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. � 2012 Arif A. M. Yunus et al.

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. � 2013 The Author(s) Published by the Royal Society. All rights reserved.

This paper presents a fast boundary integral equation method with for computing conformal mappings of multiply connected regions. We consider the canonical region consists of the entire complex plane bounded by a finite straight slit on the line Im ? = 0 and finite logarithmic spiral slits. Some numerical examples are given to show the effectiveness of the proposed method.

This paper presents a fast boundary integral equation method for numerical conformal mapping of unbounded multiply connected regions onto a disk with an infinite straight slit and finite logarithmic spiral slits. Some numerical examples are given to show the effectiveness of the proposed method.

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 paper. This method is based on a uniquely solvable boundary integral equation with the adjoint generalized Neumann kernel. This method is accurate and reliable. Some numerical examples are presented to illustrate the effectiveness of this method.

This paper presents a boundary integral equation method for conformal mapping of an unbounded multiply connected region onto a radial slits region. Two linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. These integral equations are uniquely solvable. The kernels involved in these integral equations are the adjoint generalized Neumann kernels. Two numerical examples are presented to show the effectiveness of the proposed method. � 2013 AIP Publishing LLC.