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Numerical conformal mapping via the Bergman kernel using the generalized minimum residual method

✍ Scribed by M.R.M. Razali; M.Z. Nashed; A.H.M. Murid

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
414 KB
Volume
40
Category
Article
ISSN
0898-1221

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✦ Synopsis

The Bergman kernel function is known to satisfy a certain boundary integral equation of the second kind. For boundaries that possess symmetrical qualities, the integral equation can be transformed into another integral equation that uses only a small part of the original boundary. This paper applies an iterative procedure known as the generalized minimum residual method for the computation of the Riemann mapping function via the Bergman kernel. The complexity of this procedure is O(n2), where n is the number of collocation points on the boundary of the region. Numerical implementation on some test regions is also presented.

πŸ“œ SIMILAR VOLUMES

Numerical conformal mapping via the Berg
Numerical conformal mapping via the Bergman kernel
✍ M.R.M. Razali; M.Z. Nashed; A.H.M. Murid πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 813 KB

A new method to compute the Riemann mapping function via the Bergman kernel is presented. The method expresses the Bergman kernel as the solution of a second-kind integral equation involving the Neumann kernel. For symmetric regions, the integral equation can be transformed into a new one that uses