Corner effects on the perturbation of an electric potential

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Generalized polarization tensors

Planar domain with corners

RCIP method

Riemann mapping

Schwarz-Christoffel transformation

Publication and Content Type

art (subject category)

ref (subject category)