Analysis Of Time-domain PML Problem For The Electromagnetic Scattering By Unbounded Rough Surfaces

The nonlocal perturbation surface of infinite plane is called infinite rough surface,so that the whole surface lies within the finite distance of the original plane.The scattering problem of rough surface is of great significance because it is closely related to the technology of important industrial and military applications.PML truncation technique was first proposed by Bérenger in 1994,and he found the absorbing boundary layer.The absorbing boundary layer is a layer of artificial absorbing material,which has nothing to do with the boundary conditions.When the wave enters the absorbing layer,it is absorbed and attenuated exponentially,and even if it reflects off the boundary,the returned wave decreases exponentially after a round trip through the absorbing layer.So,whenever there is a transition from one material to another,three waves are usually reflected: incident,reflected and scattered,as well as the transition from a non-absorbing material to an absorbing material.Bérenger believes that a special absorbing medium can be constructed so that waves are not reflected on the interface: perfectly matched layer(or PML)PML technology because of its effectiveness,simplicity and flexibility.It is an important and popular grid termination technique in computational wave propagation.the idea is to surround the computational domain with an immaterial PML medium which has the remarkable characteristic of non-reflection to the incident wave at any frequency or in any incident direction.In practical applications,the PML medium must be truncated,and the reflected waves generated by the truncated boundary will pollute the solution of the computing domain.Therefore,it is very important to study the error estimation of the solution of the original scattering problem and the solution of the truncation problem in the computational domain.The error between the unique solution of the truncated PML problem in the computational domain and the solution of the scattering problem is studied under the assumption of appropriate PML medium parameters.In this paper,the problem of electromagnetic scattering from unbounded rough surfaces in time domain is studied.By using the exact transparent boundary condition(TBC),the scattering problem is equivalent to the initial boundary value problem of infinite rectangular plates,and the well-posedness and stability of the reduction problem are established according to the variational method.On this basis,the electromagnetic scattering problem of perfectly matched layer(PML)method to truncate unbounded rough surface far away from rough surface is studied.Based on the abstract inversion theorem of Laplace transform and frequency domain analysis,the well-posedness and stability of truncated time-domain PML problem are established.In addition,by studying the operator error between the original scattering problem and the truncated PML problem,the exponential convergence of the solution error between the truncated PML problem and the original scattering problem is proved.