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In this paper, we present a fast boundary integral equation method for the numerical conformal mapping and its inverse of bounded multiply connected regions onto a disk and annulus with circular slits regions. The method is based on two uniquely solvable boundary integral equations with Neumann-type and generalized Neumann kernels. The integral equations related to the mappings are solved numerically using combination of Nyström method, GMRES method, and fast multipole method. The complexity of this new algorithm is O ((M + 1) n) , where M + 1 stands for the multiplicity of the multiply connected region and n refers to the number of nodes on each boundary component. Previous algorithms require O ((M + 1) 3 n 3) operations. The numerical results of some test calculations demonstrate that our method is capable of handling regions with complex geometry and very high connectivity. An application of the method on medical human brain image processing is also presented. [ABSTRACT FROM AUTHOR]

This paper presents a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto an annulus with circular slits. The method is based on some uniquely solvable linear integral equations with classical, adjoint and generalized Neumann kernels. These boundary integral equations are constructed from a boundary relationship that relates the mapping function f on a multiply connected region with f′, θ′, and ∣f∣, where θ is the boundary correspondence function. Some numerical examples are presented to illustrate the efficiency of the presented method. [ABSTRACT FROM AUTHOR]

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 amultiply connected region. Some numerical examples are presented to illustrate the efficiency of the presented method. [ABSTRACT FROM AUTHOR]