@article{41d6b3300cd9443d85dc7dfbd959f07a,

title = "An integral equation method for the Cahn-Hilliard equation in the wetting problem",

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.",

keywords = "Cahn-Hilliard equation, Convex splitting, Integral equation method, Second-kind integral equation, Volume potential, Young's angle",

author = "Xiaoyu Wei and Shidong Jiang and Andreas Kl{\"o}ckner and Wang, {Xiao Ping}",

note = "Funding Information: This research was supported in part by the National Science Foundation under grants DMS-1418961 and DMS-1654756 , and by the Hong Kong Research Grant Council ( RGC-GRF grants 605513 and 16302715 , RGC-CRF grant C6004-14G , and NSFC-RGC joint research grant N-HKUST620/15 ). Any opinions, findings, and conclusions, or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Hong Kong Research Grant Council; Neither NSF nor HKRGC has approved or endorsed its content. Part of the work was performed while the authors were participating in the HKUST-ICERM workshop {\textquoteleft}Integral Equation Methods, Fast Algorithms and Their Applications to Fluid Dynamics and Materials Science{\textquoteright} held in 2017. Funding Information: This research was supported in part by the Hong Kong RGC-GRF grants 605513 and 16302715, RGC-CRF grant C6004-14G, and NSFC-RGC joint research grant N-HKUST620/15.This research was supported by the NSF under grant DMS-1418918.This research was supported by the NSF under grant DMS-1654756.This research was supported in part by the National Science Foundation under grants DMS-1418961 and DMS-1654756, and by the Hong Kong Research Grant Council (RGC-GRF grants 605513 and 16302715, RGC-CRF grant C6004-14G, and NSFC-RGC joint research grant N-HKUST620/15). Any opinions, findings, and conclusions, or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Hong Kong Research Grant Council; Neither NSF nor HKRGC has approved or endorsed its content. Part of the work was performed while the authors were participating in the HKUST-ICERM workshop ?Integral Equation Methods, Fast Algorithms and Their Applications to Fluid Dynamics and Materials Science? held in 2017. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = oct,

day = "15",

doi = "10.1016/j.jcp.2020.109521",

language = "English (US)",

volume = "419",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

}