Moreover, they do not provide answers in shadow zones. Eikonal solvers, based on an Eulerian approach, have attracted attention in seismology with the pioneering work of Vidale (1988), while such approach has been proposed earlier by Riznichenko (1946). They have been used now for first-arrival travel-time tomography at various scales (Podvin & Lecomte (1991). The framework for solving this non-linear partial differential equation is now well understood and various finite-difference approaches have been proposed, essentially for smooth media. We propose a novel finite element approach which builds a precise solution for strongly heterogeneous anisotropic medium (still in the limit of Eikonal validity). The discontinuous Galerkin method we have developed allows local refinement of the mesh and local high orders of interpolation inside elements. High precision of the travel times and its spatial derivatives is obtained through this formulation. This finite element method also honors boundary conditions, such as complex topographies and absorbing boundaries for mimicking an infinite medium. Applications from travel-time tomography, slope tomography are expected, but also for migration and take-off angles estimation, thanks to the accuracy obtained when computing first-arrival times.References:Podvin, P. and Lecomte, I., 1991. Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 105, 271-284.Riznichenko, Y., 1946. Geometrical seismics of layered media, Trudy Inst. Theor. Geophysics, Vol II, Moscow (in Russian).Vidale, J., 1988. Finite-difference calculation of travel times, Bull. seism. Soc. Am., 78, 2062-2076.

On the practical efficiency of shape memory engines

NASA Astrophysics Data System (ADS)

McCormick, P. G.

1987-02-01

The effects of non-ideal behavior, i.e., thermal efficiencies less than perfect, on the efficiency of shape memory (SME) engines are analyzed. Account is taken of the temperature hysteresis between the forward and reverse transformation and the finite elastic compliance of the SM element and the engine. The temperature difference produced by a particular stress cycle and necessary to complete the cycle is quantified, along with the temperature penalty which arises from non-ideal behavior. The hysteresis, elastic compliance and low working strains in cycled materials are shown to yield low thermal efficiencies, e.g., 1.95 pct instead of 6.74 pct in the case of a 20 k hysteresis. Heat recycling can theoretically improve the efficiency to about 3.23 pct.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Efficient simulation of pitch angle collisions in a 2+2-D Eulerian Vlasov code

NASA Astrophysics Data System (ADS)

Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.

2014-10-01

Here we discuss pitch angle scattering collisions in the context of the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The collision operator is discretized using 4th order accurate conservative finite-differencing. The treatment of the Vlasov operator in phase-space uses an approach based on a minimally diffuse, fourth-order-accurate discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198). The overall scheme is therefore discretely conservative and controls unphysical oscillations. Some details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of collisional effects on linear and non-linear Landau damping of electron plasma waves (EPWs). In addition we will present initial results showing the effect of collisions on the evolution of EPWs in two space dimensions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking code 12-ERD-061.

Impact of isotropic constitutive descriptions on the predicted peak wall stress in abdominal aortic aneurysms.

PubMed

Man, V; Polzer, S; Gasser, T C; Novotny, T; Bursa, J

2018-03-01

Biomechanics-based assessment of Abdominal Aortic Aneurysm (AAA) rupture risk has gained considerable scientific and clinical momentum. However, computation of peak wall stress (PWS) using state-of-the-art finite element models is time demanding. This study investigates which features of the constitutive description of AAA wall are decisive for achieving acceptable stress predictions in it. Influence of five different isotropic constitutive descriptions of AAA wall is tested; models reflect realistic non-linear, artificially stiff non-linear, or artificially stiff pseudo-linear constitutive descriptions of AAA wall. Influence of the AAA wall model is tested on idealized (n=4) and patient-specific (n=16) AAA geometries. Wall stress computations consider a (hypothetical) load-free configuration and include residual stresses homogenizing the stresses across the wall. Wall stress differences amongst the different descriptions were statistically analyzed. When the qualitatively similar non-linear response of the AAA wall with low initial stiffness and subsequent strain stiffening was taken into consideration, wall stress (and PWS) predictions did not change significantly. Keeping this non-linear feature when using an artificially stiff wall can save up to 30% of the computational time, without significant change in PWS. In contrast, a stiff pseudo-linear elastic model may underestimate the PWS and is not reliable for AAA wall stress computations. Copyright © 2018 IPEM. Published by Elsevier Ltd. All rights reserved.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Zubova, N. A.

2017-06-01

This paper presents the results of numerical simulation of the Soret-induced convection of ternary mixture in the rectangular cavity elongated in horizontal direction in gravity field. The cavity has rigid impermeable boundaries. It is heated from the bellow and undergoes translational linearly polarized vibrations of finite amplitude and frequency in the horizontal direction. The problem is solved by finite difference method in the framework of full unsteady non-linear approach. The procedure of diagonalization of the molecular diffusion coefficient matrix is applied, allowing to eliminate cross-diffusion components in the equations and to reduce the number of the governing parameters. The calculations are performed for model ternary mixture with positive separation ratios of the components. The data on the vibration effect on temporal evolution of instantaneous and average fields and integral characteristics of the flow and heat and mass transfer at different levels of gravity are obtained.

A computationally efficient scheme for the non-linear diffusion equation

NASA Astrophysics Data System (ADS)

Termonia, P.; Van de Vyver, H.

2009-04-01

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

NASA Astrophysics Data System (ADS)

Voznyuk, I.; Litman, A.; Tortel, H.

2015-08-01

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.

Efficient computation of photonic crystal waveguide modes with dispersive material.

PubMed

Schmidt, Kersten; Kappeler, Roman

2010-03-29

The optimization of PhC waveguides is a key issue for successfully designing PhC devices. Since this design task is computationally expensive, efficient methods are demanded. The available codes for computing photonic bands are also applied to PhC waveguides. They are reliable but not very efficient, which is even more pronounced for dispersive material. We present a method based on higher order finite elements with curved cells, which allows to solve for the band structure taking directly into account the dispersiveness of the materials. This is accomplished by reformulating the wave equations as a linear eigenproblem in the complex wave-vectors k. For this method, we demonstrate the high efficiency for the computation of guided PhC waveguide modes by a convergence analysis.

Origin of nonsaturating linear magnetoresistivity

NASA Astrophysics Data System (ADS)

Kisslinger, Ferdinand; Ott, Christian; Weber, Heiko B.

2017-01-01

The observation of nonsaturating classical linear magnetoresistivity has been an enigmatic phenomenon in solid-state physics. We present a study of a two-dimensional ohmic conductor, including local Hall effect and a self-consistent consideration of the environment. An equivalent-circuit scheme delivers a simple and convincing argument why the magnetoresistivity is linear in strong magnetic field, provided that current and biasing electric field are misaligned by a nonlocal mechanism. A finite-element model of a two-dimensional conductor is suited to display the situations that create such deviating currents. Besides edge effects next to electrodes, charge carrier density fluctuations are efficiently generating this effect. However, mobility fluctuations that have frequently been related to linear magnetoresistivity are barely relevant. Despite its rare observation, linear magnetoresitivity is rather the rule than the exception in a regime of low charge carrier densities, misaligned current pathways and strong magnetic field.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures

NASA Astrophysics Data System (ADS)

Malomed, B. A.; Staroselsky, I. E.; Konstantinov, A. B.

1989-01-01

Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon

NASA Astrophysics Data System (ADS)

Ma, J.; Narayanan, H.; Garikipati, K.; Grosh, K.; Arruda, E. M.

The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.

Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

NASA Astrophysics Data System (ADS)

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in the frame of an ESA TRP study [1]. A bread-board including typical non-linearities has been designed, manufactured and tested through a typical spacecraft dynamic test campaign. The study has demonstrate the capabilities to perform non-linear dynamic test predictions on a flight representative spacecraft, the good correlation of test results with respect to Finite Elements Model (FEM) prediction and the possibility to identify modal behaviour and to characterize non-linearities characteristics from test results. As a synthesis for this study, overall guidelines have been derived on the mechanical verification process to improve level of expertise on tests involving spacecraft including non-linearity.

Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Chaparro, Daniel

2017-01-01

This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.

A Rewriting-Based Approach to Trace Analysis

NASA Technical Reports Server (NTRS)

Havelund, Klaus; Rosu, Grigore; Clancy, Daniel (Technical Monitor)

2002-01-01

We present a rewriting-based algorithm for efficiently evaluating future time Linear Temporal Logic (LTL) formulae on finite execution traces online. While the standard models of LTL are infinite traces, finite traces appear naturally when testing and/or monitoring red applications that only run for limited time periods. The presented algorithm is implemented in the Maude executable specification language and essentially consists of a set of equations establishing an executable semantics of LTL using a simple formula transforming approach. The algorithm is further improved to build automata on-the-fly from formulae, using memoization. The result is a very efficient and small Maude program that can be used to monitor program executions. We furthermore present an alternative algorithm for synthesizing probably minimal observer finite state machines (or automata) from LTL formulae, which can be used to analyze execution traces without the need for a rewriting system, and can hence be used by observers written in conventional programming languages. The presented work is part of an ambitious runtime verification and monitoring project at NASA Ames, called PATHEXPLORER, and demonstrates that rewriting can be a tractable and attractive means for experimenting and implementing program monitoring logics.

Real-time haptic cutting of high-resolution soft tissues.

PubMed

Wu, Jun; Westermann, Rüdiger; Dick, Christian

2014-01-01

We present our systematic efforts in advancing the computational performance of physically accurate soft tissue cutting simulation, which is at the core of surgery simulators in general. We demonstrate a real-time performance of 15 simulation frames per second for haptic soft tissue cutting of a deformable body at an effective resolution of 170,000 finite elements. This is achieved by the following innovative components: (1) a linked octree discretization of the deformable body, which allows for fast and robust topological modifications of the simulation domain, (2) a composite finite element formulation, which thoroughly reduces the number of simulation degrees of freedom and thus enables to carefully balance simulation performance and accuracy, (3) a highly efficient geometric multigrid solver for solving the linear systems of equations arising from implicit time integration, (4) an efficient collision detection algorithm that effectively exploits the composition structure, and (5) a stable haptic rendering algorithm for computing the feedback forces. Considering that our method increases the finite element resolution for physically accurate real-time soft tissue cutting simulation by an order of magnitude, our technique has a high potential to significantly advance the realism of surgery simulators.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

8-PSK Signaling over non-linear satellite channels

NASA Technical Reports Server (NTRS)

Horan, Sheila B.; Caballero, Ruben B. Eng.

1996-01-01

Space agencies are under pressure to utilize better bandwidth-efficient communication methods due to the actual allocated frequency bands becoming more congested. Also budget reductions is another problem that the space agencies must deal with. This budget constraint results in simpler spacecraft carrying less communication capabilities and also the reduction in staff to capture data in the earth stations. It is then imperative that the most bandwidth efficient communication methods be utilized. This thesis presents a study of 8-ary Phase Shift Keying (8PSK) modulation with respect to bandwidth, power efficiency, spurious emissions and interference susceptibility over a non-linear satellite channel.

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

Enhanced coupling of terahertz radiation to cylindrical wire waveguides.

PubMed

Deibel, Jason A; Wang, Kanglin; Escarra, Matthew D; Mittleman, Daniel

2006-01-09

Wire waveguides have recently been shown to be valuable for transporting pulsed terahertz radiation. This technique relies on the use of a scattering mechanism for input coupling. A radially polarized surface wave is excited when a linearly polarized terahertz pulse is focused on the gap between the wire waveguide and another metal structure. We calculate the input coupling efficiency using a simulation based on the Finite Element Method (FEM). Additional FEM results indicate that enhanced coupling efficiency can be achieved through the use of a radially symmetric photoconductive antenna. Experimental results confirm that such an antenna can generate terahertz radiation which couples to the radial waveguide mode with greatly improved efficiency.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

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

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

NASA Technical Reports Server (NTRS)

Datta, Anubhav; Johnson, Wayne R.

2009-01-01

This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.

Analysis of a Floodplain I-Wall Embedded in Horizontally Stratified Soil Layers During Flood Events Using Corps I-Wall Software Version 1.0

DTIC Science & Technology

2016-07-01

and gap propagation engineering methodology implemented within the software (CI-Wall) makes use of a hydraulic fracturing criterion, as discussed in...moist unit weight). Soil unit weights: Because of the presence of the upper moist (i.e, non - saturated) region R01 clay layer that is immediately...from two series of complete soil-structure interaction (SSI) non - linear finite element studies for I-Walls at New Orleans and other locations

Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime

NASA Astrophysics Data System (ADS)

Lorin, E.; Yang, X.; Antoine, X.

2016-06-01

The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.

Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound

NASA Astrophysics Data System (ADS)

Shiraishi, Naoto; Tajima, Hiroyasu

2017-08-01

A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.

Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound.

PubMed

Shiraishi, Naoto; Tajima, Hiroyasu

2017-08-01

A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.

High-performance coupled poro-hydro-mechanical models to resolve fluid escape pipes

NASA Astrophysics Data System (ADS)

Räss, Ludovic; Makhnenko, Roman; Podladchikov, Yury

2017-04-01

Field observations and laboratory experiments exhibit inelastic deformation features arising in many coupled settings relevant to geo-applications. These irreversible deformations and their specific patterns suggest a rather ductile or brittle mechanism, such as viscous creep or micro cracks, taking place on both geological (long) and human (short) timescales. In order to understand the underlying mechanisms responsible for these deformation features, there is a current need to accurately resolve the non-linearities inherent to strongly coupled physical processes. Among the large variety of modelling tools and softwares available nowadays in the community, very few are capable to efficiently solve coupled systems with high accuracy in both space and time and run efficiently on modern hardware. Here, we propose a robust framework to solve coupled multi-physics hydro-mechanical processes on very high spatial and temporal resolution in both two and three dimensions. Our software relies on the Finite-Difference Method and a pseudo-transient scheme is used to converge to the implicit solution of the system of poro-visco-elasto-plastic equations at each physical time step. The rheology including viscosity estimates for major reservoir rock types is inferred from novel lab experiments and confirms the ease of flow of sedimentary rocks. Our results propose a physical mechanism responsible for the generation of high permeability pathways in fluid saturated porous media and predict their propagation in rates observable on operational timescales. Finally, our software scales linearly on more than 5000 GPUs.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

NASA Astrophysics Data System (ADS)

Khusainov, T. A.; Shalashov, A. G.; Gospodchikov, E. D.

2018-05-01

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Experimental and Numerical Study of the Buckling of Composite Profiles with Open Cross Section under Axial Compression

NASA Astrophysics Data System (ADS)

Rozylo, Patryk; Teter, Andrzej; Debski, Hubert; Wysmulski, Pawel; Falkowicz, Katarzyna

2017-10-01

The object of the research are short, thin-walled columns with an open top-hat cross section made of multilayer laminate. The walls of the investigated profiles are made of plate elements. The entire columns are subjected to uniform compression. A detailed analysis allowed us to determine critical forces and post-critical equilibrium paths. It is assumed that the columns are articulately supported on the edges forming their ends. The numerical investigation is performed by the finite element method. The study involves solving the problem of eigenvalue and the non-linear problem of stability of the structure. The numerical analysis is performed by the commercial simulation software ABAQUS®. The numerical results are then validated experimentally. In the discussed cases, it is assumed that the material operates within a linearly-elastic range, and the non-linearity of the FEM model is due to large displacements.

A linear shock cell model for non-circular jets using conformal mapping with a pseudo-spectral hybrid scheme

NASA Technical Reports Server (NTRS)

Bhat, Thonse R. S.; Baty, Roy S.; Morris, Philip J.

1990-01-01

The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature

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

Patel, Niravkumar D.; Mukherjee, Anamitra; Kaushal, Nitin

Here, we employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T α for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic changemore » with U and V of the “effective” disorder, a combination of quenched disorder and intrinsic localized spins.« less

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

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.

Porosity Defect Remodeling and Tensile Analysis of Cast Steel

PubMed Central

Sun, Linfeng; Liao, Ridong; Lu, Wei; Fu, Sibo

2016-01-01

Tensile properties on ASTM A216 WCB cast steel with centerline porosity defect were studied with radiographic mapping and finite element remodeling technique. Non-linear elastic and plastic behaviors dependent on porosity were mathematically described by relevant equation sets. According to the ASTM E8 tensile test standard, matrix and defect specimens were machined into two categories by two types of height. After applying radiographic inspection, defect morphologies were mapped to the mid-sections of the finite element models and the porosity fraction fields had been generated with interpolation method. ABAQUS input parameters were confirmed by trial simulations to the matrix specimen and comparison with experimental outcomes. Fine agreements of the result curves between simulations and experiments could be observed, and predicted positions of the tensile fracture were found to be in accordance with the tests. Chord modulus was used to obtain the equivalent elastic stiffness because of the non-linear features. The results showed that elongation was the most influenced term to the defect cast steel, compared with elastic stiffness and yield stress. Additional visual explanations on the tensile fracture caused by void propagation were also given by the result contours at different mechanical stages, including distributions of Mises stress and plastic strain. PMID:28787919

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

SAGUARO: a finite-element computer program for partially saturated porous flow problems

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

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

A Navier-Strokes Chimera Code on the Connection Machine CM-5: Design and Performance

NASA Technical Reports Server (NTRS)

Jespersen, Dennis C.; Levit, Creon; Kwak, Dochan (Technical Monitor)

1994-01-01

We have implemented a three-dimensional compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the 'chimera' approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. A parallel machine like the CM-5 is well-suited for finite-difference methods on structured grids. The regular pattern of connections of a structured mesh maps well onto the architecture of the machine. So the first design choice, finite differences on a structured mesh, is natural. We use centered differences in space, with added artificial dissipation terms. When numerically solving the Navier-Stokes equations, there are liable to be some mesh cells near a solid body that are small in at least one direction. This mesh cell geometry can impose a very severe CFL (Courant-Friedrichs-Lewy) condition on the time step for explicit time-stepping methods. Thus, though explicit time-stepping is well-suited to the architecture of the machine, we have adopted implicit time-stepping. We have further taken the approximate factorization approach. This creates the need to solve large banded linear systems and creates the first possible barrier to an efficient algorithm. To overcome this first possible barrier we have considered two options. The first is just to solve the banded linear systems with data spread over the whole machine, using whatever fast method is available. This option is adequate for solving scalar tridiagonal systems, but for scalar pentadiagonal or block tridiagonal systems it is somewhat slower than desired. The second option is to 'transpose' the flow and geometry variables as part of the time-stepping process: Start with x-lines of data in-processor. Form explicit terms in x, then transpose so y-lines of data are in-processor. Form explicit terms in y, then transpose so z-lines are in processor. Form explicit terms in z, then solve linear systems in the z-direction. Transpose to the y-direction, then solve linear systems in the y-direction. Finally transpose to the x direction and solve linear systems in the x-direction. This strategy avoids inter-processor communication when differencing and solving linear systems, but requires a large amount of communication when doing the transposes. The transpose method is more efficient than the non-transpose strategy when dealing with scalar pentadiagonal or block tridiagonal systems. For handling geometrically complex problems the chimera strategy was adopted. For multiple zone cases we compute on each zone sequentially (using the whole parallel machine), then send the chimera interpolation data to a distributed data structure (array) laid out over the whole machine. This information transfer implies an irregular communication pattern, and is the second possible barrier to an efficient algorithm. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran. We make use of the Connection Machine Scientific Software Library (CMSSL) for the linear solver and array transpose operations.

On structural identifiability analysis of the cascaded linear dynamic systems in isotopically non-stationary 13C labelling experiments.

PubMed

Lin, Weilu; Wang, Zejian; Huang, Mingzhi; Zhuang, Yingping; Zhang, Siliang

2018-06-01

The isotopically non-stationary 13C labelling experiments, as an emerging experimental technique, can estimate the intracellular fluxes of the cell culture under an isotopic transient period. However, to the best of our knowledge, the issue of the structural identifiability analysis of non-stationary isotope experiments is not well addressed in the literature. In this work, the local structural identifiability analysis for non-stationary cumomer balance equations is conducted based on the Taylor series approach. The numerical rank of the Jacobian matrices of the finite extended time derivatives of the measured fractions with respect to the free parameters is taken as the criterion. It turns out that only one single time point is necessary to achieve the structural identifiability analysis of the cascaded linear dynamic system of non-stationary isotope experiments. The equivalence between the local structural identifiability of the cascaded linear dynamic systems and the local optimum condition of the nonlinear least squares problem is elucidated in the work. Optimal measurements sets can then be determined for the metabolic network. Two simulated metabolic networks are adopted to demonstrate the utility of the proposed method. Copyright © 2018 Elsevier Inc. All rights reserved.

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

NASA Astrophysics Data System (ADS)

Schaa, R.; Gross, L.; du Plessis, J.

2016-04-01

We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

Estimating and testing interactions when explanatory variables are subject to non-classical measurement error.

PubMed

Murad, Havi; Kipnis, Victor; Freedman, Laurence S

2016-10-01

Assessing interactions in linear regression models when covariates have measurement error (ME) is complex.We previously described regression calibration (RC) methods that yield consistent estimators and standard errors for interaction coefficients of normally distributed covariates having classical ME. Here we extend normal based RC (NBRC) and linear RC (LRC) methods to a non-classical ME model, and describe more efficient versions that combine estimates from the main study and internal sub-study. We apply these methods to data from the Observing Protein and Energy Nutrition (OPEN) study. Using simulations we show that (i) for normally distributed covariates efficient NBRC and LRC were nearly unbiased and performed well with sub-study size ≥200; (ii) efficient NBRC had lower MSE than efficient LRC; (iii) the naïve test for a single interaction had type I error probability close to the nominal significance level, whereas efficient NBRC and LRC were slightly anti-conservative but more powerful; (iv) for markedly non-normal covariates, efficient LRC yielded less biased estimators with smaller variance than efficient NBRC. Our simulations suggest that it is preferable to use: (i) efficient NBRC for estimating and testing interaction effects of normally distributed covariates and (ii) efficient LRC for estimating and testing interactions for markedly non-normal covariates. © The Author(s) 2013.

A Thermodynamic Theory of Solid Viscoelasticity. Part II:; Nonlinear Thermo-viscoelasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.

Simulation of laminate composites degradation using mesoscopic non-local damage model and non-local layered shell element

NASA Astrophysics Data System (ADS)

Germain, Norbert; Besson, Jacques; Feyel, Frédéric

2007-07-01

Simulating damage and failure of laminate composites structures often fails when using the standard finite element procedure. The difficulties arise from an uncontrolled mesh dependence caused by damage localization and an increase in computational costs. One of the solutions to the first problem, widely used to predict the failure of metallic materials, consists of using non-local damage constitutive equations. The second difficulty can then be solved using specific finite element formulations, such as shell element, which decrease the number of degrees of freedom. The main contribution of this paper consists of extending these techniques to layered materials such as polymer matrix composites. An extension of the non-local implicit gradient formulation, accounting for anisotropy and stratification, and an original layered shell element, based on a new partition of the unity, are proposed. Finally the efficiency of the resulting numerical scheme is studied by comparing simulation with experimental results.

Sieve estimation of Cox models with latent structures.

PubMed

Cao, Yongxiu; Huang, Jian; Liu, Yanyan; Zhao, Xingqiu

2016-12-01

This article considers sieve estimation in the Cox model with an unknown regression structure based on right-censored data. We propose a semiparametric pursuit method to simultaneously identify and estimate linear and nonparametric covariate effects based on B-spline expansions through a penalized group selection method with concave penalties. We show that the estimators of the linear effects and the nonparametric component are consistent. Furthermore, we establish the asymptotic normality of the estimator of the linear effects. To compute the proposed estimators, we develop a modified blockwise majorization descent algorithm that is efficient and easy to implement. Simulation studies demonstrate that the proposed method performs well in finite sample situations. We also use the primary biliary cirrhosis data to illustrate its application. © 2016, The International Biometric Society.

Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics

NASA Astrophysics Data System (ADS)

Bayat, Hamid Reza; Krämer, Julian; Wunderlich, Linus; Wulfinghoff, Stephan; Reese, Stefanie; Wohlmuth, Barbara; Wieners, Christian

2018-03-01

This work presents a systematic study of discontinuous and nonconforming finite element methods for linear elasticity, finite elasticity, and small strain plasticity. In particular, we consider new hybrid methods with additional degrees of freedom on the skeleton of the mesh and allowing for a local elimination of the element-wise degrees of freedom. We show that this process leads to a well-posed approximation scheme. The quality of the new methods with respect to locking and anisotropy is compared with standard and in addition locking-free conforming methods as well as established (non-) symmetric discontinuous Galerkin methods with interior penalty. For several benchmark configurations, we show that all methods converge asymptotically for fine meshes and that in many cases the hybrid methods are more accurate for a fixed size of the discrete system.

CFD Analysis of a Finite Linear Array of Savonius Wind Turbines

NASA Astrophysics Data System (ADS)

Belkacem, Belabes; Paraschivoiu, Marius

2016-09-01

Vertical axis wind turbines such as Savonius rotors have been shown to be suitable for low wind speeds normally associated with wind resources in all corners of the world. However, the efficiency of the rotor is low. This paper presents results of Computational Fluid Dynamics (CFD) simulations for an array of Savonius rotors that show a significant increase in efficiency. It looks at identifying the effect on the energy yield of a number of turbines placed in a linear array. Results from this investigation suggest that an increase in the energy yield could be achieved which can reach almost two times than the conventional Savonius wind turbine in the case of an array of 11turbines with a distance of 1.4R in between them. The effect of different TSR values and different wind inlet speeds on the farm has been studied for both a synchronous and asynchronous wind farm.

Coherent-state constellations and polar codes for thermal Gaussian channels

NASA Astrophysics Data System (ADS)

Lacerda, Felipe; Renes, Joseph M.; Scholz, Volkher B.

2017-06-01

Optical communication channels are ultimately quantum mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of particular practical relevance; their classical capacity has been recently established, but their quantum capacity remains unknown. While the capacity sets the ultimate limit on reliable communication rates, it does not promise that such rates are achievable by practical means. Here we construct efficiently encodable codes for thermal channels which achieve the classical capacity and the so-called Gaussian coherent information for transmission of classical and quantum information, respectively. Our codes are based on combining polar codes with a discretization of the channel input into a finite "constellation" of coherent states. Encoding of classical information can be done using linear optics.

Three friendly walkers

NASA Astrophysics Data System (ADS)

Jensen, Iwan

2017-01-01

More than 15 years ago Guttmann and Vöge (2002 J. Stat. Plan. Inference 101 107), introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a {{}2}{{F}1} hypergeometric function with a rational pullback and its first and second derivatives. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

Mechanically fastened composite laminates subjected to combined bearing-bypass and shear loading

NASA Technical Reports Server (NTRS)

Madenci, Erdogan

1993-01-01

Bolts and rivets provide a means of load transfer in the construction of aircraft. However, they give rise to stress concentrations and are often the source and location of static and fatigue failures. Furthermore, fastener holes are prone to cracks during take-off and landing. These cracks present the most common origin of structural failures in aircraft. Therefore, accurate determination of the contact stresses associated with such loaded holes in mechanically fastened joints is essential to reliable strength evaluation and failure prediction. As the laminate is subjected to loading, the contact region, whose extent is not known, develops between the fastener and the hole boundary through this contact region, which consists of slip and no-slip zones due to friction. The presence of the unknown contact stress distribution over the contact region between the pin and the composite laminate, material anisotropy, friction between the pin and the laminate, pin-hole clearance, combined bearing-bypass and shear loading, and finite geometry of the laminate result in a complex non-linear problem. In the case of bearing-bypass loading in compression, this non-linear problem is further complicated by the presence of dual contact regions. Previous research concerning the analysis of mechanical joints subjected to combined bearing-bypass and shear loading is non-existent. In the case of bearing-bypass loading only, except for the study conducted by Naik and Crews (1991), others employed the concept of superposition which is not valid for this non-linear problem. Naik and Crews applied a linear finite element analysis with conditions along the pin-hole contact region specified as displacement constraint equations. The major shortcoming of this method is that the variation of the contract region as a function of the applied load should be known a priori. Also, their analysis is limited to symmetric geometry and material systems, and frictionless boundary conditions. Since the contact stress distribution and the contact region are not known a priori, they did not directly impose the boundary conditions appropriate for modelling the contact and on-contact regions between the fastener and the hole. Furthermore, finite element analysis is not suitable for iterative design calculations for optimizing laminate construction in the presence of fasteners under complex loading conditions. In this study, the solution method developed by Madenci and Ileri (1992a,b) has been extended to determine the contact stresses in mechanical joints under combined bearing-bypass and shear loading, and bearing-bypass loading in compression resulting in dual contact regions.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.

PubMed

Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas

2016-01-01

In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.

An Efficient Crankshaft Dynamic Analysis Using Substructuring with Ritz Vectors

NASA Astrophysics Data System (ADS)

MOURELATOS, Z. P.

2000-11-01

A structural analysis using dynamic substructuring with Ritz vectors is presented for predicting the dynamic response of an engine crankshaft, based on the finite-element method. A two-level dynamic substructuring is performed using a set of load-dependent Ritz vectors. The rotating crankshaft is properly coupled with the non-rotating, compliant engine block. The block compliance is represented by a distributed linear elastic foundation at each main bearing location. The stiffness of the elastic foundation can be different in the vertical and horizontal planes, thereby considering the anisotropy of the engine block compliance with respect to the crankshaft rotation. The analysis accounts for the kinematic non-linearity resulting from the crankangle-dependent circumferential contact location between each journal and the corresponding bore of the engine block. Crankshaft “bent” and block “misboring” effects due to manufacturing imperfections are considered in the analysis. The superior accuracy and reduced computational effort of the present method as compared with the equivalent superelement analysis in MSC/NASTRAN, are demonstrated using the free and forced vibrations of a slender cylindrical beam and free vibrations of a four-cylinder engine crankshaft. Subsequently, the accuracy of the present method in calculating the dynamic response of engine crankshafts is shown through comparisons between the analytical predictions and experimental results for the torsional vibrations of an in-line five cylinder engine and the bending vibrations of the crankshaft-flywheel assembly of a V6 engine.

Symmetrical or Non-Symmetrical Debonds at Fiber-Matrix Interfaces: A Study by BEM and Finite Fracture Mechanics on Elastic Interfaces

NASA Astrophysics Data System (ADS)

Muñoz-Reja, Mar; Távara, Luis; Mantič, Vladislav

A recently proposed criterion is used to study the behavior of debonds produced at a fiber-matrix interface. The criterion is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Special attention is given to the discussion about the symmetry of the debond onset and growth in an isolated single fiber specimen under uniaxial transverse tension. A common composite material system, glass fiber-epoxy matrix, is considered. The present methodology uses a two-dimensional (2D) Boundary Element Method (BEM) code to carry out the analysis of interface failure. The present results show that a non-symmetrical interface crack configuration (debonds at one side only) is produced by a lower critical remote load than the symmetrical case (debonds at both sides). Thus, the non-symmetrical solution is the preferred one, which agrees with the experimental evidences found in the literature.

Acoustic Analysis of a Sandwich Non Metallic Panel for Roofs by FEM and Experimental Validation

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Rabanal, F. P. Alvarez

2007-12-01

In this paper we have studied the acoustic behavior of a sandwich non metallic panel for roofs by the finite element method (FEM). This new field of analysis is the fully coupled solution of fluid flows with structural interactions, commonly referred to as fluid-structure interaction (FSI). It is the natural next step to take in the simulation of mechanical systems. The finite element analysis of acoustic-fluid/structure interactions using potential-based or displacement-based Lagrangian formulations is now well established. The non-linearity is due to the `fluid-structure interaction' (FSI) that governs the problem. In a very considerable range of problems the fluid displacement remains small while interaction is substantial. In this category falls our problem, in which the structural motion influence and react with the generation of pressures in two reverberation rooms. The characteristic of acoustic insulation of the panel is calculated basing on the pressures for different frequencies and points in the transmission rooms. Finally the conclusions reached are shown.

In-process, non-destructive multimodal dynamic testing of high-speed composite rotors

NASA Astrophysics Data System (ADS)

Kuschmierz, Robert; Filippatos, Angelos; Langkamp, Albert; Hufenbach, Werner; Czarske, Jürgern W.; Fischer, Andreas

2014-03-01

Fibre reinforced plastic (FRP) rotors are lightweight and offer great perspectives in high-speed applications such as turbo machinery. Currently, novel rotor structures and materials are investigated for the purpose of increasing machine efficiency, lifetime and loading limits. Due to complex rotor structures, high anisotropy and non-linear behavior of FRP under dynamic loads, an in-process measurement system is necessary to monitor and to investigate the evolution of damages under real operation conditions. A non-invasive, optical laser Doppler distance sensor measurement system is applied to determine the biaxial deformation of a bladed FRP rotor with micron uncertainty as well as the tangential blade vibrations at surface speeds above 300 m/s. The laser Doppler distance sensor is applicable under vacuum conditions. Measurements at varying loading conditions are used to determine elastic and plastic deformations. Furthermore they allow to determine hysteresis, fatigue, Eigenfrequency shifts and loading limits. The deformation measurements show a highly anisotropic and nonlinear behavior and offer a deeper understanding of the damage evolution in FRP rotors. The experimental results are used to validate and to calibrate a simulation model of the deformation. The simulation combines finite element analysis and a damage mechanics model. The combination of simulation and measurement system enables the monitoring and prediction of damage evolutions of FRP rotors in process.

Designing overall stoichiometric conversions and intervening metabolic reactions

DOE PAGES

Chowdhury, Anupam; Maranas, Costas D.

2015-11-04

Existing computational tools for de novo metabolic pathway assembly, either based on mixed integer linear programming techniques or graph-search applications, generally only find linear pathways connecting the source to the target metabolite. The overall stoichiometry of conversion along with alternate co-reactant (or co-product) combinations is not part of the pathway design. Therefore, global carbon and energy efficiency is in essence fixed with no opportunities to identify more efficient routes for recycling carbon flux closer to the thermodynamic limit. Here, we introduce a two-stage computational procedure that both identifies the optimum overall stoichiometry (i.e., optStoic) and selects for (non-)native reactions (i.e.,more » minRxn/minFlux) that maximize carbon, energy or price efficiency while satisfying thermodynamic feasibility requirements. Implementation for recent pathway design studies identified non-intuitive designs with improved efficiencies. Specifically, multiple alternatives for non-oxidative glycolysis are generated and non-intuitive ways of co-utilizing carbon dioxide with methanol are revealed for the production of C 2+ metabolites with higher carbon efficiency.« less

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

MHD Simulations of Plasma Dynamics with Non-Axisymmetric Boundaries

NASA Astrophysics Data System (ADS)

Hansen, Chris; Levesque, Jeffrey; Morgan, Kyle; Jarboe, Thomas

2015-11-01

The arbitrary geometry, 3D extended MHD code PSI-TET is applied to linear and non-linear simulations of MCF plasmas with non-axisymmetric boundaries. Progress and results from simulations on two experiments will be presented: 1) Detailed validation studies of the HIT-SI experiment with self-consistent modeling of plasma dynamics in the helicity injectors. Results will be compared to experimental data and NIMROD simulations that model the effect of the helicity injectors through boundary conditions on an axisymmetric domain. 2) Linear studies of HBT-EP with different wall configurations focusing on toroidal asymmetries in the adjustable conducting wall. HBT-EP studies the effect of active/passive stabilization with an adjustable ferritic wall. Results from linear verification and benchmark studies of ideal mode growth with and without toroidal asymmetries will be presented and compared to DCON predictions. Simulations of detailed experimental geometries are enabled by use of the PSI-TET code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-TET will also be presented including work to support resistive wall regions within extended MHD simulations. Work supported by DoE.

Design of multiplier-less sharp transition width non-uniform filter banks using gravitational search algorithm

NASA Astrophysics Data System (ADS)

Bindiya T., S.; Elias, Elizabeth

2015-01-01

In this paper, multiplier-less near-perfect reconstruction tree-structured filter banks are proposed. Filters with sharp transition width are preferred in filter banks in order to reduce the aliasing between adjacent channels. When sharp transition width filters are designed as conventional finite impulse response filters, the order of the filters will become very high leading to increased complexity. The frequency response masking (FRM) method is known to result in linear-phase sharp transition width filters with low complexity. It is found that the proposed design method, which is based on FRM, gives better results compared to the earlier reported results, in terms of the number of multipliers when sharp transition width filter banks are needed. To further reduce the complexity and power consumption, the tree-structured filter bank is made totally multiplier-less by converting the continuous filter bank coefficients to finite precision coefficients in the signed power of two space. This may lead to performance degradation and calls for the use of a suitable optimisation technique. In this paper, gravitational search algorithm is proposed to be used in the design of the multiplier-less tree-structured uniform as well as non-uniform filter banks. This design method results in uniform and non-uniform filter banks which are simple, alias-free, linear phase and multiplier-less and have sharp transition width.

Finite volume solution of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Loyd, B.; Murman, E. M.

1986-01-01

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

Stochastic thermodynamics, fluctuation theorems and molecular machines.

PubMed

Seifert, Udo

2012-12-01

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Multidimensional FEM-FCT schemes for arbitrary time stepping

NASA Astrophysics Data System (ADS)

Kuzmin, D.; Möller, M.; Turek, S.

2003-05-01

The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity

NASA Astrophysics Data System (ADS)

Mapakshi, N. K.; Chang, J.; Nakshatrala, K. B.

2018-04-01

Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP). Unfortunately, many of the existing formulations for flow through porous media models do not satisfy DMP. This paper presents a robust, scalable numerical formulation based on variational inequalities (VI), to model non-linear flows through heterogeneous, anisotropic porous media without violating DMP. VI is an optimization technique that places bounds on the numerical solutions of partial differential equations. To crystallize the ideas, a modification to Darcy equations by taking into account pressure-dependent viscosity will be discretized using the lowest-order Raviart-Thomas (RT0) and Variational Multi-scale (VMS) finite element formulations. It will be shown that these formulations violate DMP, and, in fact, these violations increase with an increase in anisotropy. It will be shown that the proposed VI-based formulation provides a viable route to enforce DMP. Moreover, it will be shown that the proposed formulation is scalable, and can work with any numerical discretization and weak form. A series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity, anisotropy and non-linearity on DMP violations under the two chosen formulations (RT0 and VMS), and that of non-linearity on solver convergence for the proposed VI-based formulation. Parallel scalability on modern computational platforms will be illustrated through strong-scaling studies, which will prove the efficiency of the proposed formulation in a parallel setting. Algorithmic scalability as the problem size is scaled up will be demonstrated through novel static-scaling studies. The performed static-scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

A robust approach to measuring the detective quantum efficiency of radiographic detectors in a clinical setting

NASA Astrophysics Data System (ADS)

McDonald, Michael C.; Kim, H. K.; Henry, J. R.; Cunningham, I. A.

2012-03-01

The detective quantum efficiency (DQE) is widely accepted as a primary measure of x-ray detector performance in the scientific community. A standard method for measuring the DQE, based on IEC 62220-1, requires the system to have a linear response meaning that the detector output signals are proportional to the incident x-ray exposure. However, many systems have a non-linear response due to characteristics of the detector, or post processing of the detector signals, that cannot be disabled and may involve unknown algorithms considered proprietary by the manufacturer. For these reasons, the DQE has not been considered as a practical candidate for routine quality assurance testing in a clinical setting. In this article we described a method that can be used to measure the DQE of both linear and non-linear systems that employ only linear image processing algorithms. The method was validated on a Cesium Iodide based flat panel system that simultaneously stores a raw (linear) and processed (non-linear) image for each exposure. It was found that the resulting DQE was equivalent to a conventional standards-compliant DQE with measurement precision, and the gray-scale inversion and linear edge enhancement did not affect the DQE result. While not IEC 62220-1 compliant, it may be adequate for QA programs.

Application of the Lienard-Wiechert solution to a lightning return stroke model

NASA Technical Reports Server (NTRS)

Meneghini, R.

1983-01-01

The electric and magnetic fields associated with the lightning return stroke are expressed as a convolution of the current waveform shape and the fields generated by a moving charge of amplitude one (i.e., the Lienard-Wiechert solution for a unit charge). The representation can be used to compute the fields produced by a current waveform of non-uniform velocity that propagates along a filament of arbitrary, but finite, curvature. To study numerically the effects of linear charge acceleration and channel curvature two simple channel models are used: the linear and the hyperbolic.

Application of the Lienard-Wiechert solution to a lightning return stroke model

NASA Technical Reports Server (NTRS)

Meneghini, R.

1984-01-01

The electric and magnetic fields associated with the lightning return stroke are expressed as a convolution of the current waveform shape and the fields generated by a moving charge of amplitude one (i.e., the Lienard-Wiechert solution for a unit charge). The representation can be used to compute the fields produced by a current waveform of non-uniform velocity that propagates along a filament of arbitrary, but finite, curvature. To study numerically the effects of linear charge acceleration and channel curvature two simple channel models are used: the linear and the hyperbolic.

Capelli bitableaux and Z-forms of general linear Lie superalgebras.

PubMed Central

Brini, A; Teolis, A G

1990-01-01

The combinatorics of the enveloping algebra UQ(pl(L)) of the general linear Lie superalgebra of a finite dimensional Z2-graded Q-vector space is studied. Three non-equivalent Z-forms of UQ(pl(L)) are introduced: one of these Z-forms is a version of the Kostant Z-form and the others are Lie algebra analogs of Rota and Stein's straightening formulae for the supersymmetric algebra Super[L P] and for its dual Super[L* P*]. The method is based on an extension of Capelli's technique of variabili ausiliarie to algebras containing positively and negatively signed elements. PMID:11607048

Stochastic thermodynamics for Ising chain and symmetric exclusion process.

PubMed

Toral, R; Van den Broeck, C; Escaff, D; Lindenberg, Katja

2017-03-01

We verify the finite-time fluctuation theorem for a linear Ising chain in contact with heat reservoirs at its ends. Analytic results are derived for a chain consisting of two spins. The system can be mapped onto a model for particle transport, namely, the symmetric exclusion process in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.

Measurement-Based Linear Optics

NASA Astrophysics Data System (ADS)

Alexander, Rafael N.; Gabay, Natasha C.; Rohde, Peter P.; Menicucci, Nicolas C.

2017-03-01

A major challenge in optical quantum processing is implementing large, stable interferometers. We offer a novel approach: virtual, measurement-based interferometers that are programed on the fly solely by the choice of homodyne measurement angles. The effects of finite squeezing are captured as uniform amplitude damping. We compare our proposal to existing (physical) interferometers and consider its performance for BosonSampling, which could demonstrate postclassical computational power in the near future. We prove its efficiency in time and squeezing (energy) in this setting.

Understanding Non-Equilibrium Charge Transport and Rectification at Chromophore/Metal Interfaces

NASA Astrophysics Data System (ADS)

Darancet, Pierre

Understanding non-equilibrium charge and energy transport across nanoscale interfaces is central to developing an intuitive picture of fundamental processes in solar energy conversion applications. In this talk, I will discuss our theoretical studies of finite-bias transport at organic/metal interfaces. First, I will show how the finite-bias electronic structure of such systems can be quantitatively described using density functional theory in conjunction with simple models of non-local correlations and bias-induced Stark effects.. Using these methods, I will discuss the conditions of emergence of highly non-linear current-voltage characteristics in bilayers made of prototypical organic materials, and their implications in the context of hole- and electron-blocking layers in organic photovoltaic. In particular, I will show how the use of strongly-hybridized, fullerene-coated metallic surfaces as electrodes is a viable route to maximizing the diodic behavior and electrical functionality of molecular components. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (Argonne). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357.

Metastability of Queuing Networks with Mobile Servers

NASA Astrophysics Data System (ADS)

Baccelli, F.; Rybko, A.; Shlosman, S.; Vladimirov, A.

2018-04-01

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the metastability phenomenon. Large enough finite symmetric networks on regular graphs are proved to be transient for arbitrarily small inflow rates. However, the limiting non-linear Markov process possesses at least two stationary solutions. The proof of transience is based on martingale techniques.

Quantiles for Finite Mixtures of Normal Distributions

ERIC Educational Resources Information Center

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

Compressive mechanical characterization of non-human primate spinal cord white matter.

PubMed

Jannesar, Shervin; Allen, Mark; Mills, Sarah; Gibbons, Anne; Bresnahan, Jacqueline C; Salegio, Ernesto A; Sparrey, Carolyn J

2018-05-02

The goal of developing computational models of spinal cord injury (SCI) is to better understand the human injury condition. However, finite element models of human SCI have used rodent spinal cord tissue properties due to a lack of experimental data. Central nervous system tissues in non human primates (NHP) closely resemble that of humans and therefore, it is expected that material constitutive models obtained from NHPs will increase the fidelity and the accuracy of human SCI models. Human SCI most often results from compressive loading and spinal cord white matter properties affect FE predicted patterns of injury; therefore, the objectives of this study were to characterize the unconfined compressive response of NHP spinal cord white matter and present an experimentally derived, finite element tractable constitutive model for the tissue. Cervical spinal cords were harvested from nine male adult NHPs (Macaca mulatta). White matter biopsy samples (3 mm in diameter) were taken from both lateral columns of the spinal cord and were divided into four strain rate groups for unconfined dynamic compression and stress relaxation (post-mortem <1-hour). The NHP spinal cord white matter compressive response was sensitive to strain rate and showed substantial stress relaxation confirming the viscoelastic behavior of the material. An Ogden 1st order model best captured the non-linear behavior of NHP white matter in a quasi-linear viscoelastic material model with 4-term Prony series. This study is the first to characterize NHP spinal cord white matter at high (>10/sec) strain rates typical of traumatic injury. The finite element derived material constitutive model of this study will increase the fidelity of SCI computational models and provide important insights for transferring pre-clinical findings to clinical treatments. Spinal cord injury (SCI) finite element (FE) models provide an important tool to bridge the gap between animal studies and human injury, assess injury prevention technologies (e.g. helmets, seatbelts), and provide insight into the mechanisms of injury. Although, FE model outcomes depend on the assumed material constitutive model, there is limited experimental data for fresh spinal cords and all was obtained from rodent, porcine or bovine tissues. Central nervous system tissues in non human primates (NHP) more closely resemble humans. This study characterizes fresh NHP spinal cord material properties at high strains rates and large deformations typical of SCI for the first time. A constitutive model was defined that can be readily implemented in finite strain FE analysis of SCI. Copyright © 2018. Published by Elsevier Ltd.

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

A novel recurrent neural network with finite-time convergence for linear programming.

PubMed

Liu, Qingshan; Cao, Jinde; Chen, Guanrong

2010-11-01

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

X-ray fluorescence spectrometry-based approach to precision management of bioavailable phosphorus in soil environments

USDA-ARS?s Scientific Manuscript database

Declining nutrient use efficiency in crop production has been a global priority to preserve high agricultural productivity with finite non-renewable nutrient resources, in particular phosphorus (P). Rapid spectroscopic methods increase measurement density of soil nutrients, and the availability of ...

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

NASA Astrophysics Data System (ADS)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method

NASA Astrophysics Data System (ADS)

Ward, A. J.; Pendry, J. B.

2000-06-01

In this paper we present an updated version of our ONYX program for calculating photonic band structures using a non-orthogonal finite difference time domain method. This new version employs the same transparent formalism as the first version with the same capabilities for calculating photonic band structures or causal Green's functions but also includes extra subroutines for the calculation of transmission and reflection coefficients. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretization so the technique is ideally suited to handling systems with large and complicated unit cells.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Theoretical and experimental study of a wireless power supply system for moving low power devices in ferromagnetic and conductive medium

NASA Astrophysics Data System (ADS)

Safour, Salaheddine; Bernard, Yves

2017-10-01

This paper focuses on the design of a wireless power supply system for low power devices (e.g. sensors) located in harsh electromagnetic environment with ferromagnetic and conductive materials. Such particular environment could be found in linear and rotating actuators. The studied power transfer system is based on the resonant magnetic coupling between a fixed transmitter coil and a moving receiver coil. The technique was utilized successfully for rotary machines. The aim of this paper is to extend the technique to linear actuators. A modeling approach based on 2D Axisymmetric Finite Element model and an electrical lumped model based on the two-port network theory is introduced. The study shows the limitation of the technique to transfer the required power in the presence of ferromagnetic and conductive materials. Parametric and circuit analysis were conducted in order to design a resonant magnetic coupler that ensures good power transfer capability and efficiency. A design methodology is proposed based on this study. Measurements on the prototype show efficiency up to 75% at a linear distance of 20 mm.

Global Regularity for the Fractional Euler Alignment System

NASA Astrophysics Data System (ADS)

Do, Tam; Kiselev, Alexander; Ryzhik, Lenya; Tan, Changhui

2018-04-01

We study a pressureless Euler system with a non-linear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density dependence is natural: the alignment rate increases in the areas of high density due to species discomfort. The diffusive term has the order of a fractional Laplacian {(-partial _{xx})^{α/2}, α \\in (0, 1)}. The corresponding Burgers equation with a linear dissipation of this type develops shocks in a finite time. We show that the alignment nonlinearity enhances the dissipation, and the solutions are globally regular for all {α \\in (0, 1)}. To the best of our knowledge, this is the first example of such regularization due to the non-local nonlinear modulation of dissipation.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

A Finite-Difference Time-Domain Model of Artificial Ionospheric Modification

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

Experiments in the artificial modification of the ionosphere via a radio frequency pump wave have observed a wide range of non-linear phenomena near the reflection height of an O-mode wave. These effects exhibit a strong aspect-angle dependence thought to be associated with the process by which, for a narrow range of off-vertical launch angles, the O-mode pump wave can propagate beyond the standard reflection height at X=1 as a Z-mode wave and excite additional plasma activity. A numerical model based on Finite-Difference Time-Domain method has been developed to simulate the interaction of the pump wave with an ionospheric plasma and investigate different non-linear processes involved in modification experiments. The effects on wave propagation due to plasma inhomogeneity and anisotropy are introduced through coupling of the Lorentz equation of motion for electrons and ions to Maxwell’s wave equations in the FDTD formulation, leading to a model that is capable of exciting a variety of plasma waves including Langmuir and upper-hybrid waves. Additionally, discretized equations describing the time-dependent evolution of the plasma fluid temperature and density are included in the FDTD update scheme. This model is used to calculate the aspect angle dependence and angular size of the radio window for which Z-mode excitation occurs, and the results compared favourably with both theoretical predictions and experimental observations. The simulation results are found to reproduce the angular dependence on electron density and temperature enhancement observed experimentally. The model is used to investigate the effect of different initial plasma density conditions on the evolution of non-linear effects, and demonstrates that the inclusion of features such as small field-aligned density perturbations can have a significant influence on wave propagation and the magnitude of temperature and density enhancements.

Fatigue Life Methodology for Tapered Composite Flexbeam Laminates

NASA Technical Reports Server (NTRS)

Murri, Gretchen B.; OBrien, T. Kevin; Rousseau, Carl Q.

1997-01-01

The viability of a method for determining the fatigue life of composite rotor hub flexbeam laminates using delamination fatigue characterization data and a geometric non-linear finite element (FE) analysis was studied. Combined tension and bending loading was applied to non-linear tapered flexbeam laminates with internal ply drops. These laminates, consisting of coupon specimens cut from a full-size S2/E7T1 glass-epoxy flexbeam were tested in a hydraulic load frame under combined axial-tension and transverse cyclic bending. The magnitude of the axial load remained constant and the direction of the load rotated with the specimen as the cyclic bending load was applied. The first delamination damage observed in the specimens occurred at the area around the tip of the outermost ply-drop group. Subsequently, unstable delamination occurred by complete delamination along the length of the specimen. Continued cycling resulted in multiple delaminations. A 2D finite element model of the flexbeam was developed and a geometrically non-linear analysis was performed. The global responses of the model and test specimens agreed very well in terms of the transverse displacement. The FE model was used to calculate strain energy release rates (G) for delaminations initiating at the tip of the outer ply-drop area and growing toward the thick or thin regions of the flexbeam, as was observed in the specimens. The delamination growth toward the thick region was primarily mode 2, whereas delamination growth toward the thin region was almost completely mode 1. Material characterization data from cyclic double-cantilevered beam tests was used with the peak calculated G values to generate a curve predicting fatigue failure by unstable delamination as a function of the number of loading cycles. The calculated fatigue lives compared well with the test data.

Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2006-01-01

A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Nark, Douglas M.; Nguyen, Duc T.; Tungkahotara, Siroj

2006-01-01

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

Finite element code development for modeling detonation of HMX composites

NASA Astrophysics Data System (ADS)

Duran, Adam; Sundararaghavan, Veera

2015-06-01

In this talk, we present a hydrodynamics code for modeling shock and detonation waves in HMX. A stable efficient solution strategy based on a Taylor-Galerkin finite element (FE) discretization was developed to solve the reactive Euler equations. In our code, well calibrated equations of state for the solid unreacted material and gaseous reaction products have been implemented, along with a chemical reaction scheme and a mixing rule to define the properties of partially reacted states. A linear Gruneisen equation of state was employed for the unreacted HMX calibrated from experiments. The JWL form was used to model the EOS of gaseous reaction products. It is assumed that the unreacted explosive and reaction products are in both pressure and temperature equilibrium. The overall specific volume and internal energy was computed using the rule of mixtures. Arrhenius kinetics scheme was integrated to model the chemical reactions. A locally controlled dissipation was introduced that induces a non-oscillatory stabilized scheme for the shock front. The FE model was validated using analytical solutions for sod shock and ZND strong detonation models and then used to perform 2D and 3D shock simulations. We will present benchmark problems for geometries in which a single HMX crystal is subjected to a shock condition. Our current progress towards developing microstructural models of HMX/binder composite will also be discussed.

Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet

NASA Astrophysics Data System (ADS)

Matin, Meisam Habibi; Nobari, Mohammad Reza Heirani; Jahangiri, Pouyan

This article deals with a numerical study of entropy analysis in mixed convection MHD flow of nanofluid over a non-linear stretching sheet taking into account the effects of viscous dissipation and variable magnetic field. The nanofluid is made of such nano particles as SiO2 with pure water as a base fluid. To analyze the problem, at first the boundary layer equations are transformed into non-linear ordinary equations using a similarity transformation. The resultant equations are then solved numerically using the Keller-Box scheme based on the implicit finite-difference method. The effects of different non-dimensional governing parameters such as magnetic parameter, nanoparticles volume fraction, Nusselt, Richardson, Eckert, Hartman, Brinkman, Reynolds and entropy generation numbers are investigated in details. The results indicate that increasing the nano particles to the base fluids causes the reduction in shear forces and a decrease in stretching sheet heat transfer coefficient. Also, decreasing the magnetic parameter and increasing the Eckert number result in improves heat transfer rate. Furthermore, the surface acts as a strong source of irreversibility due to the higher entropy generation number near the surface.

Unified gas-kinetic scheme with multigrid convergence for rarefied flow study

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2017-09-01

The unified gas kinetic scheme (UGKS) is based on direct modeling of gas dynamics on the mesh size and time step scales. With the modeling of particle transport and collision in a time-dependent flux function in a finite volume framework, the UGKS can connect the flow physics smoothly from the kinetic particle transport to the hydrodynamic wave propagation. In comparison with the direct simulation Monte Carlo (DSMC) method, the current equation-based UGKS can implement implicit techniques in the updates of macroscopic conservative variables and microscopic distribution functions. The implicit UGKS significantly increases the convergence speed for steady flow computations, especially in the highly rarefied and near continuum regimes. In order to further improve the computational efficiency, for the first time, a geometric multigrid technique is introduced into the implicit UGKS, where the prediction step for the equilibrium state and the evolution step for the distribution function are both treated with multigrid acceleration. More specifically, a full approximate nonlinear system is employed in the prediction step for fast evaluation of the equilibrium state, and a correction linear equation is solved in the evolution step for the update of the gas distribution function. As a result, convergent speed has been greatly improved in all flow regimes from rarefied to the continuum ones. The multigrid implicit UGKS (MIUGKS) is used in the non-equilibrium flow study, which includes microflow, such as lid-driven cavity flow and the flow passing through a finite-length flat plate, and high speed one, such as supersonic flow over a square cylinder. The MIUGKS shows 5-9 times efficiency increase over the previous implicit scheme. For the low speed microflow, the efficiency of MIUGKS is several orders of magnitude higher than the DSMC. Even for the hypersonic flow at Mach number 5 and Knudsen number 0.1, the MIUGKS is still more than 100 times faster than the DSMC method for obtaining a convergent steady state solution.

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

PubMed

Lin, Huiming; Fu, Bo; Qin, Guoyou; Zhu, Zhongyi

2017-12-01

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study. © 2017, The International Biometric Society.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Experimental and numerical investigation of slabs on ground subjected to concentrated loads

NASA Astrophysics Data System (ADS)

Øverli, Jan

2014-09-01

An experimental program is presented where a slab on ground is subjected to concentrated loading at the centre, the edges and at the corners. Analytical solutions for the ultimate load capacity fit well with the results obtained in the tests. The non-linear behaviour of the slab is captured by performing nonlinear finite element analyses. The soil is modelled as a no-tension bedding and a smeared crack approach is employed for the concrete. Through a parametric study, the finite element model has been used to assess the influence of subgrade stiffness and shrinkage. The results indicate that drying shrinkage can cause severe cracking in slabs on grade.

Analysis of multi lobe journal bearings with surface roughness using finite difference method

NASA Astrophysics Data System (ADS)

PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.

2018-04-01

Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.

Research and development program for non-linear structural modeling with advanced time-temperature dependent constitutive relationships

NASA Technical Reports Server (NTRS)

Walker, K. P.

1981-01-01

Results of a 20-month research and development program for nonlinear structural modeling with advanced time-temperature constitutive relationships are reported. The program included: (1) the evaluation of a number of viscoplastic constitutive models in the published literature; (2) incorporation of three of the most appropriate constitutive models into the MARC nonlinear finite element program; (3) calibration of the three constitutive models against experimental data using Hastelloy-X material; and (4) application of the most appropriate constitutive model to a three dimensional finite element analysis of a cylindrical combustor liner louver test specimen to establish the capability of the viscoplastic model to predict component structural response.

Efficiency and large deviations in time-asymmetric stochastic heat engines

DOE PAGES

Gingrich, Todd R.; Rotskoff, Grant M.; Vaikuntanathan, Suriyanarayanan; ...

2014-10-24

In a stochastic heat engine driven by a cyclic non-equilibrium protocol, fluctuations in work and heat give rise to a fluctuating efficiency. Using computer simulations and tools from large deviation theory, we have examined these fluctuations in detail for a model two-state engine. We find in general that the form of efficiency probability distributions is similar to those described by Verley et al (2014 Nat. Commun. 5 4721), in particular featuring a local minimum in the long-time limit. In contrast to the time-symmetric engine protocols studied previously, however, this minimum need not occur at the value characteristic of a reversible Carnot engine. Furthermore, while the local minimum may reside at the global minimum of a large deviation rate function, it does not generally correspond to the least likely efficiency measured over finite time. Lastly, we introduce a general approximation for the finite-time efficiency distribution,more » $$P(\\eta )$$, based on large deviation statistics of work and heat, that remains very accurate even when $$P(\\eta )$$ deviates significantly from its large deviation form.« less

APPLICATION OF NEURAL NETWORK ALGORITHMS FOR BPM LINEARIZATION

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

Musson, John C.; Seaton, Chad; Spata, Mike F.

2012-11-01

Stripline BPM sensors contain inherent non-linearities, as a result of field distortions from the pickup elements. Many methods have been devised to facilitate corrections, often employing polynomial fitting. The cost of computation makes real-time correction difficult, particulalry when integer math is utilized. The application of neural-network technology, particularly the multi-layer perceptron algorithm, is proposed as an efficient alternative for electrode linearization. A process of supervised learning is initially used to determine the weighting coefficients, which are subsequently applied to the incoming electrode data. A non-linear layer, known as an activation layer, is responsible for the removal of saturation effects. Implementationmore » of a perceptron in an FPGA-based software-defined radio (SDR) is presented, along with performance comparisons. In addition, efficient calculation of the sigmoidal activation function via the CORDIC algorithm is presented.« less

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

A quantum relaxation-time approximation for finite fermion systems

NASA Astrophysics Data System (ADS)

Reinhard, P.-G.; Suraud, E.

2015-03-01

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

NASA Astrophysics Data System (ADS)

Zhai, Ding; Lu, Anyang; Li, Jinghao; Zhang, Qingling

2016-10-01

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman-Yakubovic-Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H- and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

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

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

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

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

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

NASA Astrophysics Data System (ADS)

Flores-Sola, Emilio J.; Berche, Bertrand; Kenna, Ralph; Weigel, Martin

2015-01-01

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour by simulating one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.

A finite element solution algorithm for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

Scalable algorithms for three-field mixed finite element coupled poromechanics

NASA Astrophysics Data System (ADS)

Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano

2016-12-01

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

Non-Abelian gauge preheating

NASA Astrophysics Data System (ADS)

Adshead, Peter; Giblin, John T.; Weiner, Zachary J.

2017-12-01

We study preheating in models where a scalar inflaton is directly coupled to a non-Abelian S U (2 ) gauge field. In particular, we examine m2ϕ2 inflation with a conformal, dilatonlike coupling to the non-Abelian sector. We describe a numerical scheme that combines lattice gauge theory with standard finite difference methods applied to the scalar field. We show that a significant tachyonic instability allows for efficient preheating, which is parametrically suppressed by increasing the non-Abelian self-coupling. Additionally, we comment on the technical implementation of the evolution scheme and setting initial conditions.

Generation of the September 29, 2009 Samoa Tsunami: Examination of a Possible Non-Double Couple Component (Invited)

NASA Astrophysics Data System (ADS)

Geist, E. L.; Kirby, S. H.; Ross, S.; Dartnell, P.

2009-12-01

A non-double couple component associated with the Mw=8.0 September 29, 2009 Samoa earthquake is investigated to explain direct tsunami arrivals at deep-ocean pressure sensors (i.e., DART stations). In particular, we seek a tsunami generation model that correctly predicts the polarity of first motions: negative at the Apia station (#51425) NW of the epicenter and positive at the Tonga (#51426) and Aukland (#54401) stations south of the epicenter. Slip on a single, finite fault corresponding to either nodal plane of the best-fitting double couple fails to predict the positive first-motion polarity observed at the southerly (Tonga and Aukland) DART stations. The Samoa earthquake has a significant non-double component as measured by the compensated linear vector dipole (CLVD) ratio that ranges from |ɛ|=0.15 (USGS CMT) to |ɛ| =0.37 (Global CMT). To test what effect the non-double component has on tsunami generation, the static elastic displacement field at the sea floor is computed from the full moment tensor. This displacement field represents the initial conditions for tsunami propagation computed using a finite-difference approximation to the linear shallow-water wave equations. The tsunami waveforms calculated from the full moment tensor are consistent with the observed polarities at all of the DART stations. The static displacement field is then decomposed into double-couple and non-double couple components to determine the relative contribution of each to the tsunami wavefield. Although a point-source approximation to the tsunami source is typically inadequate at near-field and regional distances, finite-fault inversions of the 2009 Samoa earthquake indicate that peak slip is spatially concentrated near the hypocenter, suggesting that the point-source representation may be acceptable in this case. Generation of the 2009 Samoa tsunami may involve earthquake rupture on multiple faults and/or along curved faults, both of which are observed from multibeam bathymetry in the epicentral region. The exact rupture path of the earthquake is presently unclear. It is evident from seismological and tsunami observations of the 2009 Samoa event, however, that uniform slip on a single, planar fault cannot explain all aspects of the observed tsunami wavefield.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Clumpy Disks as a Testbed for Feedback-regulated Galaxy Formation

NASA Astrophysics Data System (ADS)

Mayer, Lucio; Tamburello, Valentina; Lupi, Alessandro; Keller, Ben; Wadsley, James; Madau, Piero

2016-10-01

We study the dependence of fragmentation in massive gas-rich galaxy disks at z > 1 on stellar feedback schemes and hydrodynamical solvers, employing the GASOLINE2 SPH code and the lagrangian mesh-less code GIZMO in finite mass mode. Non-cosmological galaxy disk runs with the standard delayed-cooling blastwave feedback are compared with runs adopting a new superbubble feedback, which produces winds by modeling the detailed physics of supernova-driven bubbles and leads to efficient self-regulation of star formation. We find that, with blastwave feedback, massive star-forming clumps form in comparable number and with very similar masses in GASOLINE2 and GIZMO. Typical clump masses are in the range 107-108 M ⊙, lower than in most previous works, while giant clumps with masses above 109 M ⊙ are exceedingly rare. By contrast, superbubble feedback does not produce massive star-forming bound clumps as galaxies never undergo a phase of violent disk instability. In this scheme, only sporadic, unbound star-forming overdensities lasting a few tens of Myr can arise, triggered by non-linear perturbations from massive satellite companions. We conclude that there is severe tension between explaining massive star-forming clumps observed at z > 1 primarily as the result of disk fragmentation driven by gravitational instability and the prevailing view of feedback-regulated galaxy formation. The link between disk stability and star formation efficiency should thus be regarded as a key testing ground for galaxy formation theory.

Incomplete Gröbner basis as a preconditioner for polynomial systems

NASA Astrophysics Data System (ADS)

Sun, Yang; Tao, Yu-Hui; Bai, Feng-Shan

2009-04-01

Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.

Active Vibration damping of Smart composite beams based on system identification technique

NASA Astrophysics Data System (ADS)

Bendine, Kouider; Satla, Zouaoui; Boukhoulda, Farouk Benallel; Nouari, Mohammed

2018-03-01

In the present paper, the active vibration control of a composite beam using piezoelectric actuator is investigated. The space state equation is determined using system identification technique based on the structure input output response provided by ANSYS APDL finite element package. The Linear Quadratic (LQG) control law is designed and integrated into ANSYS APDL to perform closed loop simulations. Numerical examples for different types of excitation loads are presented to test the efficiency and the accuracy of the proposed model.

Identification of material parameters for plasticity models: A comparative study on the finite element model updating and the virtual fields method

NASA Astrophysics Data System (ADS)

Martins, J. M. P.; Thuillier, S.; Andrade-Campos, A.

2018-05-01

The identification of material parameters, for a given constitutive model, can be seen as the first step before any practical application. In the last years, the field of material parameters identification received an important boost with the development of full-field measurement techniques, such as Digital Image Correlation. These techniques enable the use of heterogeneous displacement/strain fields, which contain more information than the classical homogeneous tests. Consequently, different techniques have been developed to extract material parameters from full-field measurements. In this study, two of these techniques are addressed, the Finite Element Model Updating (FEMU) and the Virtual Fields Method (VFM). The main idea behind FEMU is to update the parameters of a constitutive model implemented in a finite element model until both numerical and experimental results match, whereas VFM makes use of the Principle of Virtual Work and does not require any finite element simulation. Though both techniques proved their feasibility in linear and non-linear constitutive models, it is rather difficult to rank their robustness in plasticity. The purpose of this work is to perform a comparative study in the case of elasto-plastic models. Details concerning the implementation of each strategy are presented. Moreover, a dedicated code for VFM within a large strain framework is developed. The reconstruction of the stress field is performed through a user subroutine. A heterogeneous tensile test is considered to compare FEMU and VFM strategies.

An Adaptive Multiscale Finite Element Method for Large Scale Simulations

DTIC Science & Technology

2015-09-28

Illinois at Urbana-Champaign Abstract Hypersonic vehicles are subjected to extreme acoustic, thermal and mechanical loading with strong spatial and temporal...07/15/2012 Reporting Period End Date 07/14/2015 Abstract Hypersonic vehicles are subjected to extreme acoustic, thermal and mechanical loading with...gradients and for extended periods of time. Long duration, 3-D simulations of non-linear response of these vehicles , is prohibitively expensive using

Electron Interactions with Non-Linear Polyatomic Molecules and Their Radicals

DTIC Science & Technology

1993-12-01

developed which generates SCE quantities from molecular wave functions. This progress was realized in terms of some actual calculations on some molecules...section 4.A describes the basics of the Partial Differential Equation Theory; section 4.B describes the generalization to a finite element...Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations. This technical report has been reviewed and

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

NASA Astrophysics Data System (ADS)

Raman, Venkatramanan

A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor.

Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

NASA Astrophysics Data System (ADS)

Coco, Armando; Russo, Giovanni

2018-05-01

In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

On the stimulated Raman sidescattering in inhomogeneous plasmas: revisit of linear theory and three-dimensional particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Xiao, C. Z.; Zhuo, H. B.; Yin, Y.; Liu, Z. J.; Zheng, C. Y.; Zhao, Y.; He, X. T.

2018-02-01

Stimulated Raman sidescattering (SRSS) in inhomogeneous plasma is comprehensively revisited on both theoretical and numerical aspects due to the increasing concern of its detriments to inertial confinement fusion. Firstly, two linear mechanisms of finite beam width and collisional effects that could suppress SRSS are investigated theoretically. Thresholds for the eigenmode and wave packet in a finite-width beam are derived as a supplement to the theory proposed by Mostrom and Kaufman (1979 Phys. Rev. Lett. 42 644). Collisional absorption of SRSS is efficient at high-density plasma and high-Z material, otherwise, it allows emission of sidescattering. Secondly, we have performed the first three-dimensional particle-in-cell simulations in the context of SRSS to investigate its linear and nonlinear effects. Simulation results are qualitatively agreed with the linear theory. SRSS with the maximum growth gain is excited at various densities, grows to an amplitude that is comparable with the pump laser, and evolutes to lower densities with a large angle of emergence. Competitions between SRSS and other parametric instabilities such as stimulated Raman backscattering, two-plasmon decay, and stimulated Brillouin scattering are discussed. These interaction processes are determined by gains, occurrence sites, scattering geometries of each instability, and will affect subsequent evolutions. Nonlinear effects of self-focusing and azimuthal magnetic field generation are observed to be accompanied with SRSS. In addition, it is found that SRSS is insensitive to ion motion, collision (low-Z material), and electron temperature.

Entropic anomaly and maximal efficiency of microscopic heat engines.

PubMed

Bo, Stefano; Celani, Antonio

2013-05-01

The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We show that-as a consequence of the recently discovered entropic anomaly-quasistatic engines, whose efficiency is maximal in a fluid at uniform temperature, have in fact vanishing efficiency in the presence of temperature gradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured.