Multigrid Methods for Nonlinear PDE Systems with Applications in Phase-Field Models

Peter Jimack (The University of Leeds)

FA1,

The talk will present an overview of the some of the algorithms behind, and applications of, a software tool that we have developed to combine mesh adaptivity and multigrid in 3-d for the parallel solution of stiff time-dependent systems of partial differential equations and systems. Our motivation for this work comes from phase change problems in alloy solidification, which involve multiple length scales in both space and time, however the techniques developed will also been shown to be applicable to very different problems, such as multiphase models for the simulation of tumour growth. The common element is the need to solve stiff parabolic systems in three space dimensions as efficiently as possible - ideally with linear computational complexity - and in a manner that scales when implemented in parallel.

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