Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow

作     者：Christlieb, Andrew Promislow, Keith Tan, Zengqiang Wang, Sulin Wetton, Brian Wise, Steven M. 

作者机构：Department of Mathematics Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States School of Science Wuhan University of Technology Wuhan430070 China School of Mathematics Hunan University Changsha410082 China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics Hunan University Changsha410082 China Department of Mathematics The University of British Columbia VancouverBCV6T 1Z2 Canada Department of Mathematics The University of Tennessee KnoxvilleTN37996 United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2020年

核心收录：

主　　题：Errors 

摘      要：Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard (FCH) energies. We modify these energies, mollifying the singularities to stabilize the computation of the gradient flows and develop a series of benchmark problems that emulate the morphological complexity observed in experiments. These benchmarks investigate the delicate balance between the rate of absorption of amphiphilic material onto an interface and a least energy mechanism to disperse the arriving mass. The result is a trichotomy of responses in which two-dimensional interfaces either lengthen by a regularized motion against curvature, undergo pearling bifurcations, or split directly into networks of interfaces. We evaluate a number of schemes that use second order backward differentiation formula (BDF2) type time stepping coupled with Fourier pseudo-spectral spatial discretization. The BDF2-type schemes are either based on a fully implicit time discretization with a preconditioned steepest descent (PSD) nonlinear solver or upon linearly implicit time discretization based on the standard implicit-explicit (IMEX) and the scalar auxiliary variable (SAV) approaches. We add an exponential time differencing (ETD) scheme for comparison purposes. All schemes use a fixed local truncation error target with adaptive time-stepping to achieve the error target. Each scheme requires proper preconditioning to achieve robust performance that can enhance efficiency by several orders of magnitude. The nonlinear PSD scheme achieves the smallest global discretization error at fixed local truncation error, however the IMEX and SAV schemes are the most computationally efficient as Copyright © 2020, The Authors. All rights reserved.