Conformal mapping of unbounded multiply connected regions onto logarithmic spiral slit with infinite straight slit

2017 ◽  
Author(s):  
Arif A. M. Yunus ◽  
Ali H. M. Murid
Keyword(s):  
Conformal Mapping ◽  
Logarithmic Spiral ◽  
Multiply Connected ◽  
Multiply Connected Regions

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

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130514 ◽  
Author(s):  
A. A. M. Yunus ◽  
A. H. M. Murid ◽  
M. M. S. Nasser
Keyword(s):  
Conformal Mapping ◽  
Mapping Function ◽  
Logarithmic Spiral ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Boundary Values ◽  
Multiply Connected ◽  
Multiply Connected Regions ◽  
Interior Points ◽  
Neumann Kernel

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. For each canonical region, two integral equations are solved before one can approximate the boundary values of the mapping function. Cauchy's-type integrals are used for computing the mapping function and its inverse for interior points. This method also works for regions with piecewise smooth boundaries. Three examples are given to illustrate the effectiveness of the proposed method.

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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