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Corner effects on the perturbation of an electric potential

Choi, Doo Sung ; Helsing, Johan LU orcid and Lim, Mikyoung (2018) In SIAM Journal on Applied Mathematics 78(3). p.1577-1601
Abstract

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 coeffcients 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 coeffcients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria for the existence of corner points on the inclusion boundary in terms of the geometric factors.... (More)

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 coeffcients 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 coeffcients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria 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, the Nystrom discretization, and recursively compressed inverse preconditioning.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Generalized polarization tensors, Planar domain with corners, RCIP method, Riemann mapping, Schwarz-Christoffel transformation
in
SIAM Journal on Applied Mathematics
volume
78
issue
3
pages
25 pages
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:85049398981
ISSN
0036-1399
DOI
10.1137/17M115459X
language
English
LU publication?
yes
id
4d8385e1-d372-495f-906f-8005826bb2fc
date added to LUP
2018-07-19 10:44:03
date last changed
2025-10-14 13:05:33
@article{4d8385e1-d372-495f-906f-8005826bb2fc,
  abstract     = {{<p>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 coeffcients 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 coeffcients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria 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, the Nystrom discretization, and recursively compressed inverse preconditioning.</p>}},
  author       = {{Choi, Doo Sung and Helsing, Johan and Lim, Mikyoung}},
  issn         = {{0036-1399}},
  keywords     = {{Generalized polarization tensors; Planar domain with corners; RCIP method; Riemann mapping; Schwarz-Christoffel transformation}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{3}},
  pages        = {{1577--1601}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Applied Mathematics}},
  title        = {{Corner effects on the perturbation of an electric potential}},
  url          = {{http://dx.doi.org/10.1137/17M115459X}},
  doi          = {{10.1137/17M115459X}},
  volume       = {{78}},
  year         = {{2018}},
}