Mesh independence of the generalized Davidson algorithm

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 conve...

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Published in:Journal of computational physics 2020-05, Vol.409 (C), p.109322, Article 109322
Main Authors: Kelley, C.T., Bernholc, J., Briggs, E.L., Hamilton, Steven, Lin, Lin, Yang, Chao
Format: Article
Language:English
Subjects:
Algorithms
Banach spaces
Computational physics
Convergence
Eigenvalues
Electronic structure computations
Generalized Davidson algorithm
Iterative methods
Mesh independence
Neutron transport
Norms
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description 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.
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subjects Algorithms
Banach spaces
Computational physics
Convergence
Eigenvalues
Electronic structure computations
Generalized Davidson algorithm
Iterative methods
Mesh independence
Neutron transport
Norms
title Mesh independence of the generalized Davidson algorithm
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