QMR and TFQMR Methods for Sparse Nonsymmetric Problems on Massively Parallel Systems
Basermann, Achim
Jülich Supercomputing Center; JSC
Zentralinstitut für Angewandte Mathematik; ZAM
The Mathematics of Numerical Analysis
Providence, RI American Mathematical Society 1996
59-76
0-8218-0530-4
AMS-SIAM Summer Seminar in Applied Mathematics, Park City (USA), 1995-07-17 - 1995-08-11
Contribution to a book
Contribution to a conference proceedings
ohne Topic
Lectures in applied mathematics 32
Much of the supercomputer research so far has concentrated on implementations of iterative methods for sparse symmetric positive definite matrices, in particular the preconditioned conjugate gradient algorithm, and an understanding of the parallel issues of this algorithm is emerging. Much less work has been done regarding iterative methods for nonsymmetric problems. In this article, parallel implementations of two important algorithms for nonsymmetric systems of equations, namely, the quasi-minimal residual (QMR) and transpose-free QMR (TFQMR) algorithms for solving sparse nonsymmetric systems of linear equations are investigated. The developed data distribution and communication scheme for multiprocessors with distributed memory are based on the analysis of the indices of the non-zero matrix elements. On a PARAGON XP/S 10 with 140 processors, the parallel variants of both QMR and TFQMR show an advantageous scaling behavior for matrices with different sparsity patterns stemming from real finite element applications.