Affiliation:
1. School of Mathematical Sciences and LPMC , Nankai University , 300071 Tianjin , P. R. China
Abstract
Abstract
We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve.
The scattering problem is equivalently reformulated as an initial-boundary value problem of the wave equation in a truncated bounded domain through a well-defined transparent boundary condition.
Well-posedness and stability of the reduced problem are established.
Numerically, we adopt the perfect matched layer (PML) scheme for simulating the propagation of perturbed waves.
By designing a special absorbing medium in a semi-circular PML, we show the well-posedness and stability of the truncated initial-boundary value problem.
Finally, we prove that the PML solution converges exponentially to the exact solution in the physical domain.
Numerical results are reported to verify the exponential convergence with respect to absorbing medium parameters and thickness of the PML.
Funder
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis