Parallel H-Matrix Arithmetic on Distributed-Memory Systems
Mohammad Izadi Khaleghabadi
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Submission date: 24. Dec. 2012
published in: Computing and visualization in science, 15 (2012) 2, p. 87-97
DOI number (of the published article): 10.1007/s00791-013-0198-z
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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.