This CAREER proposal outlines an integrated research and education program designed to provide significant advances in the tools, methods, and applications of high fidelity electromagnetic simulations in order to meet the challenges presented by existing and emerging technological needs. Intellectual Merit. The state-of-the-art in time-harmonic computational electromagnetics (CEM) will be advanced through the development and implementation of a novel framework for modular, fast, direct electromagnetic simulations. The central concept underlying this effort is a new, physics-based organizing principle for simulations of electromagnetic phenomena. The 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 algorithms and tools based on the LOGOS expansions for CEM applications. The resulting framework and algorithms will provide contributions to the field of CEM not afforded by existing technologies. Broader Impact. The simulation algorithms resulting from this research effort are expected to impact many areas of computational physics outside the EM field. To further broaden the educational and societal impacts of this effort, local resources will be used to attract undergraduate and graduate students from underrepresented populations. These students will in turn be asked to participate in outreach activities to regional high schools, thus providing role models to students in underrepresented STEM populations.
