四边形模量的实验研究 II

四边形模的实验

Experiments with moduli of quadrilaterals

本文回顾环与四边形的共形模的基本事实与定义，综述计算方法，给出多边形边四边形模的最新结果，并进行数值实验。

Circular arc polygons, numerical conformal mappings, and moduli of quadrilaterals

We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.

环与四边形的模：算法与实验

On moduli of rings and quadrilaterals: algorithms and experiments

提出一种新的hp-FEM算法计算环与四边形的模，并与Schwarz-Christoffel工具箱等方法比较精度和性能，同时扩展到非多边形边界并给出具体误差界。

Conformal Moduli of Symmetric Circular Quadrilaterals With Cusps

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 parameters. This method uses the Schwarz equation to determine conformal mapping of the unit disk onto a given circular quadrilateral. We also give an example of a circular quadrilateral for which the value of the conformal modulus can be found in the analytic form; this example is used to validate the numeric calculations. We also use another method, so called h…

四边形外模数的计算

Computation of exterior moduli of quadrilaterals

通过将四边形外模数问题转化为拉普拉斯方程的Dirichlet-Neumann问题，采用hp-FEM算法进行数值求解，并验证了指数收敛性。