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 algorithms for both, the approximation of the discrete operator by hierarchical matrices using adaptive cross approximation (ACA) and the parallel matrix-vector multiplication of such matrices by a vector, are presented. The first algorithm has a complexity of order p(-1) N log(2d-1) N, while the latter is of order p(-1) N log(d) N, where N, d and p are the number of unknowns, the spatial dimension and the number of processors, respectively. The approximant needs O(p(-1) N log(d) N) units of storage on each processor.