×

Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. I: Block Jacobi diagonalization. (English) Zbl 1106.65024

Summary: Linear systems in chemical physics often involve matrices with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix-vector products) in conjunction with a block Jacobi preconditioner [cf. B. Poirier, Numer. Linear Algebra Appl. 7, No. 7–8, 715–726 (2000; Zbl 1051.65059)]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements.
The present study (paper I) emphasizes construction of the block Jacobi preconditioner matrices. This is achieved in a preprocessing step, performed prior to the subsequent iterative linear solve step, considered in a companion paper (paper II: ibid. 219, No. 1, 185–197 (2006; Zbl 1106.65025, reviewed below). Results indicate that the block Jacobi routines scale remarkably well on parallel computing platforms, and should remain effective over tens of thousands of nodes.

MSC:

65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65Y05 Parallel numerical computation
PDFBibTeX XMLCite
Full Text: DOI