Mohamed M. S. Nasser

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

We present a unified boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region

A Boundary Integral Equation for Conformal Mapping of Bounded Multiply Connected Regions

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Boundary integral equations with the generalized Neumann kernel for Laplace's equation in multiply connected regions

onto the five classical canonical slit domains. The method is based on a uniquely solvable boundary integral equation with the generalized Neumann kernel. Using the proposed method, the approximate mapping functions onto the five canonical slit domains can be computed in a unified way by solving linear systems with a common coefficient matrix. The method can be also used for calculating the conformal mappings of simply and doubly connected regions. The performance of the method is illustrated by several examples for regions with smooth boundaries and with piecewise smooth boundaries.

A Fast Boundary Integral Equation Method for Conformal Mapping of Multiply Connected Regions

A boundary integral method is presented for constructing approximations to the mapping functions of bounded multiply connected regions to the standard canonical slits domains given by Nehari [11]. The method is based on expressing the mapping function in terms of the solution of a Riemann-Hilbert problem which can be solved by a uniquely solvable boundary integral equation with the generalized Neumann kernel. Three numerical examples are presented to show the effectiveness of the present method.

Linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

This paper presents a new boundary integral method for the solution of Laplace’s equation on both bounded and unbounded multiply connected regions, with either the Dirichlet boundary condition or the Neumann boundary condition. The method is based on two uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. Numerical results are presented to illustrate the efficiency of the proposed method.

A boundary integral method for the Riemann–Hilbert problem in domains with corners

This paper presents a fast boundary integral equation method for approximating the conformal mapping from bounded and unbounded multiply connected regions of connectivity

Radial Slit Maps of Bounded Multiply Connected Regions

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

onto the canonical region obtained by removing

Fast Computation of the Circular Map

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Circular Slits Map of Bounded Multiply Connected Regions

rectilinear slits from a strip. The method is based on a combination of a uniquely solvable boundary integral equation with generalized Neumann kernel and the fast multipole method. The presented method requires