A Preconditioner for the Ohta-Kawasaki Equation
A Preconditioner for the Ohta-Kawasaki Equation
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DOI：
10.1137/16m1065483
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发表时间：
2016-03
期刊：
影响因子：
--
通讯作者：
P. Farrell;J. Pearson
中科院分区：
文献类型：
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作者：
P. Farrell;J. Pearson
我们提出了一个新的预条件Ohta-川崎方程，一个非局部的Cahn-Hilliard方程，描述了两嵌段共聚物熔体的演变。我们设计了一个可计算的近似逆耦合二阶配方的舒尔补通过匹配策略。预条件子实现了网格独立性：随着网格的细化，其解所需的Krylov迭代次数保持近似恒定。此外，预条件是强大的界面厚度参数，如果时间步长标准得到满足。这使得具有超过十亿个自由度的三维二嵌段共聚物熔体的高分辨率有限元模拟成为可能。
We propose a new preconditioner for the Ohta--Kawasaki equation, a nonlocal Cahn--Hilliard equation that describes the evolution of diblock copolymer melts. We devise a computable approximation to the inverse of the Schur complement of the coupled second-order formulation via a matching strategy. The preconditioner achieves mesh independence: as the mesh is refined, the number of Krylov iterations required for its solution remains approximately constant. In addition, the preconditioner is robust with respect to the interfacial thickness parameter if a timestep criterion is satisfied. This enables the highly resolved finite element simulation of three-dimensional diblock copolymer melts with over one billion degrees of freedom.