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 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.
翻译:我们的目标是分析并计算由封闭障碍和局部扰动的非自相交叉曲线散布的取决于时间的声波。 散射问题被重新表述为通过一个明确界定的透明边界条件,在一个断裂的封闭域内,波形方程式的初始界限值问题。 确定问题减少后的准确性和稳定性。 从数字上看,我们采用完美的匹配层( PML) 方案, 模拟扰动波的传播。 通过在半圆形的PML中设计一种特殊的吸收介质, 我们显示了疏松的初始界限值问题的妥善储存性和稳定性。 最后, 我们证明PML 解决方案与物理域的精确解决方案成倍地交汇。 据报告, 数字结果可以验证在吸收介质参数和厚度方面的指数趋同。