Three-field block preconditioners for models of coupled magma/mantle dynamics
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Publication Date
2015Journal Title
SIAM Journal on Scientific Computing
ISSN
1064-8275
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Volume
37
Issue
5
Pages
A2270-A2294
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Rhebergen, S., Wells, G., Wathen, A., & Katz, R. (2015). Three-field block preconditioners for models of coupled magma/mantle dynamics. SIAM Journal on Scientific Computing, 37 (5), A2270-A2294. https://doi.org/10.1137/14099718X
Abstract
For a prescribed porosity, the coupled magma/mantle flow equations can be
formulated as a two-field system of equations with velocity and pressure as
unknowns. Previous work has shown that while optimal preconditioners for the
two-field formulation can be obtained, the construction of preconditioners that
are uniform with respect to model parameters is difficult. This limits the
applicability of two-field preconditioners in certain regimes of practical
interest. We address this issue by reformulating the governing equations as a
three-field problem, which removes a term that was problematic in the two-field
formulation in favour of an additional equation for a pressure-like field. For
the three-field problem, we develop and analyse new preconditioners and we show
numerically that they are optimal in terms of problem size and less sensitive
to model parameters, compared to the two-field preconditioner. This extends the
applicability of optimal preconditioners for coupled mantle/magma dynamics into
parameter regimes of physical interest.
Sponsorship
Natural Environment Research Council (NE/I023929/1)
Identifiers
External DOI: https://doi.org/10.1137/14099718X
This record's URL: https://www.repository.cam.ac.uk/handle/1810/275177
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