16.14 TFLOPS eigenvalue solver on the earth simulator: exact diagonalization for ultra largescale hamiltonian matrix

Authors:
Susumu Yamada;Toshiyuki Imamura;Masahiko Machida
Affiliations:
Japan Atomic Energy Agency, Tokyo, Japan and CREST, JST, Kawaguchi-City, Saitama, Japan;The University of Electro-Communications, Chofu-City, Tokyo, Japan and CREST, JST, Kawaguchi-City, Saitama, Japan;Japan Atomic Energy Agency, Tokyo, Japan and CREST, JST, Kawaguchi-City, Saitama, Japan
Venue:
ISHPC'05/ALPS'06 Proceedings of the 6th international symposium on high-performance computing and 1st international conference on Advanced low power systems
Year:
2005

Citing 6
Cited 0

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Abstract

The Lanczos method has been conventionally utilized as an eigenvalue solver for huge size matrices encountered in strongly correlated fermion systems. However, since one can not obtain the residual during the Lanczos iteration, the iteration count in the Lanczos method is not controllable. Thus, we adopt a new eigenvalue solver based on the conjugate gradient (CG) method in which the residual can be evaluated every iteration step. We confirm that the CG method with an preconditioner shows much more excellent performance than the Lanczos method. We achieve 16.14 TFLOPS on 512 nodes (4096 processors) of the Earth Simulator by the use of the CG method.