On the Acoustic Single Layer Potential: Stabilization and Fourier Analysis
On the Acoustic Single Layer Potential: Stabilization and Fourier Analysis
复制标题
关于声学单层势：稳定性和傅立叶分析
DOI：
--
复制
发表时间：
2006
影响因子：
3.1
通讯作者：
S. Sauter
中科院分区：
文献类型：
--
作者：
A. Buffa;S. Sauter
本文提出了一种稳定Helmholtz边界积分方程单层势的一般方法，并证明了它的稳定性。我们考虑Galerkin边界元离散和分析其收敛性。此外，对于曲面为$% mathbb{R}^3 $中的单位球面的特殊情况，我们推导出了伽辽金离散化的定量误差界，该误差界与网格宽度和波数有关。然后，我们进行定性分析，使我们能够选择稳定，使波数的稳定性和收敛估计的（负面）影响达到最小。
In this paper, we propose a general approach for stabilizing the single layer potential for the Helmholtz boundary integral equation and prove its stability. We consider Galerkin boundary element discretizations and analyze their convergence. Furthermore, we derive quantitative error bounds for the Galerkin discretization which are explicit with respect to the mesh width and the wave number for the special case that the surface is the unit sphere in $% mathbb{R}^3$. We perform then a qualitative analysis which allows us to choose the stabilization such that the (negative) influence of the wave number in the stability and convergence estimates attains its minumum.