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Hierarchical Matrix Techniques on Massively Parallel Computers

Hierarchical matrix (H-matrix) techniques can be used to efficiently treat dense matrices. With an H-matrix, the storage
requirements and performing all fundamental operations, namely matrix-vector multiplication, matrix-matrix multiplication and matrix inversion
can be done in almost linear complexity.

In this work, we tried to gain even further
speedup for the H-matrix arithmetic by utilizing multiple processors. Our approach towards an H-matrix distribution
relies on the splitting of the index set.

The main results achieved in this work based on the index-wise H-distribution are: A highly scalable algorithm for the H-matrix truncation and matrix-vector multiplication, a scalable algorithm for the H-matrix matrix multiplication, a limited scalable algorithm for the H-matrix inversion for a large number of processors.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-101164
Date11 December 2012
CreatorsIzadi, Mohammad
ContributorsMax Planck Institute for Mathematics in the Sciences (MIS), Scientific Computing, Prof. Dr. Dre. h.c. Wolfgang Hackbusch, Prof. Dr. Gerhard Zumbusch
PublisherUniversitätsbibliothek Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf

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