Abstract
This paper proposes a first- and second-order unconditionally stable direct discretization method based on a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation for solving the N-component Cahn-Hilliard system. We define the discretizations of the gradient, divergence, and Laplace-Beltrami operators on triangle surfaces. We prove that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable. We also prove that our method satisfies the mass conservation. The proposed scheme is solved by the biconjugate gradient stabilized (BiCGSTAB) method, which can be straightforwardly applied to GPU-accelerated biconjugate gradient stabilized implementation by using the Matlab Parallel Computing Toolbox. Several numerical experiments are performed and confirm the accuracy, stability, and efficiency of our proposed algorithm. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier