solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看2394次
Corner effects on the perturbation of an electric potential. (arXiv:1710.04006v1 [math.AP])
来源于:arXiv
We consider the perturbation of an electric potential due to an insulating
inclusion with corners. This perturbation is known to admit a multipole
expansion whose coefficients are linear combinations of generalized
polarization tensors. We define new geometric factors of a simple planar domain
in terms of a conformal mapping associated with the domain. The geometric
factors share properties of the generalized polarization tensors and are the
Fourier series coefficients of a kind of generalized external angle of the
inclusion boundary. Since the generalized external angle contains the Dirac
delta singularity at corner points, we can determine the criterion for the
existence of corner points on the inclusion boundary in terms of the geometric
factors. We illustrate and validate our results with numerical examples
computed to a high degree of precision using integral equation techniques,
Nystr\"om discretization, and recursively compressed inverse preconditioning. 查看全文>>