Collaborative Research: Parallel Hybrid Differential and Integral Equation Based Solvers for Time Domain Electromagnetic Analysis with Application to High-Speed Circuits

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The goal of this project is to develop fast and accurate physics-based parallel transient electromagnetic solvers that are geared towards applications to high-speed circuits. This is being achieved via a combination of high performance parallel algorithms, novel advances in numerical schemes that permit hierarchical computation and finally, the hybridization of different numerical techniques. More specifically, the following objectives are being pursued: (i) development of novel numerical schemes that reduce the overall computational work and the corresponding parallel schemes; (ii) development of parallel and numerical methods for analyzing transient fields in diffusive and dispersive material media; (iii) development of parallel methodologies for integrating differential equation and integral equation based schemes such that one can reap the advantages of both; (iv) and finally, integrating the EM solver developed in the last item into the circuit simulation tool SPICE, to enable fullwave EM simulation of circuits. The principal impact of the proposed research is the development of high performance transient electromagnetic analysis tools that are applicable to a variety of design and analysis problems. The techniques developed are being used to analyze issues in high-speed circuits including on-chip signal integrity, non-linear devices, cross-talk, reflections, and non-linear terminations.Electromagnetic (EM) phenomena constitute the physical underpinnings of applications ranging from electrical to electronic to communication to computer technologies and are completely described by Maxwell's equations. Fast and accurate physics-based simulation tools offer a second modality of investigation into electromagnetic phenomena, and are rapidly becoming indispensable in civilian and military R & D settings. As a part of this endeavor, researchers at Michigan State University and Iowa State University are collaborating on developing an arsenal of fast and accurate simulation tools that permit on-the-fly optimization that can be used for rapid design prototyping of electromagnetic devices. To this end, novel numerical methods for transient electromagnetic analysis and algorithms to parallelize these are being developed. The techniques developed are being applied to the design and analysis of electromagnetic devices.