MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Fast Parallel Solution of Boundary Integral Equations and Related Problems

Mario Bebendorf and Ronald Kriemann


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.

MSC Codes:
65D05, 65D15, 65F05, 65F30
integral equations, hierarchical matrices, parallel solvers

Related publications

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