Linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

Numerical conformal mapping of multiply connected regions onto the fifth category of Koebe’s canonical slit regions

“…Several numerical methods have been proposed for computing the conformal mapping of multiply connected regions (see e.g., [15][16][17][18][19][20][21][22][23][24][25][26]). However, these numerical methods have been used to calculate the conformal mapping to only the canonical regions of the first category.…”

Numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions

“…The kernels of these integral equations are the Neumann kernel and the Kerzman-Stein kernel. Extensions of this approach to conformal mappings of bounded and unbounded multiply connected regions onto some canonical regions are given in [7][8][9][10][11][12]. For some other approaches of conformal mappings of multiply connected regions, e.g.…”

The computation of zeros of Ahlfors map for doubly connected regions

“…Using the integral equation method, most of the conformal mapping of multiply connected regions can be computed efficiently. The integral equation method has been used by many authors to compute the one-to-one conformal mapping from multiply connected regions onto some standard canonical regions [1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. In [9], Nasser et al presented a fast multipole method, which is fast and accurate method for numerical conformal mapping of bounded and unbounded multiply connected regions with high connectivity and highly complex geometry.…”

“…In [1], Kerzman and Stein have derived a uniquely solvable boundary integral equation for computing the Szegö kernel of a bounded region and this method has been generalized in [18] In [4], Nazar et al extended the approach of Sangawi [11,15,16] to construct an integral equation for solving where is the boundary correspondence function of Ahlfors map of multiply connected region onto a unit disk. However the integral equation is solved numerically by assuming the zeros of the Ahlfors map are known.…”