Numerical conformal mapping of multiply connected domains to regions with circular boundaries |
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Authors: | Wei Luo Xianfeng Gu |
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Affiliation: | a Center of Mathematical Sciences, Zhejiang University, China b Computer Science Department, Stony Brook University, NY, USA c Mathematics Department, Harvard University, MA, USA |
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Abstract: | We propose a method to map a multiply connected bounded planar region conformally to a bounded region with circular boundaries. The norm of the derivative of such a conformal map satisfies the Laplace equation with a nonlinear Neumann type boundary condition. We analyze the singular behavior at corners of the boundary and separate the major singular part. The remaining smooth part solves a variational problem which is easy to discretize. We use a finite element method and a gradient descent method to find an approximate solution. The conformal map is then constructed from this norm function. We tested our algorithm on a polygonal region and a curvilinear smooth region. |
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Keywords: | 30C30 |
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