Parallel hierarchical solvers and preconditioners for boundary element methods

Ananth Grama, Vipin Kumar, Ahmed Sameh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

The method of moments is an important tool for solving boundary integral equations arising in a variety of applications. It transforms the physical problem into a dense linear system. Due to the large number of variables and the associated computational requirements, these systems are solved iteratively using methods such as GMRES, CG and its variants. The core operation of these iterative solvers is the application of the system matrix to a vector. This requires θ(n2) operations and memory using accurate dense methods. The computational complexity can be reduced to O(n log n) and the memory requirement to Θ(n) using hierarchical approximation techniques. The algorithmic speedup from approximation can be combined with parallelism to yield very fast dense solvers. In this paper, we present efficient parallel formulations of dense iterative solvers based on hierarchical approximations for solving the integral form of Laplace equation. We study the impact of various parameters on the accuracy and performance of the parallel solver. We present two preconditioning techniques for accelerating the convergence of the iterative solver. These techniques are based on an inner-outer scheme and a block diagonal scheme based on a truncated Green's function. We present detailed experimental results on up to 256 processors of a Cray T 3 D .

Original languageEnglish (US)
Title of host publicationProceedings of the 1996 ACM/IEEE Conference on Supercomputing, SC 1996
PublisherAssociation for Computing Machinery
ISBN (Electronic)0897918541
DOIs
StatePublished - 1996
Externally publishedYes
Event1996 ACM/IEEE Conference on Supercomputing, SC 1996 - Pittsburgh, United States
Duration: Nov 17 1996Nov 22 1996

Publication series

NameProceedings of the International Conference on Supercomputing
Volume1996-November

Conference

Conference1996 ACM/IEEE Conference on Supercomputing, SC 1996
Country/TerritoryUnited States
CityPittsburgh
Period11/17/9611/22/96

Bibliographical note

Publisher Copyright:
© 1996 IEEE.

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