Boundary integral solution of the exterior Helmholtz problem
Boundary integral solution of the exterior Helmholtz problem
复制标题
外亥姆霍兹问题的边界积分解
作者：
S. Amini
耦合参数存在于外域亥姆霍兹方程的几乎所有唯一可解的边界积分公式中。在这里，我们通过研究所得边界积分算子的特征值的渐近行为，对该参数的众所周知的近乎最优选择提供了新的见解。通过利用 Arnold 和 Wendland (1983, 1985) 关于强椭圆伪微分算子配置解的渐近收敛性的最新成果，我们研究了数值积分对离散配置方法可达到的精度的影响。然后，我们可以强调 Kirkup (1992) 最近发表的一篇论文中的一个错误，该论文建议耦合参数应与配置点的数量成反比。
A coupling parameter is present in almost all the uniquely solvable boundary integral formulations of the Helmholtz equation in an exterior domain. Here we provide new insight into the well-known near optimal choice of this parameter by studying the asymptotic behaviour of the eigenvalues of the resulting boundary integral operators. By taking advantage of the recent results of Arnold and Wendland (1983, 1985) for the asymptotic convergence of collocation solution of strongly elliptic pseudo-differential operators we study the effect of numerical integration on the achievable accuracy of discrete collocation methods. We are then able to highlight an error in a recent paper by Kirkup (1992) which suggested that the coupling parameter should be inversely proportional to the number of collocation points.