Exact Diagonalization of Large Sparse Matrices:
A Challenge for Modern Supercomputers

ABSTRACT:

Exact diagonalization of very large sparse matrices is a numerical problem common to various fields in science and engineering. We present an advanced eigenvalue alorithm - the so-called Jacobi-Davidson algorithm - in combination with an efficient parallel matrix-vector multiplication based on the Jagged Diagonals Storage (JDS) format. Our JDS implementation allows calculation of several specified eigenvalues with high accuracy both on vector and on RISC processor based supercomputers.
Using a 256 processor CRAY T3E-1200 we were able to discuss the fundamental question of the metal-insulator transition in one-dimensional half-filled electron-phonon systems and the properties of the 3/4 filled Peierls-Hubbard Hamiltonian in relation to recent resonant Raman experiments on MX chain [-PtCl-] complexes. In this context we present an extensive performance study on modern supercomputers such as CRAY T3E, SGI Origin3800, NEC SX5e and Hitachi SR8000.

KEYWORDS:

MPI, Benchmarks, Bandwidth, Application

LOCAL LINKS:

Full paper as PDF document, postscript, gzip'ed postscript
Slides as html-document

Authors:

G. Wellein, HPC Services, RRZE, Erlangen, Germany
G. Hager, HPC Services, RRZE, Erlangen, Germany
A. Basermann, C&C Research Lab., NEC Europe, Sankt Augustin, Germany
H. Fehske, Theoretical Physics, University of Bayreuth, Germany

Partners:

Leibniz Computing Center Munich, Germany
High Performance Computing Center Stuttgart, Germany
Neumann Institut for Computing Jülich, Germany
Technical University Dresden - Computing Center, Germany
Competence Network for Technical, Scientific High Performance Computing in Bavaria (KONWIHR)

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Dr. Gerhard Wellein

Last modified: Mon Jun 25 09:33:36 MEST 2001