An integral equation method for the Cahn-Hilliard equation in the wetting problem

Document Type

Article

Publication Date

10-15-2020

Abstract

We present an integral equation approach to solving the Cahn-Hilliard equation equipped with boundary conditions that model solid surfaces with prescribed Young's angles. The discretization of the system in time using convex splitting leads to a modified biharmonic equation at each time step. To solve it, we split the solution into a volume potential computed with free space kernels, plus the solution to a second kind integral equation (SKIE). The volume potential is evaluated with the help of a box-based volume-FMM method. For non-box domains, the source density is extended by solving a biharmonic Dirichlet problem. The near-singular boundary integrals are computed using quadrature by expansion (QBX) with FMM acceleration. Our method has linear complexity in the number of surface/volume degrees of freedom and can achieve high order convergence in space with adaptive refinement to manage error from function extension.

Identifier

85087589777 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/j.jcp.2020.109521

e-ISSN

10902716

ISSN

00219991

Volume

419

Grant

C6004-14G

Fund Ref

Research Grants Council, University Grants Committee

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