Abstract
This paper presents a fast boundary integral equation method for numerical conformal mapping of unbounded multiply connected regions onto a disk with an infinite straight slit and finite logarithmic spiral slits. Some numerical examples are given to show the effectiveness of the proposed method.
Highlights
Conformal mapping is an important tool to solve several problems in the fields of science and engineering [1]
This paper presents a fast boundary integral equation method for numerical conformal mapping of unbounded multiply connected regions onto a disk with an infinite straight slit and finite logarithmic spiral slits
For the conformal mappings of multiply connected regions, several canonical slit regions are available. Thirty nine of these canonical regions have been catalogued by Koebe in his classical paper [2]
Summary
Conformal mapping is an important tool to solve several problems in the fields of science and engineering [1]. For the conformal mappings of multiply connected regions, several canonical slit regions are available. Several numerical methods have been proposed for computing the conformal mapping of multiply connected regions onto the canonical slit regions [3]. The numerical computing of conformal mappings from bounded multiply connected regions onto Koebe’s fifth category canonical slit regions using the boundary integral equation with the generalized Neumann kernel has been presented in [6]. (i) The region Ω1 which is the unbounded region in the exterior of the unit circle |w| = 1 with an infinite straight slit on the line Im w = 0 and m − 2 finite spiral slits (see Figure 1 (left) for m = 5).
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