The Mathematical Institute, University of Oxford, Eprints Archive

Green's functions for multiply connected domains via conformal mapping

Embree, Mark and Trefethen, Lloyd N. (1998) Green's functions for multiply connected domains via conformal mapping. Technical Report. SIAM. (Submitted)

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Abstract

A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K-1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Potential theory
A - C > Approximations and expansions
D - G > Functions of a complex variable
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1298
Deposited By:Lotti Ekert
Deposited On:04 Jun 2011 09:15
Last Modified:04 Jun 2011 09:15

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