摘要：

The new and powerful wavelet and multiresolution analysis techniques offer significant performance and computational advantages in solving differential or integral equations. Wavelets are introduced here to solve problems of scattering from irregular two-dimensional objects. Two problems are considered: the special case of scattering from a uniform dielectric with irregular, small-height surface, and the general case of an arbitrary dielectric scattering region. Two corresponding approaches have been developed to exploit the application of wavelets to these problems. The special-case approach recasts the Maxwell equations into two dielectric boundary-condition integral equations. These equations are solved via a unique coordinate-spectral moment method using a wavelet testing basis. Verification of the resulting multiresolution method of moments algorithm was straightforward and successful using several problems with well-known solutions. Application of this method to periodic surfaces shows that in many cases the total scattering is a superposition of the scattering from the components of the surface, provided the surface features are not too sharp. Application of this method to fractal surfaces shows several previously-reported effects. The most notable of these effects are a decrease in Brewster's angle and enhanced backscatter. The general approach utilizes a coupled-modes expansion of the fields in the scattering region to solve the Maxwell equations. These differential equations are transformed into the wavelet domain in order to avoid any restrictive assumptions on the form of the spatially- varying permittivity, and then directly integrated numerically. Using this integration, an iterative algorithm is elucidated which should converge to a self- consistent set of scattered fields on both sides of the interface. Verification of this algorithm was only partially successful because it proved to have significant convergence problems. The culprit in this difficulty is a requirement for very small steps in the integration through the scattering region. The choice of a predictor-corrector integrator turned out to be inefficient here. Several suggestions are offered which show great promise for relieving this impediment to an approach which is extremely general and potentially very powerful.

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