Universiti Teknologi Malaysia Institutional Repository

Computation of the Riemann map using integral equation method and Cauchy’s integral formula

Murid, Ali H. M. and Mohamed, Nurul Akmal (2004) Computation of the Riemann map using integral equation method and Cauchy’s integral formula. In: Simposium Sains Matematik, 2004, Pulai Springs, Skudai. (Unpublished)

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Abstract

The Riemann map is a conformal mapping that maps a simply connected region to a unit disk. Such a map has applications in fluid mechanics,electrostatics, and image processing. We present a numerical procedure for the computation of the Riemann map based on two stages. First we compute the boundary values of the Riemann map for the region we wish to map by solving an integral equation. Then we compute the Riemann map in the interior of the region using the well-known Cauchy’s integral formula. Due to periodicity, trapezoidal rule is the most appealing procedure for these computations. We also provide some results of our numerical experiments using epitrochoid (�apple�) as a test region.

Item Type:Conference or Workshop Item (Paper)
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:1753
Deposited By: Assoc. Prof. Dr. Ali Hassan Mohamed Murid
Deposited On:14 Mar 2007 07:49
Last Modified:01 Jun 2010 02:58

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