Fast computation of the circular map
Reads0
Chats0
TLDR
In this paper, the authors presented a new numerical implementation of Koebe's iterative method for computing the circular map of bounded and unbounded multiply connected regions of connectivity, where the computational cost of the method is O(mn\ln n) where n is the number of nodes in discretization of each boundary component.Abstract:
This paper presents a new numerical implementation of Koebe's iterative method for computing the circular map of bounded and unbounded multiply connected regions of connectivity $m$. The computational cost of the method is $O(mn\ln n)$ where $n$ is the number of nodes in the discretization of each boundary component. The accuracy and efficiency of the presented method are demonstrated by several numerical examples. These examples include regions with high connectivity, regions whose boundaries are closer together, and regions with piecewise smooth boundaries.read more
Citations
More filters
Journal ArticleDOI
Condenser capacity and hyperbolic perimeter
TL;DR: In this article , the authors apply domain functionals to study the capacities of condensers in the complex plane, where the domain is a simply connected domain and the condenser is a compact subset of the domain.
Journal ArticleDOI
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals
TL;DR: In this article , the authors studied numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and computed the moduli of quadrilaterals for these domains.
Journal ArticleDOI
Numerical computation of preimage domains for spiral slit regions and simulation of flow around bodies.
TL;DR: In this article , the authors propose the iterative numerical methods to calculate the conformal preimage domains for the specified logarithmic spiral slit regions and develop the applications of conformal mappings in the simulations of the flow around bodies.
Journal ArticleDOI
Computing the zeros of the Szegö kernel for doubly connected regions using conformal mapping
TL;DR: In this article , conformal mapping via integral equation with the generalized Neumann kernel was used for computing the zeros of the Szegö kernel for smooth doubly connected regions. But the applicability was limited to a narrow region or region with boundaries that are close to each other.
References
More filters
Book
Advanced Engineering Mathematics
TL;DR: In this paper, the authors present a review of partial fraction expansions of differential algebraic expressions, as well as a discussion of the existence and uniqueness of solutions of systems of linear algebraic equations.
Journal ArticleDOI
Methods for numerical conformal mapping
Ralph Menikoff,Charles Zemach +1 more
TL;DR: In this paper, nonlinear integral equations for the boundary functions which determine conformal transformations in two dimensions are developed and analyzed for numerical computations of conformal maps including those which deal with regions having highly distorted boundaries.