Accession Number : ADA117112

Title :   Vectorized Sparse Elimination.

Descriptive Note : Interim technical rept. 1 May 81-30 Apr 82,

Corporate Author : MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB

Personal Author(s) : Calahan,D A

PDF Url : ADA117112

Report Date : May 1982

Pagination or Media Count : 12

Abstract : Single topic of general sparse matrix solution using scalar processors may be broken into specialized areas of study when implementation on vector architectures is considered. First, highly sparse matrices, usually represented ODE/algebraic-modeled systems, are easily decoupled by re-ordering. At a minimum, locally-decoupled equations may be solved in pipelined scalar mode; if the decoupled subsystems can be arranged (a) to have identical sparsity, and (b) to be stored a constant stride apart, then a simultaneous sparse solver may be invoked and a vector solution obtained. As sparse systems become locally coupled - as occurs in finite element and finite difference problems - then vectors are easily defined within the coupled subsystems. It is worth making a further distinction between: (a) intra-nodal or intra-element coupling, where the dimension of dense submatrices is proportional to the number of unknowns/node or unknowns/finite element, and (b) inter-nodal or inter-element, where the coupling between grid nodes or finite elements determines the vector length. Banded and profile matrices result from the latter. The associated vector lengths are the products of the number of unknown/node (element) and the number of coupled nodes. These lengths are therefore always longer than in the former case, so that common bandsolvers offer the highest performance of any sparse solvers.

Descriptors :   *Parallel processors, *Scalar functions, *Vector analysis, *Sparse matrix, Simultaneous equations, Algorithms, Signal processing, Circuit analysis, Kernel functions, Finite element analysis, Finite difference theory, Differential equations

Subject Categories : Theoretical Mathematics
      Computer Hardware

Distribution Statement : APPROVED FOR PUBLIC RELEASE