Diakoptic Approach to Modeling and Design of Complex Electromagnetic Systems

复杂电磁系统建模和设计的透光方法

• 批准号: 1002385
• 负责人: Branislav Notaros
• 金额: $ 36万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-01 至 2016-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1002385&HistoricalAwards=false
• 关键词: Diakoptic; Approach; Modeling; Design; Complex

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.

本研究的目的是发展和应用高阶分裂法来进行复杂电磁系统的建模和设计。该方法是将一个大系统分解成许多任意形状的子系统，使用诸如有限元和矩量法等成熟的技术独立地求解各个子系统，并获得子系统边界表面上的等效电流展开系数（diakoptic系数）之间的线性关系，从而得到原始问题的解决方案。智力优势：分解方法提供了一种通用而有效的方法来解决一个大的问题，作为一个线性组合的独立解决方案的组件问题。除了显著减少计算负担外，这种方法还可以将无法解决的问题减少为可解决的问题。作为一个独特的功能，组件的问题将其特点是诺顿定理的等价表示（在diakoptic系数的形式）。应用包括新兴的电磁材料和天线阵列。更广泛的影响：分光方法将为工程界提供一种通用的方法来解决最具挑战性的电磁场问题，这种方法的典型方式是电路理论的解决方案，但具有麦克斯韦方程的严格性。它具有改变电磁系统建模和设计方式的长期潜力。与研究完全整合的几项教育举措包括围绕diakoptic方法的课程和学生的MATLAB练习，外联以及进一步加强PI组中代表性不足的学生的强烈参与的努力。