Convergence of ℒ² methods for scattering problems

We compare 35 different methods for calculating reactance matrix elements from ℒ² basis sets. By systematically classifying the methods, we are able to draw conclusions about several lines of approach. For example, the explicit subtraction of unscattered waves or the least-squares minimization of the iterative correction do not lead to significant improvements in accuracy. However, expansions of the amplitude density are systematically more rapidly convergent than expansions of the wave function. The most efficient methods are variational methods based on expanding the amplitude density, but the method of moments for the amplitude density may also be useful since it leads to reasonable accuracy with smaller programming effort.