Preconditioning nonlocal multi-phase flow

JOURNAL OF COMPUTATIONAL PHYSICS

卷:424

Article

Kay, David¹  Styles, Vanessa² 

[1] Univ Oxford, Dept Comp Sci, Oxford OX1 3QD, England

[2] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

关键词: Allen-Cahn systems;    PDE-constrained optimization;    Primal-dual active set method;    Saddle point systems;    Preconditioning;    Krylov subspace solver;   

DOI  :  10.1016/j.jcp.2020.109715

来源: Elsevier

【 摘 要 】

We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen-Cahn variational inequalities. The solver is seen to behave mesh independently and to have only a very mild dependence on the number of phase field variables. In addition we prove convergence, in three GMRES iterations, of the approximation of the two phase problem, regardless of mesh size or interfacial width. Numerical results are presented that illustrate the competitiveness of this approach. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free