Parallel $${\mathcal {H}}$$ H -matrix arithmetic on distributed-memory systems

Abstract

In the last decade, the hierarchical matrix technique was introduced to deal with dense matrices in an efficient way. It provides a data-sparse format and allows an approximate matrix algebra of nearly optimal complexity. This paper is concerned with utilizing multiple processors to gain further speedup for the $${\mathcal {H}}$$ -matrix algebra, namely matrix truncation, matrix–vector multiplication, matrix–matrix multiplication, and inversion. One of the most cost-effective solution for large-scale computation is distributed computing. Distribute-memory architectures provide an inexpensive way for an organization to obtain parallel capabilities as they are increasingly popular. In this paper, we introduce a new distribution scheme for $${\mathcal {H}}$$ -matrices based on the corresponding index set. Numerical experiments applied to a BEM model will complement our complexity analysis.