Math @ Duke

Publications [#338332] of Nadav Dym
Papers Published
 Dym, N; Slutsky, R; Lipman, Y, Linear variational principle for Riemann mappings and discrete conformality.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 116 no. 3
(January, 2019),
pp. 732737 [doi]
(last updated on 2019/04/19)
Abstract: We consider Riemann mappings from bounded Lipschitz domains in the plane to a triangle. We show that in this case the Riemann mapping has a linear variational principle: It is the minimizer of the Dirichlet energy over an appropriate affine space. By discretizing the variational principle in a natural way we obtain discrete conformal maps which can be computed by solving a sparse linear system. We show that these discrete conformal maps converge to the Riemann mapping in [Formula: see text], even for nonDelaunay triangulations. Additionally, for Delaunay triangulations the discrete conformal maps converge uniformly and are known to be bijective. As a consequence we show that the Riemann mapping between two bounded Lipschitz domains can be uniformly approximated by composing the discrete Riemann mappings between each Lipschitz domain and the triangle.


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