An Adaptive Complete Matched Layer Method For Scattering Problem In Layered Media

As a hot research topic in the field of mathematical physics,acoustic scattering problem has attracted wide attention of researchers from all walks of life since the 1960s.The first key point in the numerical solution of acoustic scattering problem is how to deal with the radiation conditions under unbounded situation.This involves not only truncating the unbounded region into a bounded region,but also needs to consider how to impose high-precision boundary conditions on the artificial boundary.In this paper,combining the perfect matching layer technique and adaptive finite element method,the acoustic scattering problem in two-layer media was theoretically analyzed and numerically solved,and the model was simulated by using MATLAB software.The main contents and research results are as follows:The scattering model of acoustic wave in a two-layer medium was studied theoretically by using the method of perfectly matched layer.Firstly,a DtN operator was introduced to truncate the scattering problem of unbounded domain into a value problem of bounded domain.In order to obtain the exact boundary conditions of the truncated equation,we introduced the PML layer,which makes the scattering wave absorbed in PML layer by using the medium characteristics of PML layer and approximates to zero at the outer boundary of PML layer.Thus we obtained the solution form of the original equation,and the error between the value solution and the exact solution was analyzed by using two different DtN operators.At the same time,we use the theory of adaptive finite element method and Matlab software to simulate the scattering problem.Firstly,the tolerance and mesh refinement threshold were given,and parameters are set to calculate the discrete error after the initial subdivision of the soltion domain.If the calculation accuracy is sufficiently small,stop the operation.If the accuracy is not enough,the mesh with large error in subdivision is selected to be encrypted and the discrete error is calculated again until a satisfactory result is obtained.The result shows that the solution of PML problem converges exponentially to that of the original scattering problem when the thickness or the medium parameter of PML layer increases.