Hybrid Numerical Solvers for Massively Parallel Eigenvalue Computations and Their Benchmark with Electronic Structure Calculations

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. \n------------------------------ This is a preprint of an article intended for publication Journal of Information Processing(JIP). This preprint should not be cited. This article should be cited as: Journal of Information Processing Vol.24(2016) No.1(online) ------------------------------

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. \n------------------------------ This is a preprint of an article intended for publication Journal of Information Processing(JIP). This preprint should not be cited. This article should be cited as: Journal of Information Processing Vol.24(2016) No.1(online) ------------------------------