Numerical conformal mapping using cross-ratios and Delaunay triangulation

被引:60
作者
Driscoll, TA [1 ]
Vavasis, SA
机构
[1] Univ Colorado, Dept Math Appl, Boulder, CO 80309 USA
[2] Cornell Univ, Dept Comp Sci, Ithaca, NY 14853 USA
关键词
numerical conformal mapping; Schwarz-Christoffel mapping; cross-ratios; Delaunay triangulation;
D O I
10.1137/S1064827596298580
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz{Christoffel transformation. The new algorithm, CRDT (for cross-ratios of the Delaunay triangulation), is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT solves all difficulties with crowding and global convergence, although these facts depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications in two-dimensional potential theory and mesh generation. We demonstrate CRDT on problems in long, thin regions in which no other known algorithm can perform comparably.
引用
收藏
页码:1783 / 1803
页数:21
相关论文
共 20 条
[1]  
[Anonymous], 1974, APPL COMPUTATIONAL C
[2]   NONOBTUSE TRIANGULATION OF POLYGONS [J].
BAKER, BS ;
GROSSE, E ;
RAFFERTY, CS .
DISCRETE & COMPUTATIONAL GEOMETRY, 1988, 3 (02) :147-168
[3]  
Bern M., 1990, Proceedings. 31st Annual Symposium on Foundations of Computer Science (Cat. No.90CH2925-6), P231, DOI 10.1109/FSCS.1990.89542
[4]  
Bern M., 1992, COMPUTING EUCLIDEAN
[5]  
BERN M, 1992, CSL921 XER PAL ALT R
[6]  
Chew LP, 1989, 89983 CORN U DEP COM
[7]  
DAPPEN HD, 1988, THESIS ETH ZURICH SW
[8]  
DENNIS JE, 1983, NUMERICAL METHODS UN
[9]   Algorithm 756: A MATLAB toolbox for Schwarz-Christoffel mapping [J].
Driscoll, TA .
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1996, 22 (02) :168-186
[10]  
HEARI Z, 1952, COMFORMAL MAPPING