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An integral formulation of two- and three-dimensional dielectric structures using orthonormal multiresolution expansions. (English) Zbl 0911.65144

This paper presents a space domain integral formulation of planar dielectric structures based on the concepts of multiresolution analysis (MRA) theory. Battle-Lemarie multiresolution expansions are utilized in the moment method solution of a volume integral equation for the unknown electric field. The generation of sparse moment matrices is explained in view of the cancellation property of wavelet basis functions. Numerical results and consequences of matrix sparsity are discussed when this formulation is applied to two- and three-dimensional dielectric structures including wave guides and resonators.

MSC:

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
78A50 Antennas, waveguides in optics and electromagnetic theory
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