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Parallel $${\mathcal {H}}$$H-matrix arithmetic on distributed-memory systems.
- Source :
-
Computing & Visualization in Science . Apr2012, Vol. 15 Issue 2, p87-97. 11p. - Publication Year :
- 2012
-
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 $${\mathcal {H}}$$ 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 $${\mathcal {H}}$$ H -matrices based on the corresponding index set. Numerical experiments applied to a BEM model will complement our complexity analysis. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14329360
- Volume :
- 15
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Computing & Visualization in Science
- Publication Type :
- Academic Journal
- Accession number :
- 91993056
- Full Text :
- https://doi.org/10.1007/s00791-013-0198-z