Numerical conformal mapping using cross-ratios and Delaunay triangulation
- Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics
- Cornell Univ., Ithaca, NY (United States). Dept. of Computer Science
The authors 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), 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. They believe that CRDT solves all difficulties with crowding and global convergence, although these facts depend on conjectures that they have so far not been able to prove. They demonstrate convergence with computational experiments. The Riemann mapping has applications in two-dimensional potential theory and mesh generation. They demonstrate CRDT on problems in long, thin regions in which no other known algorithm can perform comparably.
- Sponsoring Organization:
- USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States); National Aeronautics and Space Administration, Washington, DC (United States); Argonne National Lab., IL (United States)
- DOE Contract Number:
- FG02-94ER25199
- OSTI ID:
- 321028
- Journal Information:
- SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 6 Vol. 19; ISSN 1064-8275; ISSN SJOCE3
- Country of Publication:
- United States
- Language:
- English
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