Journal Article

FZJ-2020-00420

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Rational Spectral Filters with Optimal Convergence Rate

Kollnig, K. ; Bientinesi, P. ; Di Napoli, E. (Corresponding author)FZJ*

2021
SIAM Philadelphia, Pa.

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Please use a persistent id in citations: http://hdl.handle.net/2128/28400  doi:10.1137/20M1313933

Abstract: In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through nonlinear least-squares optimization of so-called rational filters, we introduce a systematic method to design these filters by minimizing the worst-case convergence rate and eliminate the parametric dependence on weight functions. Further, we provide an efficient way to deal with the box-constraints which play a central role for the use of iterative linear solvers in contour-based eigensolvers. Indeed, these parameter-free filters consistently minimize the number of iterations and the number of FLOPs to reach convergence in the eigensolver. As a byproduct, our rational filters allow for a simple solution to load balancing when the solution of an interior eigenproblem is approached by the slicing of the sought after spectral interval.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Appears in the scientific report 2021

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Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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