scholarly journals A simplified Fornberg-like method for the conformal mapping of multiply connected regions—Comparisons and crowding

2007 ◽  
Vol 209 (1) ◽  
pp. 1-21 ◽  
Author(s):  
N. Benchama ◽  
T.K. DeLillo ◽  
T. Hrycak ◽  
L. Wang
Keyword(s):  
Conformal Mapping ◽  
Multiply Connected ◽  
Multiply Connected Regions

scholarly journals Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Arif A. M. Yunus ◽  
Ali H. M. Murid ◽  
Mohamed M. S. Nasser
Keyword(s):  
Integral Equation ◽  
Conformal Mapping ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Linear Boundary ◽  
Multiply Connected ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels.

scholarly journals Integral and differential equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

2014 ◽  
Vol 7 (1) ◽  
Author(s):  
Ali H.M. Murid ◽  
Ali W. Kareem Sangawi ◽  
M.M.S. Nasser
Keyword(s):  
Integral Equation ◽  
Conformal Mapping ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Science And Engineering ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region ◽  
Neumann Kernel

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

scholarly journals Numerical Conformal Mapping of Unbounded Multiply Connected Regions onto Circular Slit Regions

2014 ◽  
Vol 8 (1) ◽  
Author(s):  
A.A.M. Yunus ◽  
A.H.M. Murid ◽  
M.M. S. Nasser
Keyword(s):  
Conformal Mapping ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

This paper presents a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto circular slit regions. Three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the classical and the adjoint generalized Neumann kernels. Several numerical examples are presented.

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