A look at some challenging problems in computational electromagnetics

Recent years have seen a spectacular increase in our capability to model, simulate the performance of, and design complex electromagnetic systems. Much progress has been made in enhancing the available numerical techniques, viz., the method of moments (MoM), the finite-element method (FEM), and the finite-difference time-domain (FDTD) or its variants. Great strides have recently been made in enlarging the scope of MoM via the use of the fast multipole method (FMM), which has made it feasible for us to solve problems that require the handling of 106 degrees of freedom, or even higher, and distributed processing has enabled the FDTD to handle upward of 109 degrees of freedom on a moderate-size computing platform. Despite this recent progress, many practical computational electromagnetic (CEM) modeling problems of interest present formidable challenges, and the search for numerically efficient techniques to solve large problems involving complex structures continues unabated. The objectives of this paper are to identify some of these challenging problems encountered by the author during the last five years, and to present the results of application of a technique called CBFM - developed at the EMC Laboratory at Penn State - that has been found useful for addressing them.