An efficient and novel numerical method for quasiconformal mappings of doubly connected domains |
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Authors: | Prabir Daripa Daoud Mashat |
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Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA |
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Abstract: | A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The ratio R of the radii of the annulus is not known a priori and is determined as part of the solution procedure. The numerical method presented in this paper requires solving iteratively a sequence of inhomogeneous Beltrami equations, each for a different R. R is updated using a procedure based on the bisection method. The new method is an extension of Daripa s method for the quasiconformal mapping of the exterior of simply connected domains onto the interior of unit disks 15]. It uses fast and accurate algorithms for evaluating certain singular integrals and is, thus, very efficient and accurate. Its performance is demonstrated for several doubly connected domains. |
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Keywords: | quasiconformal mapping Beltrami equation fast algorithm 17-08 30C75 45G05 65E05 65Y20 |
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