Error estimation for quadrature by expansion in layer potential evaluation
Error estimation for quadrature by expansion in layer potential evaluation
复制标题
层势评估中通过扩展求积的误差估计
DOI：
10.1007/s10444-016-9484-x
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
A. Tornberg
中科院分区：
文献类型：
--
作者：
Ludvig af Klinteberg;A. Tornberg
在边界积分方法中，常常需要对边界上或边界附近的层势进行计算，而在这种情况下，底层积分很难用数值方法计算。展开正交法（QBX）是处理这类积分的一种新方法，它基于在靠近边界处形成层势的局部展开。在这样做时，由于在计算膨胀系数时的近似奇异积分，引入了一个新的正交误差。采用基于轮廓积分和残数微积分的方法，可以准确估计近奇异积分的正交误差。当应用于二维和三维的层势时，这使得得到与QBX相关的正交误差的准确估计成为可能。作为例子，我们导出了拉普拉斯和亥姆霍兹单层势的估计。这些结果可用于实际应用中的参数选择。
In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is difficult to evaluate numerically. Quadrature by expansion (QBX) is a new method for dealing with such integrals, and it is based on forming a local expansion of the layer potential close to the boundary. In doing so, one introduces a new quadrature error due to nearly singular integration in the evaluation of expansion coefficients. Using a method based on contour integration and calculus of residues, the quadrature error of nearly singular integrals can be accurately estimated. This makes it possible to derive accurate estimates for the quadrature errors related to QBX, when applied to layer potentials in two and three dimensions. As examples we derive estimates for the Laplace and Helmholtz single layer potentials. These results can be used for parameter selection in practical applications.