Adaptive refinement of higher order method of moment applied to surface integral equations

Optimal choice of expansion orders for currents is of crucial importance for efficient use of higher order basis functions in method of moment solution of surface integral equations. In this paper it is shown that accuracy of a solution for a given set of expansion orders can be estimated using the residuum of the system of linear equations, obtained by increasing expansion orders by one. Based on such estimation, an iterative procedure is proposed for determination of a minimum set of basis functions needed for given accuracy. In the first iteration 1^st order is adopted for all patches. In each iteration patches having insufficient order of current expansion are detected and their orders are increased in the next iteration. Iterative procedure is stopped when a sufficient order of current expansion is detected. The method is illustrated on examples of a cube and a fighter airplane scatterer.