The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density, wavespeed and frequency. In particular, high contrast in density and wavespeed across a material interface leads to an ill-conditioned discretisation matrix. Therefore, the convergence of Krylov methods to solve the linear system is slow. Here, specialised boundary integral formulations are designed for the case of acoustic scattering at high-contrast media. The eigenvalues of the resulting system matrix accumulate at two points in the complex plane that depend on the density ratio and stay away from zero. The spectral analysis of the Calder\'on preconditioned PMCHWT formulation yields a single accumulation point. Benchmark simulations demonstrate the computational efficiency of the high-contrast Neumann formulation for scattering at high-contrast media.
翻译:边界要素法是通过自由空间内嵌的同质物体模拟声波传播的有效算法。系统矩阵的调节在很大程度上取决于密度、波速和频率等物理参数。特别是,材料界面的密度和波速差异很大,导致一个条件不完善的离散矩阵。因此,Krylov解决线性系统的方法的趋同速度缓慢。这里,专门设计的边界整体配方是为高调介质的声波散布情况设计的。由此产生的系统矩阵的元值在复杂平面的两个点积累,这两个点取决于密度比率,远离零。Calder\'on PMCHWT先决条件的配方的光谱分析得出了一个单一的累积点。基准模拟显示了高调Neuumann配方在高调介质上撒散的计算效率。