Fast Parallel Solution of Boundary Integral Equations and Related Problems

This article is concerned with the efficient numerical solution of Fredholm integral equations on a parallel computer with shared or distributed memory. Parallel algo-rithms for both, the approximation of the discrete operator by hierarchical matrices and the parallel matrix-vector multiplication of such matrices by a vector, are pre-sented. The first algorithm has a complexity of order 1pN log 2d−1 N, while the latter is of order 1pN log d N, where N and p are the number of unknowns and the number of processors, respectively. The H-approximant needs O 1 pN log d N units of storage on each processor