Diakoptic Approach to Modeling and Design of Complex Electromagnetic Systems

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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.