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This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.
Parallel adaptive mesh refinement (AMR) is an important numerical technique that leads to the efficient solution of many physical and engineering problems.
Computing speed is leaping forward by several orders of magnitude each decade. Engineers and scientists gathered at a NASA Langley symposium to discuss these exciting trends as they apply to parallel computational methods for large-scale structural analysis and design. Among the topics discussed were: large-scale static analysis; dynamic, transient, and thermal analysis; domain decomposition (substructuring); and nonlinear and numerical methods.
In this paper the implementation of an ADI method for solving the diffusion equation on three parallel/vector computers is discussed. The computers were chosen so as to encompass a variety of architectures. They are the MPP, an SIMD machine with 16-Kbit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2, an MIMD machine with four vector processors. The Gaussian elimination algorithm is used to solve a set of tridiagonal systems on the Flex/32 and Cray/2 while the cyclic elimination algorithm is used to solve these systems on the MPP. The implementation of the method is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally conclusions are presented.
The Lanczos (1950), multisectioning, and subspace iteration sequential methods for vibration analysis presently used as bases for three parallel algorithms are noted, in the aftermath of three example problems, to maintain reasonable accuracy in the computation of vibration frequencies. Significant computation time reductions are obtained as the number of processors increases. An analysis is made of the performance of each method, in order to characterize relative strengths and weaknesses as well as to identify those parameters that most strongly affect computation efficiency.
This paper contains a overview of the methods used in decomposing solutions to scattering problems onto coarse-grained parallel processors. Initially, a short summary of relevant computer architecture is presented as background to the subsequent discussion. After the introduction of a programming model for problem decomposition, specific decompositions of finite difference time domain, finite element, and integral equation solutions to Maxwell's equations are presented. The paper concludes with an outline of possible software-assisted decomposition methods and a summary.
A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.
A new numerical algorithm for the solution of large-order eigenproblems typically encountered in linear elastic finite element systems is presented. The architecture of parallel processing is used in the algorithm to achieve increased speed and efficiency of calculations. The algorithm is based on the frontal technique for the solution of linear simultaneous equations and the modified subspace eigenanalysis method for the solution of the eigenproblem. The advantages of this new algorithm in parallel computer architecture are discussed.
A novel method for solution of the acoustic wave equation is.
Advanced technologies with the capability of detecting microbial contamination remain an integral tool for the next stage of space agency proposed exploration missions. To maintain a clean, operational spacecraft environment with minimal potential for forward contamination, such technology is a necessity, particularly, the ability to analyze samples near the point of collection and in real-time both for conducting biological scientific experiments and for performing routine monitoring operations. Multiple molecular methods for detecting microbial contamination are available, but many are either too large or not validated for use on spacecraft. Two methods, the adenosine- triphosphate (ATP) and Limulus Amebocyte Lysate (LAL) assays have been approved by the NASA Planetary Protection Office for the assessment of microbial contamination on spacecraft surfaces. We present the first parallel field analysis of microbial contamination pre- and post-cleaning using these two methods as well as universal primer-based polymerase chain reaction (PCR).
This paper describes the implementation of a parallelized method of moments (MOM) code into an interactive workstation environment. The workstation allows interactive solid body modeling and mesh generation, MOM analysis, and the graphical display of results. After describing the parallel computing environment, the implementation and results of parallelizing a general MOM code are presented in detail.
This report presents a method for doing load-flow analysis of a power system by using a decomposition approach. The power system for the Space Shuttle is used as a basis to build a model for the load-flow analysis. To test the decomposition method for doing load-flow analysis, simulations were performed on power systems of 16, 25, 34, 43, 52, 61, 70, and 79 nodes. Each of the power systems was divided into subsystems and simulated under steady-state conditions. The results from these tests have been found to be as accurate as tests performed using a standard serial simulator. The division of the power systems into different subsystems was done by assigning a processor to each area. There were 13 transputers available, therefore, up to 13 different subsystems could be simulated at the same time. This report has preliminary results for a load-flow analysis using a decomposition principal. The report shows that the decomposition algorithm for load-flow analysis is well suited for parallel processing and provides increases in the speed of execution.
The paper considers the 'ijk forms' of LU and Cholesky factorization on certain parallel computers. This extends an earlier analysis for vector computers. Attention is restricted to local memory systems with processors that may or may not have vector capability. Special attention is given to bus architectures but qualitative analyses are given for other interconnection systems.
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.
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The invention analyzes areas of conditions with an expert knowledge base of rules using plural separate nodes which fire respective rules of said knowledge base, each of said rules upon being fired altering certain of said conditions predicated upon the existence of other said conditions. The invention operates by constructing a P representation of all pairs of said rules which are input dependent or output dependent; constructing a C representation of all pairs of said rules which are communication dependent or input dependent; determining which of the rules are ready to fire by matching the predicate conditions of each rule with the conditions of said set; enabling said node means to simultaneously fire those of the rules ready to fire which are defined by said P representation as being free of input and output dependencies; and communicating from each node enabled by said enabling step the alteration of conditions by the corresponding rule to other nodes whose rules are defined by said C matrix means as being input or communication dependent upon the rule of said enabled node.
This viewgraph presentation reviews the use Adaptive Mesh Refinement (AMR) in simulating the Crustal Dynamics of Earth's Surface. AMR simultaneously improves solution quality, time to solution, and computer memory requirements when compared to generating/running on a globally fine mesh. The use of AMR in simulating the dynamics of the Earth's Surface is spurred by future proposed NASA missions, such as InSAR for Earth surface deformation and other measurements. These missions will require support for large-scale adaptive numerical methods using AMR to model observations. AMR was chosen because it has been successful in computation fluid dynamics for predictive simulation of complex flows around complex structures.
Eigenvalue analyses of complex structures is a computationally intensive task which can benefit significantly from new and impending parallel computers. This study reports on a parallel computer implementation of the Lanczos method for free vibration analysis. The approach used here subdivides the major Lanczos calculation tasks into subtasks and introduces parallelism down to the subtask levels such as matrix decomposition and forward/backward substitution. The method was implemented on a commercial parallel computer and results were obtained for a long flexible space structure. While parallel computing efficiency for the Lanczos method was good for a moderate number of processors for the test problem, the greatest reduction in time was realized for the decomposition of the stiffness matrix, a calculation which took 70 percent of the time in the sequential program and which took 25 percent of the time on eight processors. For a sample calculation of the twenty lowest frequencies of a 486 degree of freedom problem, the total sequential computing time was reduced by almost a factor of ten using 16 processors.