CONSTRUCTING DIFFEOMORPHISMS BETWEEN SIMPLY CONNECTED PLANE DOMAINS

被引：0

作者：

Atkinson K. ^{[1
]}

Chien D. ^{[2
]}

Hansen O. ^{[2
]}

机构：

[1] University of Iowa, United States

[2] California State University San Marcos, United States

来源：

Electronic Transactions on Numerical Analysis | 2022年 / 55卷

关键词：

constructing diffeomophisms; domain transformations; shape blending;

D O I：

10.1553/etna_vol55s671

中图分类号：

学科分类号：

摘要：

Consider a simply connected domain Ω ⊂ R2 with boundary ∂Ω that is given by a smooth function φ : [a, b] 7→ R2. Our goal is to calculate a diffeomorphism Φ: B1(0) 7→ Ω, B1(0) the open unit disk in R2. We present two different methods where both methods are able to handle boundaries ∂Ω that are not star-shaped. The first method is based on an optimization algorithm that optimizes the curvature of the boundary, and the second method is based on the physical principle of minimizing a potential energy. Both methods construct first a homotopy between the boundary ∂B1(0) and ∂Ω and then extend the boundary homotopy to the inside of the domains. Numerical examples show that the method is applicable to a wide variety of domains Ω. Copyright © 2022, Kent State University.

引用

页码：671 / 686

页数：15