Math Technical Report Series
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Browsing Math Technical Report Series by Author "Colton, David"
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Item The Direct and Inverse Scattering Problems for Partially Coated Obstacles(Department of Mathematical Sciences, 2002) Cakoni, Fioralba; Colton, David; Monk, Peter B.We consider the direct and inverse scattering problems for partially coated obstacles. To this end, we first use the method of integral equations of the first kind to solve a scattering problem for the Helmholtz equation where the scattered field satisfies mixed Dirichlet-impedance boundary conditions on the Lipschitz boundary of the scatterer D. We then use the linear sampling method to solve the inverse scattering problem of determining D from a knowledge of the far field pattern of the scattered field. Numerical examples are given showing the performance of the linear sampling method in this case.Item Inverse Electromagnetic Scattering Problem for a Partially Coated Dielectric(Department of Mathematical Sciences, 2004) Cakoni, Fioralba; Colton, David; Monk, Peter B.We use the linear sampling method to determine the shape and surface conductivity of a partially coated dielectric from a knowledge of the far field pattern of the scattered electromagnetic wave at fixed frequency. A mathematical justification of the method is provided for both the scalar and vector case based on the use of a complete family of solutions. Numerical examples are given for the scalar case.Item On the Mathematical Basis of the Linear Sampling Method(Department of Mathematical Sciences, 2002) Cakoni, Fioralba; Colton, DavidThe linear sampling method is an algorithm for solving the inverse scattering problem for acoustic and electromagnetic waves. There are two versions of the linear sampling method. Although the second version is on a firm mathematical foundation, it is restricted to the case of non-absorbing media, full aperture scattering data or, more specifically, to the cases when the far field operator is normal. The first version of the linear sampling method is more flexible, being able to treat the aforementioned cases as well as partially coated obstacles. However, its mathematical foundation is less well established. In this paper we provide arguments giving a mathematical justification of the first version of the linear sampling method.Item Recent Developments in Inverse Acoustic Scattering Theory(Department of Mathematical Sciences, 2000) Colton, David; Coyle, J.; Monk, Peter B.We survey some of the highlights of inverse scattering theory as it has developed over the past fifteen years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects.