CAREER: A Framework for Modular Fast Direct Electromagnetic Simulations

This CAREER proposal presents an integrated research and education program which will produce revolutionary advances in the tools, methods, and applications of high fidelity numerical electromagnetic models. The proposed developments will be accomplished in an educational atmosphere promoting respect for others, collaborative learning, research experiences for undergraduates, and outreach to underrepresented groups. The research component of this CAREER proposal will advance the state-of-the-art in time-harmonic computational electromagnetics (CEM) through the development of a revolutionary framework for modular, fast, direct electromagnetic simulations. This framework will be based on the systematic, numerically efficient application of a fundamentally new, physics-based organizing principle for simulations of time harmonic electromagnetic phenomena. The new organizing principle consists of representing electromagnetic solution operators in a complete basis of localized solution modes which satisfY global boundary conditions. These modes are referred to as LOGOS (local-global solution) modes. The proposed research activities will develop new algorithms based on the LOGOS expansions for broadband simulations via both integral and differential representations of the underlying electromagnetic phenomena. The resulting LOGOS framework will provide several important contributions to the fields of applied and computational electromagnetics not afforded by any other simulation technology. These contributions will include the first general, error-controllable method which provides fast, sparse representations of the electromagnetic solution operator at all frequencies. While this will significantly impact all application areas in which CEM tools are used to model large, complex systems, the proposed LOGOS-based simulation technologies will have an even broader significance. For example, the LOGOS organizational principle can be used to: develop modular full-wave design tools for electromagnetic modeling of complex scenes, rapidly perform perturbative design in a small portion of an electrically large simulation domain, and develop sparse full-wave reduced-order models for electromagnetic interactions with complex environments. These new capabilities are expected to both overcome many limitations of existing CEM tools, and open doors to exciting new research opportunities in which highfidelity CEM models playa much more active role in system performance. In order to increase the benefits of the proposed computational technologies to the applied electromagnetics community, the resulting code will be freely distributed in the form of a CEM "toolbox" for the widely used MATLABTM computing environment. The CEM toolbox will contain a suite of functions for tasks including mesh generation, solver control, post processing, and visualization. The resulting CEM toolbox will be distributed through the World Wide Web. A web page for this project will provide source code, documentation, and numerical examples illustrating the use of the toolbox. The web page will also facilitate user interaction by providing a discussion forum, a file repository for user contributions, and a database of examples obtained from user applications of the CEM toolbox in specific applications. Finally, the proposed CEM toolbox and web pages will provide a primary means by which students at various stages in their educational careers can contribute to and learn from the proposed research program.