CUED Publications database

Three-field block preconditioners for models of coupled magma/mantle dynamics

Rhebergen, S and Wells, GN and Wathen, AJ and Katz, RF (2015) Three-field block preconditioners for models of coupled magma/mantle dynamics. SIAM Journal on Scientific Computing, 37. A2270-A2294. ISSN 1064-8275

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© 2015 Society for Industrial and Applied Mathematics. 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 favor of an additional equation for a pressure-like field. For the three-field problem, we develop and analyze 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.

Item Type: Article
Divisions: Div C > Applied Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:41
Last Modified: 17 May 2018 07:16