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We aim to analyze and calculate time-dependent acoustic wave scattering by abounded obstacle and a locally perturbed non-selfintersecting curve. Thescattering problem is equivalently reformulated as an initial-boundary valueproblem of the wave equation in a truncated bounded domain through awell-defined transparent boundary condition. Well-posedness and stability ofthe reduced problem are established. Numerically, we adopt the perfect matchedlayer (PML) scheme for simulating the propagation of perturbed waves. Bydesigning a special absorbing medium in a semi-circular PML, we showwell-posedness and stability of the truncated initial-boundary value problem.Finally, we prove that the PML solution converges exponentially to the exactsolution in the physical domain. Numerical results are reported to verify theexponential convergence with respect to absorbing medium parameters andthickness of the PML.

Well-posedness and convergence analysis of PML method for time-dependent acoustic scattering problems over a locally rough surface