Optimal grouping of basis functions

When using the method of moments to solve scattering problems, a crucial factor is the appropriate choice of basis functions. A judicious choice of the basis functions can lead to a sparse impedance matrix or to a sparse solution vector, both of which will reduce the computational burden. However, pulse basis functions are usually used, both due to their simple description and because there are already many software tools written for this aim. Therefore, some efforts have been invested in transforming a formulation that is the result of using pulse basis functions to one using preferred basis functions. This transform produces grouping of the pulse functions into a new, more appropriate set of basis functions. This paper discusses the search for an optimal grouping, where optimality is measured in terms of the sparseness of the resulting solution vector. Various options are demonstrated and discussed, and numerical examples are given. It is important to note that the optimal grouping suggested herein is expected to be optimal on the average, when tried on many sample problems. Adjusting the optimization to a more specific set of problems and scenarios will lead to even better performances and is a viable option in practical cases.