论文标题
聚合物自谐场理论的一种自适应虚拟元素方法
An adaptive virtual element method for the polymer self-consistent field theory
论文作者
论文摘要
在本文中，我们开发了一个高阶自适应虚拟元素方法（VEM），以模拟任意域中的自洽场理论（SCFT）模型。 VEM在处理一般多边形元件方面非常灵活，并且可以将悬挂的节点视为多边形顶点，而无需其他处理。此外，为了有效地模拟强隔离系统中的相分离行为，开发了针对具有新标记策略的多边形网格的自适应方法。这种新的标记策略将表明要完善和粗糙的标记元素的时代，从而充分利用当前数值结果中包含的信息。使用HalfEdge数据结构，我们可以将自适应方法应用于任意多边形网格。数值结果表明，开发的方法在模拟复杂几何域中的聚合物相位行为有效。准确性与理论结果一致。自适应方法可以 大大降低了计算成本，以获得强大的隔离系统的规定数值准确性。
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.
