Node-Based Finite Element Methods for Helmholtz Forms of Maxwell's Equations

麦克斯韦方程的亥姆霍兹形式的基于节点的有限元方法

• 批准号: 9218750
• 负责人: Daniel Lynch
• 金额: $ 62万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-08-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9218750&HistoricalAwards=false
• 关键词: Node; Based; Finite; Element; Methods

A Three year study will be undertaken to advance to the theoretical and algorithmic foundations of this new class of solution methods. There are three main thrusts: -boundary conditions, including radiation conditions and more precise hybrid coupling conditions to far-field via Boundary Element and Moment methods;-iterative matrix solution methods for very large, sparse, indefinite systems which these new weak forms generate;-time domain methods which combine the geometric flexibility of finite elements with the efficiencies of finite differences. Analysis, numerical analysis, and computational experiment are planned in pursuit of these goals. Industrial and biomedical applications will be used as test problems, covering a wide range of dielectric properties, geometry, and problem size. Results are expected to support the widespread application of these finite element ideas in engineering and scientific practice.

将进行为期三年的研究，以推进这类新的求解方法的理论和算法基础。有三个主要推力：-边界条件，包括辐射条件和通过边界元和矩对远场的更精确的混合耦合条件方法：研究方法：-由这些新的弱形式产生的超大型、稀疏、不确定系统的迭代矩阵求解方法；-将有限元的几何灵活性与有限差分的效率相结合的时域方法。为了实现这些目标，计划进行分析、数值分析和计算实验。工业和生物医学应用将被用作测试问题，涵盖范围广泛的介电性能、几何形状、以及问题的大小。这些结果有望支持这些有限元思想在工程和科学实践中的广泛应用。