%0 Journal Article
%T Numerical solution of the Beltrami equation via a purely linear system
%A R. Michael Porter
%A Hirokazu Shimauchi
%J Mathematics
%D 2014
%I arXiv
%X 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 Teichm\"uller space of a Fuchsian group.
%U http://arxiv.org/abs/1405.7359v1