Multiresolution expansions for efficient moment method solution of wave guiding problems

It was shown that the use of orthonormal wavelets in the numerical solution of certain integral equations leads to sparsely populated matrices. This idea was employed in the moment method formulation of electromagnetic scattering problems, where a specific example of a double-slot aperture in a planar conducting screen is presented using Battle-Lemarie wavelets. A concern in the application of wavelet expansions to electromagnetic problems is the restoration of the DC or lowpass part of the fields. We show how to make this provision by a systematic use of the multiresolution analysis theory. In this way, the number of expansion functions can also be reduced to a minimum. It is believed that using wavelets with a large number of vanishing moments leads to an increase in the sparsity of the matrices. This issue is examined by a discussion of orthonormal wavelets with both infinite and compact supports. Numerical results are presented for the case of an open dielectric strip waveguide.<>