Journal of Engineering Mathematics· 2026Q2
On composite conformal mapping of an annulus to a plane with two holes
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- Q2SCImago
- 2026year
Short summary
A novel composite conformal mapping method creates a plane with two holes, where one boundary is controlled by an exterior map and the second is nearly circular.
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Key points
- Develops a composite conformal mapping for an infinite plane with two holes.
- One boundary is determined by a chosen exterior map, the second is nearly circular.
- Method is applicable when the exterior map is available in Laurent series form.
- Illustrates applications in solving harmonic potential problems (heat conduction, potential flow).
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract A semi-inverse composite conformal mapping is considered for an infinite plane containing two holes. The construction combines a bilinear map from an annulus with a prescribed exterior map for one hole. This produces one boundary controlled by the chosen exterior map and a second boundary that is circular or nearly circular in the physical plane. When the exterior map is available in Laurent series form, the same representation can be used in truncated series solutions of selected harmonic potential problems, such as steady heat conduction and ideal potential flow. The method is illustrated by bilinear–hypotrochoid and bilinear–Schwarz–Christoffel examples.
The authors' abstract, as published at the source. Journal of Engineering Mathematics, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics