Vectorized Sparse Elimination.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1982
- Accession Number
- ADA117112
Entities
People
- Donald Albert Calahan
Organizations
- University of Michigan