Contribution to a conference proceedings/Contribution to a book

FZJ-2014-04412

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png New Preconditioned Solvers for Large Sparse Eigenvalue Problems on Massively Parallel Computers

Basermann, A. (Corresponding Author) ; Steffen, B.FZJ*

1997
Society for Industrial and Applied Mathematics Philadelphia, Pa.
ISBN: 0-89871-395-1

Abstract: We present preconditioned solvers to find a few eigenvalues and eigenvectors of large dense or sparse symmetric matrices based on the Jacobi-Davidson (JD) method by G. L. G. Sleijpen and H. A. van der Vorst. For preconditioning, we apply a new adaptive approach using the QMR iteration. To parallelize the solvers, we divide the interesting part of the spectrum into a few overlapping intervals and asynchronously exchange eigenvector approximations from neighboring intervals to keep the solutions separated. Per interval, matrix-vector and vector-vector operations of the JD iteration are parallelized by determining a data distribution and a communication scheme from an automatic analysis of the sparsity pattern of the matrix. We demonstrate the efficiency of these parallelization strategies by timings on an Intel Paragon and a Cray T3E system with matrices from real applications.

Keyword(s): Parallelverarbeitung

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Contributing Institute(s):

1. Zentralinstitut für Angewandte Mathematik (ZAM)
2. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 899 - ohne Topic (POF2-899) (POF2-899)

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