Novel Nonconforming Finite Element Methods for Maxwell's Equations

麦克斯韦方程组的新颖非协调有限元方法

基本信息

批准号：
0713835
负责人：
Susanne Brenner
金额：
$ 26万
依托单位：
Louisiana State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2007
资助国家：
美国
起止时间：
2007-07-15 至 2011-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0713835&HistoricalAwards=false
关键词：
Novel Nonconforming Finite Element Methods

项目摘要

The research in this project is based on the recent discovery of the PIs that numerical solutions of Maxwell's equations can be based on variational formulations that use function spaces where the divergence free condition is enforced. This is made possible by combining classical nonconforming finite elements for incompressible fluid flows and techniques from discontinuous Galerkin methods. In this new approach the boundary value problems of the time-harmonic (frequency-domain) Maxwell's equations are solved as elliptic problems, and the performance of the new nonconforming finite element methods for both the source (deterministic) problem and the eigenproblem (cavity resonance problem) is comparable to the performance of classical finite element methods for computational mechanics. In particular the discrete eigenvalues have neither spurious modes nor nonphysical zero eigenvalues. The proposed research will design and analyze many novel schemes for the Maxwell equations and the Maxwell eigenproblem using this new approach. Fast solvers (multigrid and domain decomposition methods) and adaptive algorithms will also be developed, with applications to related electromagnetic problems.The results of the proposed research will provide powerful computational tools for the design and analysis of electromagnetic devices such as antennas, radar sensors, waveguides, photonic crystals, magnetoresistive sensors and particle accelerators, with applications to diverse areas such as telecommunications, integrated optics, lasers, high energy physics, plasma physics, and nondestructive damage detection.

该项目中的研究基于PI的最新发现，即Maxwell方程的数值解决方案可以基于使用函数空间的变异配方，在该函数空间中执行了无差异条件。通过将经典不合格的有限元元素组合为不可压缩的流体流量和不连续的盖尔金方法的技术来实现这一可能。在这种新方法中，时间谐波（频率域）麦克斯韦方程的边界价值问题被求解为椭圆问题，以及针对源（确定性）问题和特征性的新型不合格有限元方法的性能（腔共振）问题）与计算力学的经典有限元方法的性能相当。特别是离散的特征值既没有虚假模式，也没有非物理零特征值。拟议的研究将使用这种新方法设计和分析Maxwell方程和Maxwell本本题的许多新方案。还将开发快速求解器（Multigrid和域分解方法）和自适应算法，并应用于相关的电磁问题。拟议的研究的结果将为设计和分析提供强大的计算工具，用于设计和分析电磁设备，例如雷达传感器，雷达传感器，，雷达传感器，，雷达传感器，，，雷达传感器，，雷达传感器，，雷达传感器，，雷达传感器，，雷达传感器，雷达传感器，，雷达传感器，雷达传感器，雷达传感器，雷达传感器，雷达传感器，雷达传感器，雷达传感器，雷达传感器，雷达传感器的设计和分析。波导，光子晶体，磁化传感器和粒子加速器，应用于电信，集成光学，激光，高能量物理，血浆物理学和非损害损伤检测等不同区域。