2020/02/18 by Huayi Wei, Wei, Huayi, Xin Wang +5
Chemical Engineering · Engineering · Materials Science · #Advanced Numerical Methods in Computational Mathematics #Block Copolymer Self-Assembly #FOS: Mathematics #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.2002.08187
openalex publication_date 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging nodes as polygon vertices without additional processing. Besides, to effectively simulate the phase separation behavior in strong segregation systems, an adaptive method on polygonal mesh equipped with a new marking strategy is developed. This new marking strategy will indicate the times of marked elements to be refined and coarsened, making full use of the information contained in the current numerical results. Using the halfedge data structure, we can apply the adaptive method to the arbitrary polygonal mesh. Numerical results demonstrate that the developed method is efficient in simulating polymers' phase behavior in complex geometric domains. The accuracy is consistent with theoretical results. The adaptive method can greatly reduce computational costs to obtain prescribed numerical accuracy for strong segregation systems.