Numerical conformal mapping of multiply connected regions by Fornberg-like methods

1999 ◽  
Vol 83 (2) ◽  
pp. 205-230 ◽  
Author(s):  
Thomas K. DeLillo ◽  
Mark A. Horn ◽  
John A. Pfaltzgraff
Keyword(s):  
Conformal Mapping ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Multiply Connected Regions

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.

scholarly journals Circular Slits Map of Bounded Multiply Connected Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Ali W. K. Sangawi ◽  
Ali H. M. Murid ◽  
M. M. S. Nasser
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Connected Region ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

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.

scholarly journals Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method

2000 ◽  
Vol 24 (2) ◽  
pp. 129-137 ◽  
Author(s):  
Tetsuo Inoue ◽  
Hideo Kuhara ◽  
Kaname Amano ◽  
Dai Okano
Keyword(s):  
Dirichlet Problem ◽  
Conformal Mapping ◽  
Fundamental Solutions ◽  
Multiply Connected Domains ◽  
Multiply Connected Domain ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Theoretical Scheme ◽  
Weighted Polynomials ◽  
Numerical Conformal Mappings

A potentially theoretical scheme in the fundamental solutions method, different from the conventional one, is proposed for numerical conformal mappings of unbounded multiply connected domains. The scheme is introduced from an algorithm on numerical Dirichlet problem, based on the asymptotic theorem on extremal weighted polynomials. The scheme introduced in this paper has the characteristic called “invariant and dual.”

Sign in / Sign up

Export Citation Format

Share Document