We present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto circular slit region. The is based on some uniquely solvable equations with adjoint classical, generalized, and modified Neumann kernels. These are constructed from relationship satisfied by function analytic Some examples presented to illustrate efficiency method.

This paper presents a new boundary integral equation with the adjoint Neumann kernel associated where is correspondence function of Ahlfors map bounded multiply connected region onto unit disk. The proposed constructed from relationship satisfied by region. solved numerically for using combination Nystrom method, GMRES and fast multiple method. From computed values we solve which then gives map. numerical examples presented here prove effectiveness

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and inverse from bounded multiply connected regions onto five classical canonical slit regions. The is derived by reformulating mapping as an adjoint Riemann-Hilbert problem. From problem, we derive with generalized Neumann kernel of correspondence function $θ'$. Only right-hand side different region to another. $θ'$ integrated obtain $θ$. integration constants well...

The Ahlfors map and Szegö kernel are both classically related to each other. can be computed using without relying on the zeros of map. is a solution Fredholm integral equation second kind with Kerzman-Stein kernel. exact unknown except for annulus region. This paper presents numerical method computing any bounded doubly connected depends values kernel, its derivative boundary correspondence function Using combination Nyström method, GMRES fast multiple Newton's examples presented here prove...

Views Icon Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Twitter Facebook Reddit LinkedIn Tools Reprints and Permissions Cite Search Site Citation Kashif Nazar, Ali H. M. Murid, W. K. Sangawi; Some integral equations related to the Ahlfors map for multiply connected regions. AIP Conf. Proc. 11 December 2015; 1691 (1): 040021. https://doi.org/10.1063/1.4937071 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote...

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The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. a solution of Fredholm integral equation second kind with Kerzman-Stein kernel. exact zeros are known for particular family doubly connected regions triply region. This paper presents numerical method computing any bounded multiply smooth boundaries. depends on values (z(t), a), S′(z(t), θ′(t), where θ(t) boundary correspondence function map. A formula derived a). An θ′(t) used finding examples presented here...

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Abstract In this paper, we present a fast boundary integral equation method for the numerical conformal mapping and its inverse of bounded multiply connected regions onto disk annulus with circular slits regions. The is based on two uniquely solvable equations Neumann-type generalized Neumann kernels. related to mappings are solved numerically using combination Nyström method, GMRES multipole method. complexity new algorithm $$O((M + 1)n)$$ <mml:math...

Conformal mapping is a useful tool in science and engineering. On the other hand exact functions are unknown except for some special regions.In this paper we present new boundary integral equation with classical Neumann kernel associated to f , where conformal ofbounded multiply connected regions onto disk circular slit domain. This constructed from relationshipsatisfied by function analytic on region. With known, one can then treat it as differential computing .

The Ahlfors map of an n-connected region is a n-to-one from the onto unit disk. being n-toone has n zeros. Previously, exact zeros are known only for annulus region. general bounded doubly connected regions been unknown many years. This paper presents numerical method computing any depends on values Szego kernel, its derivative and boundary correspondence function map. kernel both classically related to each other. can be computed using without relying solution Fredholm integral equation...

The relation between the Ahlfors map and Szeg\"o kernel S(z, a) is classical. a solution of Fredholm integral equation second kind with Kerzman-Stein kernel. exact zeros are unknown except for annulus region. This paper presents numerical method computing any bounded doubly connected depends on values S(z(t),a), S'(z(t),a) \theta'(t) where \theta(t) boundary correspondence function map. A formula derived S'(z(t),a). An constructed solving \theta'(t). examples presented here prove...

This article proposes a boundary integral equation method for computing numerical conformal mappings of bounded multiply connected region Ω onto the disk with rectilinear slit and spiral slits regions, Ω1 Ω2 Initially, process involves calculating value canonical region. Cauchy’s formula can then be used to compute mapping interior values. The effectiveness proposed is demonstrated using several examples.

We study a numerical approach for solving integral equation with adjoint generalized Neumann kernel related to conformal mapping. Previously, computation of mapping M + 1 connected regions require at least equations separately. apply global simpler GMRES which solve nonsymmetric system multiple right-hand sides simultaneously. also fast multipole method several matrix vector products in every iteration GMRES. Numerical example is given illustrate the effectiveness proposed method.

We present a boundary integral equation method for the numerical conformal mappings and their inverses of bounded multiply connected regions onto circular parallel slits regions.The is based on two uniquely solvable equations with Neumann-type generalized Neumann kernels.These are constructed from relationship satisfied by function analytic region.A to calculate inverse mapping functions original region presented.Some examples results graphical user interface presented illustrate efficiency method.