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An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces

An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces

Year:    2025

Author:    Kai Jiang, Xin Wang, Jianggang Liu, Huayi Wei

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 123–147

Abstract

In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved surfaces. The high-order surface FEM is obtained by the high-order surface geometrical approximation and the high-order function space approximation. Numerical results demonstrate that the precision order of these methods is consistent with theoretical prediction. In order to describe the sharp interface in the strongly segregated system more accurately, an adaptive FEM equipped with a new $Log$ marking strategy is proposed. The $Log$ marking strategy can not only label the elements that need to be refined or coarsened, but also give the refined or coarsened times, which can make full use of the information of a posterior error estimator and improve the efficiency of the adaptive algorithm. To demonstrate the power of our approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces. Numerical results illustrate the efficiency of the proposed method, especially for strongly segregated systems with economical discretization nodes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0061

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 123–147

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Self-consistent field theory block copolymers adaptive high-order surface finite element method general curved surfaces self-assembled patterns $Log$ marking strategy.

Author Details

Kai Jiang

Xin Wang

Jianggang Liu

Huayi Wei