A numerically efficient technique for orthogonalizing the basis functions arising in the solution of electromagnetic scattering problems using the CBFM

Abstract

The characteristic basis function method (CBFM) (V.V.S. Prakash and R. Mittra, 2003) embodies an efficient way to handle large electromagnetic problems in a rigorous manner by defining a reduced set of precomputed characteristic basis functions (CBFs), which represent the currents along the target surface. By utilizing the CBFs, the number of unknowns which arise in the application of the conventional method of moments can be decreased by an order of magnitude, enabling the use of direct solvers even for large problems. In the CBFM, the CPU-time is mainly consumed in carrying out the following two operations: calculating the characteristic basis functions and computation of the matrix-vector products required to generate the reduced matrix elements. After splitting the geometry into several blocks, the CBFs for each is generated from a set of solutions for the induced currents in the subdomains that are illuminated by plane waves incident from different angles. The orthogonalization of these solutions, via an SVD procedure (M. DeGiorgi et al., 2005), is an important step that reduces the final number of CBFs by eliminating the redundancy in these functions, that also serves to improve the condition number of the reduced matrix.