Conformal Maps via Sinc Methods (1999)
| Venue: | Proc. Conf. Computational Methods in Function Theory |
| Citations: | 2 - 1 self |
BibTeX
@INPROCEEDINGS{Stenger99conformalmaps,
author = {Frank Stenger and Ross Schmidtlein},
title = {Conformal Maps via Sinc Methods},
booktitle = {Proc. Conf. Computational Methods in Function Theory},
year = {1999},
pages = {505--549},
publisher = {World Scientific}
}
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Abstract
In this paper we derive a Sinc procedure for the construction of a conformal map, f , of a simply connected domain, or Riemann surface B in the complex plane to the unit disc U . The construction is based on the solution of a boundary integral equation which always has a unique solution. We assume that @B, the boundary of B, consists of a finite number of analytic arcs, with well defined angles at the junctions. We also give an explicit procedure for evaluating f in the interior of B. We furthermore give a brief description of an explicit Sinc construction which enables the computation of the inverse map F = f \Gamma1 from U to B, based on the computed f on @B. Given any " ? 0, the time complexity of sequential computation of f " on @B such that sup i2@B jf(i) \Gamma f " (i)j ! " is O \Gamma (log(")) 6 \Delta . 1 Introduction and Summary This paper deals with the construction of a conformal map, f , from a simply connected domain or Riemann surface B ae C to the unit disc U ...
