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

TL;DR

This paper introduces a three-field formulation for coupled magma/mantle dynamics that enables the development of more robust and parameter-insensitive preconditioners, improving computational efficiency in practical regimes.

Contribution

The paper proposes a novel three-field reformulation of magma/mantle flow equations and develops new preconditioners that are optimal and less sensitive to model parameters.

Findings

Preconditioners are optimal in problem size.

Preconditioners show reduced sensitivity to model parameters.

Extends applicability of preconditioners to practical regimes.

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.