High Performance Preconditioned Iterative Methods

摘要

High performance approximate inverse preconditioning for solving sparse linear systems is examined using various architectural and software platforms. Parallel normalized explicit preconditioned iterative methods in conjunction with parallel normalized approximate inverse finite element matrix algorithms for solving efficiently sparse finite element linear systems on symmetric multiprocessor and distributed memory systems is presented along with theoretical estimates on speed-ups and efficiency. The performance of parallel approximate inverses on multiprocessor systems, using OpenMP, is given along with the performance of parallel preconditioned conjugate gradient type methods on multiprocessor and multicomputer machines, using OpenMP and the Message Passing Interface (MPI) communication library and the Globus toolkit, is also presented.