VEMcomp:一个虚拟元件MATLAB包,用于2D和3D的散装表面PDEs.
Massimo Frittelli1, Anotida Madzvamuse2,3,4,5, Ivonne Sgura1
1Department of Mathematics and Physics "E. De Giorgi", Via per Arnesano, University of Salento, 73100 Lecce, Italy.
概括
本研究介绍了VEMcomp,这是一个虚拟元素方法 (VEM) MATLAB解决器,用于部分微分方程 (PDEs). VEMcomp有效地处理复杂的几何形状和各种PDE类型,为科学计算提供了一种多功能工具.
科学领域:
- 计算数学 计算数学 计算数学
- 数字分析 数字分析
- 科学计算科学计算
背景情况:
- 部分微分方程 (PDEs) 在材料科学,工程和生物学领域的建模现象中是至关重要的.
- 现有的数值方法经常面临复杂的几何形状和多种PDE配方的挑战.
- 需要灵活和高效的解决方案,适用于广泛的科学问题.
研究的目的:
- 介绍VEMcomp,一个虚拟元件MATLAB解决器,用于2D和3D的圆和抛物线,线性和半线性PDEs.
- 为生成网格,计算矩阵和解决PDE问题提供统一的库.
- 为各种 PDE 模型提供一个用户友好的界面,用于将虚拟元素方法 (VEM) 和有限元素方法 (FEM) 应用于各种 PDE 模型.
主要方法:
- 在一般多边形和多面网格上实施最小多项式顺序 (k=1) 的虚拟元素方法 (VEM).
- 集成用于多角形和多面体域的网格生成能力,包括对表面PDE与DistMesh的兼容性.
- 利用IMEX Euler在短暂问题中的时间步骤,再加上VEM/FEM空间分密化.
主要成果:
- VEMcomp成功生成了优化的网格,并计算了VEM和FEM所需的矩阵 (质量和刚度).
- 解决器处理线性和非线性模型,包括时间依赖的批量,表面和批量-表面 PDEs.
- 提供可选的后处理功能用于可视化和错误估计.
结论:
- 在科学和工程领域,VEMcomp提供了一种强大而灵活的工具,用于解决广泛的PDE问题.
- 图书馆能够处理复杂的几何形状和各种PDE类型,这使得它对研究人员非常有价值.
- VEMcomp促进了VEM和FEM的应用,增强了对具有挑战性的问题的数值解决方案.
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