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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

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.


Related publications

2012 Repository Open Access
Mohammad Izadi

Parallel \(\mathscr {H}\)-matrix arithmetic on distributed-memory systems

In: Computing and visualization in science, 15 (2012) 2, pp. 87-97