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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1992

Unsteady flowfield simulation of ducted prop-fan configurations

A technique for the simulation of unsteady flows in and around complex rotating machinery is presented. Additional domain decomposition mechanisms are introduced which extend the range of applicability of software developed for the time-accurate simulation of rotating machinery flowfields. The flow models uses the unsteady 3D Euler equations, discretized as a finite-volume method, utilizing a high-resolution approximate Riemann solver for cell interface flux definitions. Multiblock domain decomposition is used to partition the field radially, axially, as well as circumferentially into an ordered arrangement of blocks which exhibit varying degrees of similarity. A general high-order numerical scheme is applied to satisfy the geometric conservation law. Two configurations are presented - ducted single rotation prop-fan and a rotor-deswirl vane combination which form a single stage fan. Comparisons are made to other numerical solutions for these geometries and to available experimental data.

Janus, J. M.↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Impacts of Hybrid Parallelism and Vectorization on the Performance of Newton-Krylov Methods in Computational Aerodynamics

Finding the numerical solution of moderate and high-fidelity aerodynamics problems on modern computer architectures involves, 1) decomposing the domain into smaller regions of nearly equal size, and 2) allocating computational resources for calculations on each domain and communication between domains. Modern computer clusters are composed from hierarchies of processing, memory, and communication resources with varying capabilities and latencies.This paper focuses on the combination of domain decomposition provided by ParMETIS [1]and Newton-Krylov Methods [2–5] for the solution of Computational Aerodynamics problems of interest to NASA. Herein, trade-offs encountered when mapping aerodynamics problems to modern computer architectures are explored through examples and discussions of trade-offs in parallelism from MPI [6], Open MP [7], and vectorization as partition sizes and computational resources are varied. An example of the impact that domain decomposition and MPI+OpenMPresource allocation can have on an adjoint calculation is presented in this abstract. The full paper will include more detailed examples, discussions of difficulties and potential methods to overcome them, and topics identified for future study.

Computational Aerodynamics, Hybrid Parallelism, Ve↗
NASA NTRS1991

A Lagrange multiplier based divide and conquer finite element algorithm

A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.

Farhat, C.↗
NASA NTRS1997

RNS Applications for Interacting Sub- and Supersonic Flows

A solution based grid adaptation method that combines elements of the multigrid method for solution acceleration and the domain decomposition philosophy for grid optimization is described. Unlike other solution based adaptive gridding schemes, wherein the overhead of recomputing the grid and re-evaluating the solution on the adapted grid leads to higher computational costs compared to a non-adapted calculation, the present methodology reduces the computational time required to obtain the solution. The computational effort involved in the present calculation is significantly lower than a non-adapted calculation that utilizes the multigrid method purely as a convergence acceleration tool. In addition to convergence acceleration, the multigrid framework provides a mechanism of information transfer from regions wherein grid refinement is specified to unrefined coarse grid regions. The basis for domain decomposition in the current procedure is the variation in grid refinement requirements for each coordinate direction in different portions of the flow field. The method is demonstrated herein on an efficient set of governing equations termed the reduced Navier Stokes equations, applied in conjunction with a set of physical boundary conditions. The governing equations are discretized through a pressure based flux splitting procedure that is uniformly applicable from incompressible to supersonic Mach numbers.

Rubin, Stanley G.↗
DOE OSTI2022

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding of their convergence and generalization properties remains unexplored. In this study, we take an initial step towards understanding how and when XPINNs outperform PINNs. Specifically, for general multilayer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem and a posterior generalization bound via the posterior matrix norms of the networks after optimization. Moreover, based on our bounds, we analyze the conditions under which XPINNs improve generalization. Concretely, our theory shows that the key building block of XPINN, namely, the domain decomposition, introduces a tradeoff for generalization. On the one hand, XPINNs decompose the complex PDE solution into several simple parts, which decreases the complexity needed to learn each part and boosts generalization. On the other hand, decomposition leads to less training data being available in each subdomain, and hence such a model is typically prone to overfitting and may become less generalizable. Empirically, we choose five PDEs to show when XPINNs perform better than, similar to, or worse than PINNs, hence demonstrating and justifying our new theory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Extending substructure based iterative solvers to multiple load and repeated analyses

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Farhat, Charbel↗
DOE OSTI2022

A weighted state redistribution algorithm for embedded boundary grids

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions. Second, we discuss several algorithmic changes and improvements motivated by the more complicated cut cell geometries that can occur in higher dimensions. In particular, we introduce a weighted version with less dissipation in an easily generalizable framework. Third, we demonstrate that state redistribution can also stabilize a solution update that includes both advective and diffusive contributions. Notably, the stabilization algorithm is shown to be effective for incompressible as well as compressible reacting flows. Finally, we discuss the implementation of the algorithm for several exascale-ready simulation codes based on AMReX, demonstrating ease of use in combination with domain decomposition, hybrid parallelism and complex physics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

Airbreathing Propulsion System Analysis Using Multithreaded Parallel Processing

In this paper, parallel processing is used to analyze the mixing, and combustion behavior of hypersonic flow. Preliminary work for a sonic transverse hydrogen jet injected from a slot into a Mach 4 airstream in a two-dimensional duct combustor has been completed [Moon and Chung, 1996]. Our aim is to extend this work to three-dimensional domain using multithreaded domain decomposition parallel processing based on the flowfield-dependent variation theory. Numerical simulations of chemically reacting flows are difficult because of the strong interactions between the turbulent hydrodynamic and chemical processes. The algorithm must provide an accurate representation of the flowfield, since unphysical flowfield calculations will lead to the faulty loss or creation of species mass fraction, or even premature ignition, which in turn alters the flowfield information. Another difficulty arises from the disparity in time scales between the flowfield and chemical reactions, which may require the use of finite rate chemistry. The situations are more complex when there is a disparity in length scales involved in turbulence. In order to cope with these complicated physical phenomena, it is our plan to utilize the flowfield-dependent variation theory mentioned above, facilitated by large eddy simulation. Undoubtedly, the proposed computation requires the most sophisticated computational strategies. The multithreaded domain decomposition parallel processing will be necessary in order to reduce both computational time and storage. Without special treatments involved in computer engineering, our attempt to analyze the airbreathing combustion appears to be difficult, if not impossible.

Schunk, Richard Gregory↗
NASA NTRS1995

Implementation and Characterization of Three-Dimensional Particle-in-Cell Codes on Multiple-Instruction-Multiple-Data Massively Parallel Supercomputers

A three-dimensional electrostatic particle-in-cell (PIC) plasma simulation code has been developed on coarse-grain distributed-memory massively parallel computers with message passing communications. Our implementation is the generalization to three-dimensions of the general concurrent particle-in-cell (GCPIC) algorithm. In the GCPIC algorithm, the particle computation is divided among the processors using a domain decomposition of the simulation domain. In a three-dimensional simulation, the domain can be partitioned into one-, two-, or three-dimensional subdomains ("slabs," "rods," or "cubes") and we investigate the efficiency of the parallel implementation of the push for all three choices. The present implementation runs on the Intel Touchstone Delta machine at Caltech; a multiple-instruction-multiple-data (MIMD) parallel computer with 512 nodes. We find that the parallel efficiency of the push is very high, with the ratio of communication to computation time in the range 0.3%-10.0%. The highest efficiency (> 99%) occurs for a large, scaled problem with 64(sup 3) particles per processing node (approximately 134 million particles of 512 nodes) which has a push time of about 250 ns per particle per time step. We have also developed expressions for the timing of the code which are a function of both code parameters (number of grid points, particles, etc.) and machine-dependent parameters (effective FLOP rate, and the effective interprocessor bandwidths for the communication of particles and grid points). These expressions can be used to estimate the performance of scaled problems--including those with inhomogeneous plasmas--to other parallel machines once the machine-dependent parameters are known.

Lyster, P. M.↗