Workshop on Wave Propagation

Date: November 21 Sun. 9:00am

Venue: Room316, Ouyang Chunmei Building, Yuquan Campus, Zhejiang University

Iterative pure source transfer domain decomposition methods for Helmholtz equations in heterogeneous media

Speaker: Haijun Wu (Nanjing University)

Abstract: In this paper we extend the pure source transfer domain decomposition method (PSTDDM) to solve the truncated perfectly matched layer approximation of Helmholtz scattering problems by heterogeneous media. We first present somenew source transfer operators and then introduce the layer-wise and block-wise PSTDDMs based on them. In particular, it is prove that the solution obtained by the layer-wise PSTDDM in R^2 coincides with the exact solution to the heterogeneous Helmholtz problem in the computational domain. Secondly, we propose the iterative layer-wise and block-wise PSTDDMs which are designed by simply iterating the PSTDDM alternatively on two staggered decompositions of the domain. Finally, extensive numerical tests in twoand three dimensions show that, as preconditioners for the GMRES method, the iterative PSTDDMs are more robust and efficient than the PSTDDMs for solving heterogeneous Helmholtz problems.

Inverse problems for Nonlinear PDEs

Speaker: Ting Zhou (Zhejiang Univeristy)

Abstract: In this talk, I will demonstrate the higher order linearization approach to solve several inverse boundary value problems for nonlinear PDEs modeling nonlinear electromagnetic optics including nonlinear time-harmonic Maxwell’s equations with Kerr-type and second harmonic generation nonlinearity. The problem will be reduced to solving for the coefficient functions from their integrals against multiple linear solutions. We will focus our discussion on different choices of linear solutions. A similar problem for nonlinear magnetic Schrodinger equation will be considered as a comparison.

Electromagnetic field enhancement in a subwavelength rectangular open cavity

Speaker: Yixian Gao (Northeast Normal University)

Abstract: In this talk, we will present the enhancement for the electric and magnetic fields in a two-dimensional subwavelength rectangular cavity. We show that the significant field enhancement may be achieved in both non-resonant and resonant regimes. The proofs are based on variational approaches, layer potential techniques, boundary integral equations, and asymptotic analysis. Numerical experiments are also presented to confirm the theoretical finding.

High-resolution numerical reconstruction of low-amplitude surface profile with superlens

Speaker: Yuliang Wang (Beijing Normal University-Hong Kong Baptist University United International College)

Abstract: We consider the problem of imaging a periodic surface by acoustic or electromagnetic waves. A slab of double negative metamaterial is placed above the surface and the scattered field is measured on the top boundary of the slab. The imaged surface is assumed to be a small perturbation of the flat surface so that we can make a transformed field expansion to linearize the problem and obtain a simple reconstruction formula. We show by analysis of the formula and numerical experiments that the resolution of the reconstruction can be greatly enhanced due to the double negative slab.

Neutral inclusions and weakly neutral inclusions

Speaker: Xiaofei Li (Zhejiang University of Technology)

Abstract: An inclusion is said to be neutral to uniform fields if upon insertion into a homogeneous medium with a uniform field it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such inclusions are of interest in relation to invisibility cloaking and effective medium theory. There have been some attempts lately to construct or to show existence of such inclusions in the form of core-shell structure or a single inclusion with theimperfect bonding parameter attached to its boundary. This talk is to review recent progress in such attempts.