On the use of SVD-improved point matching in the current-model method (EM scattering)

An approach which uses the singular value decomposition (SVD) to improve the accuracy of the numerical solution obtained with fictitious current models is introduced. In this approach, the SVD is essentially facilitating a systematic way to optimally reduce the generalized inverse matrix used in the solution to a submatrix of smaller rank. This reduction strikes a balance between the fulfillment of the boundary conditions at the matching points and that between them. Clearly, the boundary conditions errors at the matching points are no longer strictly zero. However, the previously discernible errors between the matching points are markedly suppressed. The approach is efficacious not only when the impedance matrix is inherently singular or highly ill conditioned, but also when this matrix is entirely well conditioned. It can be generalized and implemented in any method of moments code which uses point matching for testing. The approach has been incorporated into an existing solution based on the current-model method for the problem of scattering from periodic sinusoidal surfaces, and is shown to render the solution more accurate. >