MULTIPLE MULTIPOLE EXPANSIONS FOR ELASTIC-SCATTERING

This paper presents a new approach to solve scattering of elastic wave s in two dimensions. Traditionally, wave fields are expanded into an o rthogonal set of basis functions. Unfortunately, these expansions conv erge rather slowly for complex geometries. The new approach enhances c onvergence by summing multiple expansions with different centers of ex pansions. This allows irregularities of the boundary to be resolved lo cally from the neighboring center of expansion. Mathematically, the wa ve fields are expanded into a set of nonorthogonal basis functions. Th e incident wave field and the fields induced by the scatterers are mat ched by evaluating the boundary conditions at discrete matching points along the domain boundaries. Due to the nonorthogonal expansions, mor e matching points are used than actually needed, resulting in an overd etermined system which is solved in the least-squares sense. Since the re are free parameters, such as location and number of expansion cente rs, as well as kind and orders of expansion functions used, numerical experiments are performed to measure the performance of different disc retizations. An empirical set of rules governing the choice of these p arameters is found from these experiments. The resulting algorithm is a very general tool to solve relatively large and complex two-dimensio nal scattering problems. (C) 1996 Acoustical Society of America.