TY - JOUR

T1 - An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations

AU - Hoshi, Takeo

AU - Ogita, Takeshi

AU - Ozaki, Katsuhisa

AU - Terao, Takeshi

PY - 2020/10/1

Y1 - 2020/10/1

N2 - An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a two-stage process in which the approximate solution is computed by existing numerical libraries and is then verified in a moderate computational time. The procedure returns intervals containing one exact eigenvalue in each interval. Test calculations were carried out for organic device materials, and the verification method confirms that all exact eigenvalues are well separated in the obtained intervals. This verification method will be integrated into EigenKernel (https://github.com/eigenkernel/), which is middleware for various parallel solvers for the generalized eigenvalue problem. Such an a posteriori verification method will be important in future computational science.

AB - An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a two-stage process in which the approximate solution is computed by existing numerical libraries and is then verified in a moderate computational time. The procedure returns intervals containing one exact eigenvalue in each interval. Test calculations were carried out for organic device materials, and the verification method confirms that all exact eigenvalues are well separated in the obtained intervals. This verification method will be integrated into EigenKernel (https://github.com/eigenkernel/), which is middleware for various parallel solvers for the generalized eigenvalue problem. Such an a posteriori verification method will be important in future computational science.

KW - Electronic state calculation

KW - Generalized real-symmetric eigenvalue problem

KW - Supercomputer

KW - Verification method

UR - http://www.scopus.com/inward/record.url?scp=85081133612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85081133612&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2020.112830

DO - 10.1016/j.cam.2020.112830

M3 - Article

AN - SCOPUS:85081133612

VL - 376

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 112830

ER -