Exact Radiation Conditions on Spheroidal Boundaries with Sparse Iterative Methods for Efficient Computation of Exterior Acoustics

Lonny L. Thompson, Cristian Ianculescu, and Runnong Huan

Advanced Computational Mechanics Research Laboratory
Department of Mechanical Engineering
Clemson University
Clemson, South Carolina 29634-0921

Proceedings of the Seventh International Congress on Sound and Vibration, 4-7 July 2000, Garmisch-Partenkirchen, Germany. pp. 2101-2108

Abstract

Exact Dirichlet-to-Neumann (DtN) maps are derived on spheroidal boundaries for finite element implementation. The use of spheroidal boundaries enables the efficient solution of scattering from elongated objects. Comparisons of sparse preconditioned iterative solvers, including BiCG-Stab and QMR with Jacobi and SSOR preconditioning are discussed. Matrix-vector products are computed efficiently in block form using Level-2 BLAS and the special product decomposition structure of the DtN matrix. Preconditioners based on the sparse matrix partition associated with the interior mesh and local part of the radiation boundary operator are used to accelerate convergence of the Krylov-subspace iterative solution methods. In this way, the full DtN matrix block is never assembled. Three-dimensional numerical examples demonstrate the efficiency and accuracy of the boundary treatments for high-frequency scattering from elongated structures.

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