Journal of Information Processing
Online ISSN : 1882-6652
ISSN-L : 1882-6652
Hybrid Numerical Solvers for Massively Parallel Eigenvalue Computations and Their Benchmark with Electronic Structure Calculations
Hiroto ImachiTakeo Hoshi
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2016 Volume 24 Issue 1 Pages 164-172


Optimally hybrid numerical solvers were constructed for massively parallel generalized eigenvalue problems (GEP). The strong scaling benchmark was carried out on the K computer and other supercomputers for electronic structure calculation problems in the matrix sizes of M=104-106 with up to 105 cores. The procedure of GEP is decomposed into the two subprocedures of the reducer to the standard eigenvalue problem (SEP) and the solver of SEP. A hybrid solver is constructed, when a routine is chosen for each subprocedure from the three parallel solver libraries of ScaLAPACK, ELPA and EigenExa. The hybrid solvers with the two newer libraries, ELPA and EigenExa, give better benchmark results than the conventional ScaLAPACK library. The detailed analysis on the results implies that the reducer can be a bottleneck in next-generation (exa-scale) supercomputers, which provides guidance for future research. The code was developed as a middleware and a mini-application and will appear online.

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© 2016 by the Information Processing Society of Japan
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