相关论文: Circular arc polygons, numerical conformal mapping…
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…
We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions…
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We investigate moduli of planar circular quadrilaterals symmetric with respect to both the coordinate axes. First we develop an analytic approach which reduces this problem to ODEs and devise a numeric method to find out the accessory…
An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) in the complex plane. As an immediate application, an error…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function method is extended to cover conformal mappings between Riemannian…
This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse. The toolbox can be used for multiply connected domains with…
Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by K\"uhnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…
We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…
We study moduli of planar ring domains whose complements are linear segments and establish formulas for their moduli in terms of the Weierstrass elliptic functions. Numerical tests are carried out to illuminate our results.
An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However,…
We study the problem of computing the conformal modulus of rings and quadrilaterals with strong singularities and cusps on their boundary. We reduce this problem to the numerical solution of the associated Dirichlet and Dirichlet-Neumann…
New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
In the early 1980's an elementary algorithm for computing conformal maps was discovered by R. K\"uhnau and the first author. The algorithm is fast and accurate, but convergence was not known. Given points z_0,...,z_n in the plane, the…
We study the approximation of J-holomorphic maps continuous to the boundary from ma domain in the complex plane into an almost complex manifold by maps J-holomorphic to the boundary, giving partial results in the non-integrable case. For…