Diakoptic Approach to Modeling and Design of Complex Electromagnetic Systems

这项研究的目的是开发和应用一种用于复杂电磁系统建模和设计的高阶分裂方法。其方法是将一个大系统分解成若干个任意形状的子系统，利用有限元和矩方法等成熟的技术独立地求解各个子系统，并获得子系统边界面上的等效电流展开式系数(径向系数)之间的线性关系，从而得到原始问题的解。智能优点：诊断方法为解决大型问题提供了一种通用而有效的方法，它是组件问题的独立解决方案的线性组合。除了显著减少计算负担外，这种方法还允许将无法解决的问题减少为可解决的问题。作为一个独特的特征，分量问题将由其类似诺顿定理的等价表示(以径向光学系数的形式)来表征。应用包括新兴的电磁材料和天线阵列。更广泛的影响：诊断方法将为工程界提供一种通用方法，以电路理论解决方案的典型方式解决最具挑战性的电磁场问题，但具有麦克斯韦方程的严密性。它具有改变电磁系统建模和设计方式的长期潜力。与研究完全结合的几项教育举措包括开设一门课程，为学生提供诊断方法和MatLab练习，开展外联活动，并努力进一步加强代表人数不足的学生在国际和平协会小组中的积极参与。

The objective of this research is the development and application of a higher order diakoptic method for modeling and design of complex electromagnetic systems. The approach is to break a large system into a number of subsystems of arbitrary shapes, solve the individual subsystems independently using well established techniques such as finite-element and moment methods, and obtain linear relations between the coefficients of equivalent current expansions over the boundary surfaces of the subsystems (diakoptic coefficients), which yield the solution to the original problem. Intellectual Merit: The diakoptic approach provides a general and efficient way to solve a large problem as a linear combination of independent solutions of component problems. In addition to a significant reduction of the computational burden, this approach will allow reducing an unsolvable problem to solvable ones. As a unique feature, component problems will be characterized by their Norton-theorem-like equivalent representations (in the form of diakoptic coefficients). Applications include emerging electromagnetic materials and antenna arrays.Broader Impacts: The diakoptic approach will provide the engineering community with a general method for solving the most challenging electromagnetic-field problems in a fashion typical for circuit-theory solutions, but with the rigor of Maxwell's equations. It has the long-term potential to transform the way modeling and design of electromagnetic systems is done. Several educational initiatives, fully integrated with the research, include a course around the diakoptic approach and MATLAB exercises for students, outreach, and efforts to further enhance strong participation of underrepresented students in the PI's group.