Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
Parallel H-Matrix Arithmetic on Distributed-Memory Systems
Mohammad Izadi Khaleghabadi
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 $\mcH$-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 $\mcH$-matrices based on the corresponding index set. Numerical experiments applied to a BEM model will complement our complexity analysis.