Scalability Analysis of Linear Equation Solvers for Sparse Positive Definite Systems

Report No. ARL-TR-3076
Authors: Robert L. Davis, Brian J. Henz, and Dale R. Shires
Date/Pages: September 2003; 34 pages
Abstract: The U.S. Army Research Laboratory (ARL) is currently developing a suite of parallel codes to model liquid composite molding (LCM) manufacturing processes. This software suite utilizes the finite element method in order to model the LCM process, thus requiring the solution of sparse linear equations. Code profiles have revealed that, similar to other scientific computing codes, the majority of the execution time is spent solving large systems of linear equations. Accordingly, it is desirable to use the most efficient solver package or combination of packages to quickly solve large sparse symmetric positive definite systems of equations as found in the LCM simulation software. A collection of linear equation solvers is being developed at ARL that the process simulation code accesses in order to automatically select the optimal solver for the given problem at runtime. The optimal solver is determined by considering factors such as architecture type, number of processors, matrix size and type, etc. This report evaluates several different linear equation solver packages to determine their applicability to this and other unstructured grid problems. Several factors, including accuracy, error, scalability, and runtime, are analyzed and reported.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2003