论文标题
从广义阻抗边界条件通过边界元素和卷积正交开始的时间依赖的声学散射
Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature
论文作者
论文摘要
广义阻抗边界条件是有效的，近似边界条件描述了波浪相互作用与材料涉及多个尺度的情况下的波散射。特别是，这包括带有薄涂层的材料（涂层的厚度为小尺度）和强大的吸收材料。对于来自广义阻抗边界条件的声学散射，此处采用的方法首先确定来自与通常的边界积分算子的时间相关边界积分方程系统的Dirichlet和Neumann边界数据，然后从Kirchhoff表示获得了散射波。时间相关边界积分方程的系统被及时的空间和卷积正交中的边界元素离散。该问题的适当性和数值离散化的稳定性取决于Calderón运算符对Helmholtz方程的强制性，并具有复杂半平面中的频率。自然规范中最佳顺序的融合被证明是为了全部离散化。数值实验说明了提出的数值方法的行为。
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes materials with a thin coating (with the thickness of the coating as the small scale) and strongly absorbing materials. For the acoustic scattering from generalized impedance boundary conditions, the approach taken here first determines the Dirichlet and Neumann boundary data from a system of time-dependent boundary integral equations with the usual boundary integral operators, and then the scattered wave is obtained from the Kirchhoff representation. The system of time-dependent boundary integral equations is discretized by boundary elements in space and convolution quadrature in time. The well-posedness of the problem and the stability of the numerical discretization rely on the coercivity of the Calderón operator for the Helmholtz equation with frequencies in a complex half-plane. Convergence of optimal order in the natural norms is proved for the full discretization. Numerical experiments illustrate the behaviour of the proposed numerical method.
