Mesh independence of the generalized Davidson algorithm

C. T. Kelley; J. Bernholc; E. L. Briggs; Steven Hamilton; Lin Lin; Chao Yang

doi:10.1016/j.jcp.2020.109322

Mesh independence of the generalized Davidson algorithm

C. T. Kelley
, J. Bernholc
, E. L. Briggs
, Steven Hamilton
, Lin Lin
, Chao Yang

Radiation Transport and HPC Methods

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We give conditions under which the generalized Davidson algorithm for eigenvalue computations is mesh-independent. In this case mesh-independence means that the iteration statistics (residual norms, convergence rates, for example) of a sequence of discretizations of a problem in a Banach space converge the statistics for the infinite-dimensional problem. We illustrate the result with several numerical examples.

Original language	English
Article number	109322
Journal	Journal of Computational Physics
Volume	409
DOIs	https://doi.org/10.1016/j.jcp.2020.109322
State	Published - May 15 2020

Funding

LL: National Science Foundation Grant DMS-1652330 , the Scientific Discovery through Advanced Computing (SciDAC) program and the Center for Applied Mathematics for Energy Research Applications (CAMERA) funded by U.S. Department of Energy , Office of Science, Advanced Scientific Computing Research under Contract No. DE-AC02-05CH11231 . SH: This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy . CTK, SH: The Consortium for Advanced Simulation of Light Water Reactors (www.casl.gov), an Energy Innovation Hub (http://www.energy.gov/hubs) for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy Contract No. DE-AC05-00OR22725.CTK: Army Research Office Grant W911NF-16-1-0504 and National Science Foundation Grants DMS-1745654, and DMS-1906446.ELB, JB, CTK: National Science Foundation Grant OAC-1740309.JB: DOE grant DE-FG02-98ER45685.SH: This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy.LL: National Science Foundation Grant DMS-1652330, the Scientific Discovery through Advanced Computing (SciDAC) program and the Center for Applied Mathematics for Energy Research Applications (CAMERA) funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research under Contract No. DE-AC02-05CH11231.CY: This work was supported by the Scientific Discovery through Advanced Computing (SciDAC) program and the Center for Applied Mathematics for Energy Research Applications (CAMERA) funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research under Contract No. DE-AC02-05CH11231. CTK: Army Research Office Grant W911NF-16-1-0504 and National Science Foundation Grants DMS-1745654 , and DMS-1906446 . ELB, JB, CTK: National Science Foundation Grant OAC-1740309 . The research reported in this paper has been partially supported by the following sources. JB: DOE grant DE-FG02-98ER45685 .

Keywords

Electronic structure computations
Generalized Davidson algorithm
Mesh independence
Neutron transport

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10.1016/j.jcp.2020.109322

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title = "Mesh independence of the generalized Davidson algorithm",

abstract = "We give conditions under which the generalized Davidson algorithm for eigenvalue computations is mesh-independent. In this case mesh-independence means that the iteration statistics (residual norms, convergence rates, for example) of a sequence of discretizations of a problem in a Banach space converge the statistics for the infinite-dimensional problem. We illustrate the result with several numerical examples.",

keywords = "Electronic structure computations, Generalized Davidson algorithm, Mesh independence, Neutron transport",

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AU - Kelley, C. T.

AU - Bernholc, J.

AU - Briggs, E. L.

AU - Hamilton, Steven

AU - Lin, Lin

AU - Yang, Chao

PY - 2020/5/15

Y1 - 2020/5/15

N2 - We give conditions under which the generalized Davidson algorithm for eigenvalue computations is mesh-independent. In this case mesh-independence means that the iteration statistics (residual norms, convergence rates, for example) of a sequence of discretizations of a problem in a Banach space converge the statistics for the infinite-dimensional problem. We illustrate the result with several numerical examples.

AB - We give conditions under which the generalized Davidson algorithm for eigenvalue computations is mesh-independent. In this case mesh-independence means that the iteration statistics (residual norms, convergence rates, for example) of a sequence of discretizations of a problem in a Banach space converge the statistics for the infinite-dimensional problem. We illustrate the result with several numerical examples.

KW - Electronic structure computations

KW - Generalized Davidson algorithm

KW - Mesh independence

KW - Neutron transport

UR - https://www.scopus.com/pages/publications/85079881505

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DO - 10.1016/j.jcp.2020.109322

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VL - 409

JO - Journal of Computational Physics

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Mesh independence of the generalized Davidson algorithm

Abstract

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Keywords

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