In this paper,we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition.Different from the problem with Dirichlet boundary condition,the Green function of ...In this paper,we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition.Different from the problem with Dirichlet boundary condition,the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line.A uniaxial perfectly matched layer(UPML)method is proposed to truncate the half plane into a bounded computational domain.The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases.展开更多
基金supported by China NSF grants Nos.11771057,11401040 and 11671052.The research of X.J.Li is supported by China NSF grant Nos.11805049 and 11771440 and by the National Magnetic Confinement Fusion Science Program No.2015GB110003.
文摘In this paper,we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition.Different from the problem with Dirichlet boundary condition,the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line.A uniaxial perfectly matched layer(UPML)method is proposed to truncate the half plane into a bounded computational domain.The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases.
