MiS Preprint Repository

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.