Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics
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Publication Date
2014-08-19Journal Title
SIAM Journal on Scientific Computing
ISSN
1064-8275
Publisher
SIAM
Volume
36
Pages
A1960-A1977
Language
en_US
Type
Article
Metadata
Show full item recordCitation
Rhebergen, S., Wells, G., Katz, R. F., & Wathen, A. J. (2014). Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics. SIAM Journal on Scientific Computing, 36 A1960-A1977. https://doi.org/10.1137/130946678
Abstract
This article considers the iterative solution of a finite element discretization of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyze, and numerically test an Elman, Silvester, and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optimality of the preconditioner. The presented analysis highlights the dependence of the preconditioner on parameters in the magma dynamics equations that can affect convergence of iterative linear solvers. The analysis is verified through a range of two- and three-dimensional numerical examples on unstructured grids, from simple illustrative problems through to large problems on subduction zone–like geometries. The computer code to reproduce all numerical examples is freely available as supporting material.
Sponsorship
NERC (NE/I023929/1)
Identifiers
External DOI: https://doi.org/10.1137/130946678
This record's URL: https://www.repository.cam.ac.uk/handle/1810/245773
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