The Mathematical Institute, University of Oxford, Eprints Archive

A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides

Banjai, Lehel and Trefethen, Lloyd N. (2002) A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides. Technical Report. Unspecified. (Submitted)

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Abstract

A method is presented for the computation of Schwarz-Christoffel maps to polygons with tens of thousands of vertices. Previously published algorithms have CPU time estimates of the order O(N^3) for the computation of a conformal map of a polygon with N vertices. This has been reduced to O(N log N) by the use of the Fast Multipole Method and Davis's method for solving the parameter problem. The method is illustrated by a number of examples, the largest of which has N approx 2 × 10^5.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Functions of a complex variable
H - N > Mechanics of particles and systems
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1214
Deposited By:Lotti Ekert
Deposited On:19 May 2011 07:39
Last Modified:19 May 2011 07:39

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