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Preconditioning and iterative solution of all-at-once systems for evolutionary partial differential equations

Abstract:

Standard Krylov subspace solvers for self-adjoint problems have rigorous convergence bounds based solely on eigenvalues. However, for non-self-adjoint problems, eigenvalues do not determine behavior even for widely used iterative methods. In this paper, we discuss time-dependent PDE problems, which are always non-self-adjoint. We propose a block circulant preconditioner for the all-at-once evolutionary PDE system which has block Toeplitz structure. Through reordering of variables to obtain a ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1137/16M1062016

Authors


McDonald, E More by this author
Pestana, J More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
New College
ORCID:
0000-0001-9992-5588
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Scientific Computing Journal website
Volume:
40
Issue:
2
Pages:
A1012–A1033
Publication date:
2018-04-03
Acceptance date:
2018-01-31
DOI:
EISSN:
1095-7197
ISSN:
1064-8275
Pubs id:
pubs:822219
URN:
uri:1b4c6ea1-bb34-446a-8a88-8cd02a807c51
UUID:
uuid:1b4c6ea1-bb34-446a-8a88-8cd02a807c51
Local pid:
pubs:822219

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