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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