Parallel solution of the generalized Helmholtz equation

Abstract

Uses the reduced system conjugate gradient algorithm to find the solution of large, sparse, symmetric, positive definite systems of linear equations arising from finite difference discretization of the generalized Helmholtz equation. The authors examine in detail three spatial domain decompositions on distributed memory machines. They use a two-step damped Jacobi preconditioner for the Schur complement system and find that although the number of iterations required for convergence is nearly halved, overall solution time is slightly increased. The authors introduce a modification to the preconditioner in order to reduce overhead.<>