9622555 Reitich This project deals with analytical and computational issues in electromagnetic and acoustic scattering problems. It relates to a new method for the solution of such problems, based on high-order boundary perturbation and analytic continuation techniques, that was introduced by the principal investigator in the context of diffraction gratings. There, the numerical algorithms produced, in many cases, results with substantially improved accuracy over that given by classical approaches. The proposed research concerns new applications of the method in other challenging areas of current interest in electromagnetics and acoustics and the further study and improvement of the numerical properties of the resulting algorithms. Both the forward and inverse scattering problems will be investigated for a variety of configurations, including scattering by electrically large bounded bodies and in ocean waveguides. In particular, the benchmark problems of electromagnetic scattering by three-dimensional cubes and of sound propagation in oceans with rough surfaces will be treated. Based on some preliminary studies, it is expected that the performance of the method in these areas will be of a quality comparable to the one it exhibited in prior implementations. %%% The ability to predict the shape of the electromagnetic or acoustic field scattered as an incident wave encounters an obstacle or interface has been long recognized as having major implications in a great number of scientific and engineering disciplines. Indeed, much of what we "see" --be it through visible light or x-rays, radio or microwaves-- or "hear" reaches us through a complicated combination of phenomena among which scattering is, in most cases, an essential element. As such, a better understanding of how light and sound waves propagate and diffract has led, in the last few decades, to substantial advances in a variety of fields; these include communications, monitoring, s eismic profiling, tomography and target detection, to name just but a few. An important role in these advances was the one played by mathematical modeling and, with the advent of computers, that of computational science. The present and future needs, however, demand the development of more efficient, accurate and reliable algorithms to deal with complex geometries and media. Indeed, the resolution of the scattering in such situations (such as when dealing with human tissue or undersea topography) often entails calculating a highly oscillatory field. When using most classical algorithms these oscillations translate into high computational costs, as these methods attempt to capture the variations of the field at each point in time and space. Therefore, alternative approaches whose complexity does not correlate to that of the field under study become very desirable. The present project relates to one such approach, that was successfully developed by the principal investigator in the context of micro-optical devices. The proposed research concerns new applications of this novel method in other challenging areas of current interest in electromagnetics and acoustics where it is expected to provide a valuable computational tool. ***
