Corner effects on the perturbation of an electric potential
(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
- Choi, Doo Sung ; Helsing, Johan LU and Lim, Mikyoung
- organization
- publishing date
- 2018-01-01
- 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
- 2022-03-09 19:45:30
@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}}, }