Numerical Solution Of The Truncated Acoustic Scattering PML Problem By Using Two-grid Element Method

The Helmoheltz equation has important application in acoustic,electromagnetic and elastic scattering problems,and has been investigated in many ways.In the area of numerical method,how to solve the problem that those problems are posed on infinite domains is always a popular subject.In late work[4][5],Bramble transforms the acoustic scattering problem on infinite domain to the truncated domain using perfectly matched layer method(PML).This work will be continent to simulation,however,it also brings some new problems.The original problem is symmetric with real coefficients,but now is nonsymmetric with complex coefficients.We consider the truncated acoustic scattering PML problem and develop an efficient approximate method based on two-grid method.The method is to solve a small and complex original problem by standard finite element discretization on a coarse space V_H. Based on the coarse solution u_H∈V_H;we solve a simple problem in the fine space V_h, which is only have the high order terms of original problem,and get a correction u_h∈V_h. We prove the existence and uniqueness and the error bound of optimal order of accuracy which is consistent with the standard finite element discretization.Finally,some numerical experiments are performed to support our theoretical claims.