DMCA
A Parallel Fictitious Domain Method for the Three-dimensional Helmholtz Equation (2000)
| Citations: | 16 - 10 self |
BibTeX
@MISC{Heikkola00aparallel,
author = {Erkki Heikkola and Tuomo Rossi and Jari Toivanen},
title = {A Parallel Fictitious Domain Method for the Three-dimensional Helmholtz Equation},
year = {2000}
}
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Abstract
The application of fictitious domain methods to the three-dimensional Helmholtz equation with absorbing boundary conditions is considered. The finite element discretization is performed by using locally fitted meshes, and algebraic fictitious domain methods with separable preconditioners are used in the iterative solution of the resultant linear systems. These methods are based on embedding the original domain into a larger one with a simple geometry. With this approach, it is possible to realize the GMRES iterations in a low-dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner. An efficient parallel implementation of the iterative algorithm is introduced. Results of numerical experiments demonstrate good scalability properties on distributed-memory parallel computers and the ability to solve high frequency acoustic scattering problems.
Keyphrases
three-dimensional helmholtz equation parallel fictitious domain method fictitious domain method finite element discretization separable prec distributed-memory parallel computer resultant linear system linear system separable preconditioners iterative solution good scalability property simple geometry high frequency acoustic scattering problem efficient parallel implementation original domain boundary condition iterative algorithm acoustic scattering helmholtz equation numerical experiment gmres iteration low-dimensional subspace key word partial solution method
