Parallel solution of the Helmholtz equation in a multilayer domain

Abstract

We study time-harmonic wave propagation in layered, heterogeneous media. Solving this relatively complex application problem numerically is a challenging task. The full potential of algorithms, parallel programming models and computer architectures must be exploited. Our aim is to give a broad perspective on the various considerations that come into play. The basic parts of our algorithms consist of finite difference discretizations, domain decomposition and preconditioned iterative methods. We present two serial algorithms with different properties. Then, we discuss parallelization strategies using a local memory model, a shared memory model, or a combination of the two. The numerical experiments highlight the differences between the approaches and show results for three different combinations of algorithm and computer architecture that lead to viable solution methods.