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DOE OSTI2023

Sierra/Solid Mechanics 5.16 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

36 MATERIALS SCIENCE↗

NASA NTRS1985

Methods for design and evaluation of integrated hardware-software systems for concurrent computation

Research activities and publications are briefly summarized. The major tasks reviewed are: (1) VAX implementation of the PISCES parallel programming environment; (2) Apollo workstation network implementation of the PISCES environment; (3) FLEX implementation of the PISCES environment; (4) sparse matrix iterative solver in PSICES Fortran; (5) image processing application of PISCES; and (6) a formal model of concurrent computation being developed.

Pratt, T. W.↗

NASA NTRS1990

Fast secant methods for the iterative solution of large nonsymmetric linear systems

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

Deuflhard, Peter↗

NASA NTRS1990

Optimal parallel solution of sparse triangular systems

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

Alvarado, Fernando L.↗

NASA NTRS1993

Fast structural design and analysis via hybrid domain decomposition on massively parallel processors

A hybrid domain decomposition framework for static, transient and eigen finite element analyses of structural mechanics problems is presented. Its basic ingredients include physical substructuring and /or automatic mesh partitioning, mapping algorithms, 'gluing' approximations for fast design modifications and evaluations, and fast direct and preconditioned iterative solvers for local and interface subproblems. The overall methodology is illustrated with the structural design of a solar viewing payload that is scheduled to fly in March 1993. This payload has been entirely designed and validated by a group of undergraduate students at the University of Colorado using the proposed hybrid domain decomposition approach on a massively parallel processor. Performance results are reported on the CRAY Y-MP/8 and the iPSC-860/64 Touchstone systems, which represent both extreme parallel architectures. The hybrid domain decomposition methodology is shown to outperform leading solution algorithms and to exhibit an excellent parallel scalability.

Farhat, Charbel↗

NASA NTRS1996

A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps

We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement domain decomposition methods, and which successfully addresses the problems of subdomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.

Farhat, Charbel↗

NASA NTRS2001

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

Kassab, A. J.↗

NASA NTRS2005

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Nguyen, Duc T.↗

NASA NTRS2011

Efficient Kriging Algorithms

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Memarsadeghi, Nargess↗

NASA NTRS2014

Propulsion System Simulation Using the Toolbox for the Modeling and Analysis of Thermodynamic System T-MATS

A simulation toolbox has been developed for the creation of both steady-state and dynamic thermodynamic software models. This paper describes the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS), which combines generic thermodynamic and controls modeling libraries with a numerical iterative solver to create a framework for the development of thermodynamic system simulations, such as gas turbine engines. The objective of this paper is to present an overview of T-MATS, the theory used in the creation of the module sets, and a possible propulsion simulation architecture. A model comparison was conducted by matching steady-state performance results from a T-MATS developed gas turbine simulation to a well-documented steady-state simulation. Transient modeling capabilities are then demonstrated when the steady-state T-MATS model is updated to run dynamically.

gas path dynamics↗

NASA NTRS2014

T-MATS Toolbox for the Modeling and Analysis of Thermodynamic Systems

The Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS) is a MATLABSimulink (The MathWorks Inc.) plug-in for creating and simulating thermodynamic systems and controls. The package contains generic parameterized components that can be combined with a variable input iterative solver and optimization algorithm to create complex system models, such as gas turbines.

system modeling↗

NASA NTRS2014

Propulsion System Simulation Using the Toolbox for the Modeling and Analysis of Thermodynamic System (T-MATS)

A simulation toolbox has been developed for the creation of both steady-state and dynamic thermodynamic software models. This presentation describes the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS), which combines generic thermodynamic and controls modeling libraries with a numerical iterative solver to create a framework for the development of thermodynamic system simulations, such as gas turbine engines. The objective of this presentation is to present an overview of T-MATS, the theory used in the creation of the module sets, and a possible propulsion simulation architecture.

aerothermodynamics↗

NASA NTRS2014

Propulsion System Simulation Using the Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS)

aerothermodynamics↗

NASA NTRS2011

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

sound-soft acoustic scattering↗

NASA NTRS2021

Evaluation of Higher-order Quadrature Schemes in Improving Computational Efficiency for Orientation-averaged Single-Scattering Properties of Nonspherical Ice Particles

We evaluate several high-order quadrature schemes for accuracy and efficacy in obtaining orientation-averaged single-scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation-averaged SSPs derived from realistic hydrometeors as input to radiative transfer Models (RTMs). The DDA has been a popular choice for single-scattering calculations, due to its versatility with respect to target geometry. However, being iterative-solver-based (ISB), the most used DDA codes, e.g. DDSCAT and ADDA, must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation-averages can increase drastically and so does the computation cost incurred by the ISB-DDA methods. MIDAS is a Direct-Solver-Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB-DDA methods. MIDAS, when combined with high-order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM-ready SSPs of complex-shaped hydrometeors than existing ISB-DDA methods, with the native quadrature schemes they offer.

Ines Fenni↗

NASA NTRSDate not supplied

Performance Optimization Methods for a Memory-Bound, Unstructured-Grid CFD Application on Massively Parallel GPU Platforms

Computational performance of the FUN3D unstructured-grid computational fluid dynamics (CFD) application on massively parallel GPU environments is memory-bound and highly dependent upon efficient reads from and atomic updates to the irregular cell-, edge-, and node-based data structures. In this talk, we present recent efforts into optimizing select performance-critical kernels on NVIDIA Tesla V100 and A100 GPUs and AMD CDNA MI100 GPUs. A novel use of L2 cache residency controls and asynchronous loads into on-chip shared memory are explored on the A100 GPU for the sparse iterative solver, which is dominated by mixed-precision, sparse matrix vector multiplication. Demonstrations show that these methods improve global memory bandwidth utilization by 13.5% on the A100 GPU. Several techniques are also presented that use registers and/or shared memory to facilitate array transposition and aggregation which combine to reduce the frequency and increase the cache efficiency of floating-point atomic updates to the irregular data structures. These methods are demonstrated to improve the kernel throughput by nearly 500% on select kernels on the AMD MI100 over atomic updates directly to global memory. Overall, both V100 and A100 GPUs outperformed the MI100 GPU on kernels dominated by double-precision atomic updates; however, the techniques demonstrated here reduced the performance gap and improved the MI100 performance.

GPU CPU unstructured CFD memory↗

DOE OSTI2017

Xyce

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.

Thomquist, Heidi K.↗

DOE OSTI2023

An efficient solution of low-frequency magnetic problems with voltage sources using all-frequency stable formulation

The modeling and simulation of magnetic problems at low frequencies are considered in this paper. When excited with a voltage source, conduction current is induced in the circuit of interest, which generates the magnetic field. This type of problems is modeled using the all-frequency stable formulation, which employs the potential description of fields with an inhomogeneous Coulomb gauge. With the aid of the stable formulation, the low-frequency breakdown problem is circumvented and both electric and magnetic fields can be solved in a single simulation. To solve large magnetic problems efficiently, it is necessary to employ an iterative solver with an efficient preconditioner. In this work, a preconditioner based on the incomplete LU decomposition is constructed and applied in a wide frequency range. Several numerical examples are given to demonstrate the performance of the proposed method.

Mekonnen, Minyechil↗