Hybrid Numerical Solvers for Massively Parallel Eigenvalue Computations and Their Benchmark with Electronic Structure Calculations
| Autor: | Takeo Hoshi, Hiroto Imachi |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Condensed Matter - Materials Science
65F15 General Computer Science Computer science Computation Computer Science - Numerical Analysis Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences Numerical Analysis (math.NA) 010103 numerical & computational mathematics Parallel computing Electronic structure Computational Physics (physics.comp-ph) 01 natural sciences 010101 applied mathematics FOS: Mathematics Benchmark (computing) Mathematics - Numerical Analysis 0101 mathematics Physics - Computational Physics Massively parallel Eigendecomposition of a matrix Eigenvalues and eigenvectors |
| Zdroj: | Journal of Information Processing. 24:164-172 |
| ISSN: | 1882-6652 |
| DOI: | 10.2197/ipsjjip.24.164 |
| Popis: | Optimally hybrid numerical solvers were constructed for massively parallel generalized eigenvalue problem (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 = 10^4-10^6 with upto 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 indicates the guidance for future research. The code was developed as a middleware and a mini-application and will appear online. Comment: 9 pages, 8 figures |
| Databáze: | OpenAIRE |
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