Harmonic Shears and Numerical Conformal Mappings
Tri Quach
TL;DR
This paper presents a numerical algorithm for harmonic mappings using shear construction, implemented in MATLAB with examples, and explores related minimal surfaces.
Contribution
It introduces a MATLAB-based numerical algorithm for harmonic mappings utilizing shear construction and demonstrates its application with examples.
Findings
Effective numerical harmonic mapping algorithm developed
Implementation using Schwarz-Christoffel toolbox in MATLAB
Numerical examples of harmonic mappings and minimal surfaces provided
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic and Geometric Analysis · Polynomial and algebraic computation