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Bibliographic Details
Main Authors: Porter, R. Michael, Shimauchi, Hirokazu
Format: Preprint
Published: 2014
Subjects:
Online Access:https://arxiv.org/abs/1405.7359
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Table of Contents:
  • An effective algorithm is presented for solving the Beltrami equation df/dz = mu (df/dzbar) in a planar disk. The disk is triangulated in a simple way and f is approximated by piecewise linear mappings; the images of the vertices of the triangles are defined by an overdetermined system of linear equations. (Certain apparently nonlinear conditions on the boundary are eliminated by means of a symmetry construction.) The linear system is sparse and its solution is obtained by standard least-squares, so the algorithm involves no evaluation of singular integrals nor any iterative procedure for obtaining a single approximation of f. Numerical examples are provided, including a deformation in a Teichmüller space of a Fuchsian group.