Efficient iterative solution of high frequency acoustic scattering problems

Abstract A fictitious domain method for the solution of the 3D Helmholtz equation with absorbing boundary conditions is considered. The finite element discretization leads to a large-scale linear system, which is solved by the algebraic fictitious domain method with GMRES iterations. With this approach the iterations can be realized in a lowdimensional subspace and thereby the partial solution method can be used to solve the linear systems with the preconditioner. An efficient parallel implementation of the subspace iterations is used. Numerical experiments demonstrate ability to solve high frequency scattering problems on a SGI Origin 2000. 1 Introduction Numerical solution methods for scattering problems facilitate the simulation of important physical phenomena in many fields such as underwater acoustics, medicine, and radar technology. In real-life wave propagation problems, the frequencies are often high, and either the computational cost or the memory usage becomes the bottleneck. We tackle this problem by using special techniques to reduce the memory consumption and the computational cost of the finite element method and by distributing the computational work and data among parallel processors. We consider the application of algebraic fictitious domain methods to the numerical solution of 3D exterior Helmholtz equation, which models, for example, the scattering of high frequency time-harmonic acoustic waves by an obstacle. This paper is based on the results of the previous works [4, 5, 6, 7]. We briefly describe the iterative solution procedure and report new results obtained in a SGI Origin 2000