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 Dirichlet problem is solved by the “lightning Laplace solver” with poles exponentially clustered near each singularity. For polygons and circular polygons, further simplifications are possible.

中文翻译：

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具有有理函数的数值保形映射

提出了基于有理逼近的数字共形映射新算法，并通过边界上的最小二乘拟合对Dirichlet问题进行了求解。该方法针对具有拐角的区域，在该区域中Dirichlet问题由“闪电拉普拉斯求解器”解决，其极点在每个奇点附近呈指数聚集。对于多边形和圆形多边形，可以进一步简化。