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This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the problem are first established by using the Laplace transform and the energy method. A perfectly matched layer (PML) is then introduced to truncate the interaction problem above a finite layer containing the elastic body, leading to a PML problem in a finite strip domain. We further establish the existence, uniqueness and stability estimate of solutions to the PML problem. Finally, we prove the exponential convergence of the PML problem in terms of the thickness and parameter of the PML layer, based on establishing an error estimate between the DtN operators of the original problem and the PML problem.
We consider the numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nystr{o}m method is proposed for the scattering problem based on the integral equation
The optical resonance problem is similar to but different from time-steady Schr{o}dinger equation. One big challenge is that the eigenfunctions in resonance problem is exponentially growing. We give physical explanation to this boundary condition and
In this paper, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems in 3D effectively. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coor
In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotr
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded scatterin