ProV Logo
0
Approximation of conformal mappings usin...
Bücking, Ulrike...

Free

Approximation of conformal mappings using conformally equivalent triangular lattices by Bücking, Ulrike ( Author )
Lemonjar Open Access
N.A
23-07-2015
Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map f, we show that it can be approximated by such discrete conformal maps fϵ. In particular, let T be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ <π/2). We scale this tiling by ϵ>0 and approximate a compact subset of the domain of f with a portion of it. For ϵ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by log|f′| on the boundary. Furthermore we show that the corresponding discrete conformal maps fϵ converge to f uniformly in C1 with error of order ϵ.
-
Article
pdf
36.88 KB
English
-
MYR 0.00
-
https://arxiv.org/abs/1507.06449
Share this eBook