Collaborative Proposal: SGER: Conforming Polygonal Finite Elements

协作提案：SGER：相容多边形有限元

• 批准号: 0352654
• 负责人: Natarajan Sukumar
• 金额: $ 3万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-03-01 至 2005-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0352654&HistoricalAwards=false
• 关键词: Collaborative; Proposal; SGER; Conforming; Polygonal

In this Small Grant Exploratory Research proposal, a new and novel direction in finite element methodology is pursued. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this proposal, recent advances in meshfree approximations, computational geometry, and computer graphics will be used to construct conforming trial and test approximations onpolygonal finite elements. Computational algorithms (optimization scheme) for mesh generation with polygonal elements will be developed, and numerical studies on the accuracy and convergenceof the finite element technique will be conducted forelliptic boundary-value problems. The results of this study can potentially open-up new pathways in finite element research, lead to the wider usage of polygonal finite element methods in solid mechanicsand computational materials science, and also provide impetus for the construction of cubature rules on polytopes.

在这项小额资助探索性研究提案中，追求有限元方法学的新方向。 多边形有限元在网格生成方面提供了更大的灵活性，并且更适合涉及材料域拓扑发生重大变化的固体力学应用。在该提案中，无网格近似、计算几何和计算机图形学的最新进展将用于在多边形有限元上构建一致的试验和测试近似。 将开发多边形单元网格生成的计算算法（优化方案），并对椭圆边值问题的有限元技术的精度和收敛性进行数值研究。这项研究的结果可能会开辟有限元研究的新途径，导致多边形有限元方法在固体力学和计算材料科学中更广泛的应用，并为多面体体积规则的构建提供动力。