一类三维椭圆界面问题的虚单元计算  

The virtual element calculation for a class of two-dimensional elliptic interface problems

作　　者：张浦帆 阳莺[1] 黄凌涵 沈瑞刚 ZHANG Pufan;YANG Ying;HUANG Linghan;SHEN Ruigang(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期63-67,共5页Journal of Guilin University of Electronic Technology

基　　金：广西科技基地和人才专项(桂科AD23026048);国家自然科学基金(12161026,12101595);广西自然科学基金(2020GXNSFAA159098)。

摘　　要：椭圆界面问题是一种常出现在力学、材料科学、生物化学等领域的数值模拟中的经典模型问题。该模型问题具有间断系数和不规则界面两大特点。采用虚单元方法求解三维椭圆界面问题,与传统有限元法相比,该方法更适用于一般的多面体网格,这使得网格的选取变得自由与多样。基于这种特点,给出虚单元法求解一类三维椭圆界面问题的计算公式,并使用3种不同的多面体网格完成数值实验。数值结果表明,虚单元方法应用于该问题是有效的。The elliptic interface problem is a classical model problem that frequently occurs in numerical simulations in fields such as mechanics,materials science,and biochemistry.This model problem is characterized by discontinuous coefficients and irregular interfaces.The use of the virtual element method to solve three-dimensional elliptic interface problems is more suitable for general polyhedral meshes compared to traditional finite element methods,allowing for greater freedom and diversity in mesh selection.Based on this characteristic,this paper presents the computational formula for solving a class of three-dimensional elliptic interface problems using the virtual element method and conducts numerical experiments using three different polyhedral meshes.The numerical results demonstrate that the virtual element method is effective for this problem.

关 键 词：椭圆界面问题 虚单元方法 多面体网格 Voronoi网格 三维 

分 类 号：O246.82[理学—计算数学]