Vem++,一个C++库来处理和玩虚拟元素方法
1Dipartimento di Matematica e Applicazioni, Università Milano - Bicocca, via Cozzi 55, Milano, 20126 Italy.
概括
虚拟元件方法 (VEM) 是复杂网格的有限元件方法 (FEM) 的扩展. Vem++是一个C++库,解决了VEM实现的挑战,使其在各种问题中灵活使用.
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:
- 有限元法 (FEM) 是一种用于解决微分方程的强大数值技术.
- 处理复杂的,非标准的几何形状 (多重形网格) 对传统的FEM构成了挑战.
- 虚拟元件方法 (VEM) 为这种复杂的网格提供了FEM的通用方法.
研究的目的:
- 介绍虚拟元件方法 (VEM) 对于一个二维拉普拉斯问题.
- 要突出与FEM相比,VEM的实施差异和挑战.
- 介绍Vem++,一个C++库,旨在促进VEM的实现和应用.
主要方法:
- 介绍VEM用于2D拉普拉斯问题.
- 对VEM和FEM实施策略的比较分析.
- 开发和描述Vem++ C++库. 开发和描述Vem++ C++库.
主要成果:
- 确定与VEM框架相关的关键实施问题.
- 展示Vem++作为解决这些VEM挑战的解决方案.
- Vem++提供了一个灵活的平台,可以将VEM应用于各种PDE.
结论:
- 在复杂的网格场景中,VEM为FEM提供了可行的扩展.
- Vem++库有效地解决了VEM实施的障碍.
- Vem++ 能够实现"插即用"的集成,用于高级 VEM 应用程序的新功能.
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