A Parallel Multigrid Solver For Block-Tridiagonal Stencil Matrices Derived From Acoustic Wave Equation On Large Finite Difference Grids

Abstract

In this work we present efficient numerical solvers for large linear systems originated from a second-order finite difference discretization of three-dimensional acoustic wave problems in the frequency domain. We consider Geometric Multigrid strategies combined with the well known Conjugate Gradient and Red-Black SOR algorithms. Our method is designed for parallel execution on shared-memory platforms using the OpenMP paradigm. The experiments show that the parallel Conjugate Gradient method applying Multigrid as a preconditioner offers the best results in terms of CPU time and number of iterations.