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MiS Preprint
10/2004

Fast Parallel Solution of Boundary Integral Equations and Related Problems

Mario Bebendorf and Ronald Kriemann

Abstract

This article is concerned with the efficient numerical solution of Fredholm integral equations on a parallel computer with shared or distributed memory. Parallel algorithms for both, the approximation of the discrete operator by hierarchical matrices and the parallel matrix-vector multiplication of such matrices by a vector, are presented. The first algorithm has a complexity of order $\frac{1}{p} N \log^{2d-1}{N}$, while the latter is of order $\frac{1}{p} N\log^d{N}$, where $N$ and $p$ are the number of unknowns and the number of processors, respectively. The $\mathcal{H}$-approximant needs $\mathcal{O}(\frac{1}{p}N\log^d{N})$ units of storage on each processor.

Received:
Mar 5, 2004
Published:
Mar 5, 2004
MSC Codes:
65D05, 65D15, 65F05, 65F30
Keywords:
integral equations, hierarchical matrices, parallel solvers

Related publications

inJournal
2005 Repository Open Access
Mario Bebendorf and Ronald Kriemann

Fast parallel solution of boundary integral equations and related problems

In: Computing and visualization in science, 8 (2005) 3/4, pp. 121-135