Accession Number : ADA309945
Title : Inverse Scattering via Skin Effect.
Descriptive Note : Research rept.,
Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
Personal Author(s) : Chen, Yu
PDF Url : ADA309945
Report Date : MAY 1996
Pagination or Media Count : 35
Abstract : We present a stable method for the inverse scattering problem of the Helmholtz equation in two dimensions. The algorithm requires single-frequency scattering data, and is an iterative procedure which resembles the process of layer-stripping. The inversion method is based on the observation that the ill-posedness of the inverse scattering problem causes it to be almost linear in certain regimes. In these regimes, the algorithm solves the resulting quasi-linear equations to produce approximate solution to the inverse problem within a narrow circular layer surrounding the yet unrecovered part of the scatterer. This approximation is used to linearize the underlying narrow circular strip; in the process, the previously obtained solution is refined. The performance of the algorithm is demonstrated with several numerical examples for the special case of radially symmetric scatterers.
Descriptors : *INVERSE SCATTERING, *HELMHOLTZ EQUATIONS, MATHEMATICAL MODELS, ALGORITHMS, LINEAR SYSTEMS, UNCERTAINTY, TWO DIMENSIONAL, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, RECURSIVE FUNCTIONS, LEAST SQUARES METHOD, CONVERGENCE, PERTURBATIONS, OPERATORS(MATHEMATICS), NUMERICAL METHODS AND PROCEDURES, GREENS FUNCTIONS, ITERATIONS, LAPLACE TRANSFORMATION, RICCATI EQUATION.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE