Numerical Conformal Mapping via a Boundary Integral Equation with the Generalized Neumann Kernel

2009 ◽  
Vol 31 (3) ◽  
pp. 1695-1715 ◽  
Author(s):  
Mohamed M. S. Nasser
Keyword(s):  
Integral Equation ◽  
Conformal Mapping ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Numerical Conformal Mapping ◽  
Generalized Neumann Kernel ◽  
Neumann Kernel

scholarly journals A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mohamed M. S. Nasser ◽  
Ali H. M. Murid ◽  
Samer A. A. Al-Hatemi
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
Numerical Examples ◽  
Multiply Connected ◽  
Generalized Neumann Kernel ◽  
Multiply Connected Regions ◽  
Neumann Kernel

We present a uniquely solvable boundary integral equation with the generalized Neumann kernel for solving two-dimensional Laplace’s equation on multiply connected regions with mixed boundary condition. Two numerical examples are presented to verify the accuracy of the proposed method.

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 .

Integral Equation Approach for Computing Green’s Function on Doubly Connected Regions via the Generalized Neumann Kernel

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Siti Zulaiha Aspon ◽  
Ali Hassan Mohamed Murid ◽  
Mohamed M. S. Nasser ◽  
Hamisan Rahmat
Keyword(s):  
Integral Equation ◽  
Dirichlet Problem ◽  
Linear System ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Integral ◽  
Generalized Neumann Kernel ◽  
Integral Equation Approach ◽  
Gauss Elimination ◽  
Neumann Kernel

This research is about computing the Green’s function on doubly connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystrӧm method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica plots of Green’s functions for several test regions are also presented.

scholarly journals Integral equation with the generalized neumann kernel for computing green’s function on simply connected regions

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Ali H. M. Murid ◽  
Mohmed M. A. Alagele ◽  
Mohamed M. S. Nasser
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Gaussian Elimination ◽  
Linear Equations ◽  
Boundary Integral ◽  
System Of Linear Equations ◽  
Generalized Neumann Kernel ◽  
Simply Connected ◽  
Neumann Kernel

This research is about computing the Green’s functions on simply connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The numerical method for solving this integral equation is the Nystrӧm method with trapezoidal rule which leads to a system of linear equations. The linear system is then solved by the Gaussian elimination method. Mathematica plot of Green’s function for atest region is also presented.

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