Circular arc polygons, numerical conformal mappings, and moduli of quadrilaterals
Mohamed Nasser, Oona Rainio, Antti Rasila, Matti Vuorinen, Terry, Wallace, Hang Yu, Xiaohui Zhang
TL;DR
This paper develops numerical methods for conformal mappings of planar domains bounded by circular arcs, enabling computation of quadrilateral moduli with error estimates and comparisons to exact solutions.
Contribution
It introduces a boundary integral equation approach combined with the fast multipole method for efficient and accurate computation of conformal mappings and moduli of circular arc polygons.
Findings
Accurate numerical conformal mappings achieved for domains with circular arc boundaries.
Error estimates provided for the numerical methods.
Comparison with exact values demonstrates the method's effectiveness.
Abstract
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.
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.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsElectromagnetic Scattering and Analysis · Numerical methods in engineering · Electromagnetic Simulation and Numerical Methods