High-Performance Banded and Profile Equation Solvers for the CRAY-1. I. The Unsymmetric Case.
MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB
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This report describes algorithms, performance, applications, and user information associated with two equation-solving codes for the CRAY-1 1 Solution of a single banded matrix equation, unsymmetric in value but symmetric in structure 2 Solution of a single profile matrix equation, unsymmetric in value and in structure. Both solvers assume that the matrix is main-memory resident. The former partitions the matrix internally to achieve high performance. The latter requires a user-supplied blocking of the LU structure, an inconvenience compensated by higher performance in solution of finite difference and a finite element grids. These codes are available as part of a library of CAL-coded equation-solvers. The mathematical software described herein is the result of experimental research on vector algorithms for the direct solution of 2-D two dimensional finite difference and finite element grids. The latter code represents what is thought to be the best compromise between vectorizability, sparsity exploitation, and user convenience for such problems for the CRAY-1.
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- Computer Programming and Software