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RECONSTRUCTION OF A SMALL INCLUSION IN A TWODIMENSIONAL OPEN WAVEGUIDE ∗
"... Abstract. We consider wave propagation in a perturbed open waveguide. We provide a new asymptotic expansion for the scattered wave when the inclusion is of small diameter. We design a MUSIC (multiple signal classification) type of algorithm for locating the inclusion and illustrate its viability in ..."
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Abstract. We consider wave propagation in a perturbed open waveguide. We provide a new asymptotic expansion for the scattered wave when the inclusion is of small diameter. We design a MUSIC (multiple signal classification) type of algorithm for locating the inclusion and illustrate its viability in numerical examples.
Research Article The Problem of Scattering by a Mixture of Cracks and Obstacles
, 2009
"... Consider the scattering of an electromagnetic timeharmonic plane wave by an infinite cylinder having an open crack Γ and a bounded domain D in R2 as cross section. We assume that the crack Γ is divided into two parts, and one of the two parts is possibly coated on one side by a material with surfa ..."
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Consider the scattering of an electromagnetic timeharmonic plane wave by an infinite cylinder having an open crack Γ and a bounded domain D in R2 as cross section. We assume that the crack Γ is divided into two parts, and one of the two parts is possibly coated on one side by a material with surface impedance λ. Different boundary conditions are given on Γ and ∂D. Applying potential theory, the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of a solution to the system by using Fredholm theory. Copyright q 2009 Guozheng Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Chinese Academy of Sciences
"... In this paper, a unified approach for analyzing finite dimensional approximations to a class of partial differential equations boundary value problems (secondkind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular ..."
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In this paper, a unified approach for analyzing finite dimensional approximations to a class of partial differential equations boundary value problems (secondkind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Key words. Convergence, error analysis, finite dimensional approximation, Fredholm differential equation 2000 AMS subject classifications. 65N15, 65N30. 1