2021/06/14 by Kai Jiang, Xin Wang, Jiang, Kai +5
Chemical Engineering · Computer Science · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Block Copolymer Self-Assembly #Computer science #Discretization #Engineering #Estimator #FOS: Mathematics #Field (mathematics) #Finite element method #Function (biology) #Geometry #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Order (exchange) #Rheology and Fluid Dynamics Studies #Space (punctuation) #Structural engineering #Surface (topology) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2106.07405
published in arXiv (Cornell University) (Cornell University) · 23 pages, 14 figures
openalex publication_date 2021/06/14 · arxiv created 2021/08/01 · arxiv updated 2021/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the 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 the 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. Compared with the traditional strategy, 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 ecciency 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 ecciency of the proposed method, especially for strongly segregated systems with economical discretization nodes.