Fast Parallel Solution of Boundary Integral Equations and Related Problems

Mario Bebendorf and Ronald Kriemann

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Submission date: 05. Mar. 2004
Pages: 25
published in: Computing and visualization in science, 8 (2005) 3/4, p. 121-135 
DOI number (of the published article): 10.1007/s00791-005-0001-x
Bibtex
MSC-Numbers: 65D05, 65D15, 65F05, 65F30
Keywords and phrases: integral equations, hierarchical matrices, parallel solvers
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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 , while the latter is of order , where N and p are the number of unknowns and the number of processors, respectively. The -approximant needs units of storage on each processor.