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

将进行为期三年的研究，以推进这类新解方法的理论和算法基础。主要有三个推力：边界条件，包括辐射条件和更精确的远场混合耦合条件，通过边界元和矩法；-由这些新的弱形式产生的非常大的、稀疏的、不定系统的迭代矩阵求解方法；将有限元的几何柔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，计划了分析、数值分析和计算实验。工业和生物医学应用将用作测试问题，涵盖广泛的介电特性，几何形状和问题大小。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。

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.