Circular Slits Map of Bounded Multiply Connected Regions
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In this paper, a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a circular slit region is presented, which is based on some uniquely solvable boundary integral equations with adjoint classical, adjoint generalized, and modified Neumann kernels.Abstract:
We present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a circular slit region. The method is based on some uniquely solvable boundary integral equations with adjoint classical, adjoint generalized, and modified Neumann kernels. These boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. Some numerical examples are presented to illustrate the efficiency of the presented method.read more
Citations
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Numerical conformal mapping of multiply connected regions onto the fifth category of Koebe’s canonical slit regions
TL;DR: In this article, a boundary integral method for approximating the conformal mapping from bounded multiply connected regions onto the fifth category of Koebe's classical canonical slit regions is presented, based on a uniquely solvable boundary integral equation with generalized Neumann kernel.
Journal ArticleDOI
Numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions
TL;DR: This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions.
Journal Article
Numerical evaluation of conformal mapping and its inverse for unbounded multiply connected regions
TL;DR: A boundary integral equation method for numerical evaluation of the conformal mapping and its inverse from unbounded multiply connected regions onto five canonical slit regions is presented in this article, which is based on a uniquely solvable boundary integral equations with the adjoint generalized Neumann kernel.
Annulus with spiral slits map and its inverse of bounded multiply connected regions
TL;DR: Sangawi et al. as mentioned in this paper presented a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse.
Journal ArticleDOI
Spiral slits map and its inverse of bounded multiply connected regions
TL;DR: This paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse and several numerical examples are given to prove the effectiveness of the proposed methods.
References
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Book
The Numerical Solution of Integral Equations of the Second Kind
TL;DR: In this paper, a brief discussion of integral equations is given, and the Nystrom method is used to solve multivariable integral equations on a piecewise smooth planar boundary.
Journal ArticleDOI
On the evaluation of layer potentials close to their sources
Johan Helsing,Rikard Ojala +1 more
TL;DR: The paper focuses on the solution of the Dirichlet problem for Laplace's equation in the plane with a new scheme based on a mix of composite polynomial quadrature, layer density interpolation, kernel approximation, rational quadratures, highPolynomial order corrected interpolation and differentiation, temporary panel mergers and splits, and a particular implementation of the GMRES solver.