Parallel iterative solution of large‐scale acoustic scattering problems using exact non reflecting conditions on distributed memory computer systems

Abstract

Parallel iterative methods for fast solution of large‐scale acoustic radiation and scattering problems are developed using exact Dirichlet‐to‐Neumann (DtN) nonreflecting boundaries. For elongated scatterers such as submarines, it is shown that the generalization of the DtN to elliptical/spheroidal artificial boundaries improves significantly the computational efficiency of accurate finite element methods for the solution of acoustic scattering problems. The outer‐product structure of the DtN map is exploited as a low‐rank update of the system matrix to efficiently compute the matrix‐by‐vector products found in Krylov subspace based iterative methods. For the complex non‐Hermitian matrices resulting from the Helmholtz equation, a distributed‐memory parallel BICG‐STAB iterative method is used in conjunction with a hybrid parallel SSOR/Jacobi preconditioner. The domain decomposition with interface minimization was performed to ensure optimal inter‐processor communication. For the distributed memory architectures tested, including Linux/Intel Beowulf clusters, when implemented as a low‐rank update, the nonlocal character of the DtN map shows little impact on the scale up or parallel efficiency compared to approximate local boundary conditions. [Work supported by NSF.]