A Three year study will be undertaken to advance to the theoretical and algorithmic foundations of this new class of solution methods. There are three main thrusts: -boundary conditions, including radiation conditions and more precise hybrid coupling conditions to far-field via Boundary Element and Moment methods;-iterative matrix solution methods for very large, sparse, indefinite systems which these new weak forms generate;-time domain methods which combine the geometric flexibility of finite elements with the efficiencies of finite differences. Analysis, numerical analysis, and computational experiment are planned in pursuit of these goals. Industrial and biomedical applications will be used as test problems, covering a wide range of dielectric properties, geometry, and problem size. Results are expected to support the widespread application of these finite element ideas in engineering and scientific practice.
