Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation

AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.