Harmonic Shears and Numerical Conformal Mappings
For researchers in complex analysis and numerical conformal mapping, this provides a practical computational tool for harmonic mappings, but the contribution is incremental.
The paper presents a numerical algorithm for computing harmonic mappings via the shear construction, implemented in MATLAB using the Schwarz-Christoffel toolbox, with several numerical examples and a minimal surface example.
In this article we introduce a numerical algorithm for finding harmonic mappings by using the shear construction introduced by Clunie and Sheil-Small in 1984. The MATLAB implementation of the algorithm is based on the numerical conformal mapping package, the Schwarz-Christoffel toolbox, by T. Driscoll. Several numerical examples are given. In addition, we discuss briefly the minimal surfaces associated with harmonic mappings and give a numerical example of minimal surfaces.