Parallel Iterative Finite Element Solution Methods For
Three-Dimensional Acoustic Scattering
Cristian Ianculescu and Lonny L. Thompson
Department of Mechanical Engineering and Engineering Mechanics
Clemson University
Clemson, South Carolina 29634-0921
Paper IMECE2003-44266,
Proc. IMECE'03, 2003 ASME International
Mechanical Engineering Congress and Exposition, Washington, D.C.,
Nov. 15-21, 2003.
Abstract
Efficient and scalable parallel solution methods are presented for
three-dimensional acoustic scattering problems on unbounded domains. A
separable boundary is applied at an arbitrary distance from the
scatterer, to define a finite computational domain, and thus enable application
of the Finite Element Method (FEM). A modified
non-reflecting Dirichlet-to-Neumann (DtN) boundary condition is applied
along the truncation boundary, in the form of local second-order
differential operators, and a harmonic series. For elongated scatterers
(e.g. a submarine or ship), suitable finite element formulations are
derived and implemented on spheroidal coordinates, reducing the size of
computational domain without affecting the accuracy of the numerical
solution.
The outer-product structure of the DtN boundary operator is exploited to
efficiently handle non-locality in an iterative process.
Computational performance
of the DtN condition is analyzed and shown to be significantly more
cost-effective when compared with local boundary conditions producing
similar accuracy. The effective use of non-local DtN conditions in a
32-processor parallel distributed memory environment is demonstrated for
a three-dimensional submarine scatterer. By
exploiting the outer-product structure, it is shown that communication
costs due to non-locality depend only on a small number of harmonics in the
DtN operator, and thus have little impact on the scalability of the
solution on multiple processors.