Abstract
This paper presents a fast boundary integral equation method with for computing conformal mappings of multiply connected regions. We consider the canonical region consists of the entire complex plane bounded by a finite straight slit on the line Im ω = 0 and finite logarithmic spiral slits. Some numerical examples are given to show the effectiveness of the proposed method.
Highlights
Conformal mapping is a special mapping that transform a region onto another region while preserving the angle between curves in the sense of magnitude and direction
Because of this unique characteristic, the idea of conformal mapping have been applied in several real life problems as discussed in [1, 2]
Trefethen [3] has discussed several method for computing the conformal maps based on expansion methods, iterative methods and integral equation methods
Summary
Conformal mapping is a special mapping that transform a region onto another region while preserving the angle between curves in the sense of magnitude and direction. A canonical region is known for a region that has simpler geometry and can be uniquely determined by specifying the conformal moduli. From these thirty nine canonical region, Koebe [4] have cataloged it into five categories. For the numerical computation of the conformal mapping onto these categories, see [5, 6, 7, 8, 9, 10, 11] Beside these thirty nine canonical regions, circular region which is a region bounded by multiple circle is another important canonical region[12, 13].
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