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Article
Publication date: 1 February 1992

Maqsood A. CHAUDHRY and Roland SCHINZINGER

An iterative algorithm is described to compute Schwarz‐Christoffel transformations which map the upper half of a complex plane into the interior of a polygon in another…

Abstract

An iterative algorithm is described to compute Schwarz‐Christoffel transformations which map the upper half of a complex plane into the interior of a polygon in another complex plane. An efficient method of numerically integrating the S‐C integral over the singularities is presented. The algorithm is easily programmable in FORTRAN. Convergence rate is high and accuracy is excellent. Examples are provided and wherever possible, analytically obtained results are also presented for comparison. The importance of the algorithm is described and a brief comparison with some of the existing algorithms is made. Potential application of the S‐C transformation are in the solution of Laplace's and Poisson's equation in two‐dimensional domains with polygonal boundary.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 11 no. 2
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 1 August 2003

Maqsood A. Chaudhry and Roland Schinzinger

Finite difference and finite element methods have serious limitations when applied to unbounded regions. This paper describes a hybrid method which uses a conformal…

Abstract

Finite difference and finite element methods have serious limitations when applied to unbounded regions. This paper describes a hybrid method which uses a conformal transformation to map the original boundaries, including those at infinity, to a bounded region and only then applies a numerical method based on finite differences or finite elements when no direct solution is obvious. Testing this approach by means of examples for which exact solutions are obtainable, the hybrid method is applied to determine the electrical potential at specific points in the field of a capacitor with long plates that in their cross‐sectional view are parallel to each other, and in the field of a microstrip line at some distance from it. In both the cases, the results are in agreement with analytically derived results. The method is simple, readily applied by undergraduate students, yet accurate and thus of use in professional engineering work as well.

Details

Microelectronics International, vol. 20 no. 2
Type: Research Article
ISSN: 1356-5362

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