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.

中文翻译：

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预处理非局部多相流

对于非局部多相Allen-Cahn变分不等式的有限元逼近引起的鞍点问题，我们提出了一种有效的求解器。可以看出，求解器的行为独立于网格，并且对相场变量的数量仅具有很小的依赖性。另外，我们证明了在三个GMRES迭代中，无论网格大小或界面宽度如何，两相问题的逼近都具有收敛性。数值结果表明了该方法的竞争力。