Algorithm 785: a software package for computing Schwarz-Christoffel conformal transformation for doubly connected polygonal regions

ABSTRACT

A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this article from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping “difficult” regions (to be specified in Section 2), and being user friendly. Several examples are presented to demonstrate the capabilities of the package.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Reliability and robustness; Efficiency

General Terms:
Algorithms

Keywords:
Schwarz-Christoffel conformal transformation, accessory parameters, doubly connected region, numerical conformal mapping, system of nonlinear equations