Chen, Wenwu; Poirier, Bill Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. I: Block Jacobi diagonalization. (English) Zbl 1106.65024 J. Comput. Phys. 219, No. 1, 198-209 (2006). 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. Cited in 2 ReviewsCited in 3 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling 65Y05 Parallel numerical computation Keywords:sparse matrix; parallel computing; eigensolver; numerical examples; iterative methods Citations:Zbl 1051.65059; Zbl 1106.65025 PDFBibTeX XMLCite \textit{W. Chen} and \textit{B. Poirier}, J. Comput. Phys. 219, No. 1, 198--209 (2006; Zbl 1106.65024) Full Text: DOI