Over 10 TFLOPS Computation for a Huge Sparse Eigensolver on the Earth Simulator

Toshiyuki Imamura (), Susumu Yamada () and Masahiko Machida ()
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Toshiyuki Imamura: the University of Electro-Communications, Department of Computer Science
Susumu Yamada: Japan Atomic Energy Agency, Center for Computational Science and Engineering
Masahiko Machida: Japan Atomic Energy Agency, Center for Computational Science and Engineering

A chapter in High Performance Computing on Vector Systems, 2006, pp 51-61 from Springer

Abstract: Abstract To investigate a possibility of special physical properties like superfluidity, we implement a high performance exact diagonalization code for the trapped Hubbard model on the Earth Simulator. From the numerical and computational point of view, it is found that the performance of the preconditioned conjugate gradient (PCG) method is excellent in our case. It is 1.5 times faster than the conventional Lanczos one since it can conceal the communication overhead much more effectively. Consequently, the PCG method shows 16.14 TFLOPS on 512 nodes. Furthermore, we succeed in solving a 120-billion-dimensional matrix. To our knowledge, this dimension is a world-record.

Keywords: Hubbard Model; Communication Overhead; Preconditioned Conjugate Gradient; Hamiltonian Matrix; Earth Simulator (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/3-540-35074-8_4

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