共形不变量的计算
Computation of conformal invariants
摘要：
研究了复平面中域的共形不变量的数值计算。特别是，我们提供了一个算法计算的保形电容器的容量。该算法适用于广泛的几何形状：域被假定为具有光滑或分段光滑的边界。我们使用的方法是基于[30]中开发和实现的边界积分方程方法。这种方法的一个特点是，通过对代码进行小的更改，可以处理各种各样的问题，并且我们在文本中包含代码片段以指示实现细节。我们比较的性能和准确性，以前的结果的情况下，数值数据是可用的，也在几个模型问题的情况下，精确的结果。
英文摘要：
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 are assumed to have smooth or piecewise smooth boundaries. The method we use is based on the boundary integral equation method developed and implemented in [30]. A characteristic feature of this method is that, with small changes in the code, a wide spectrum of problems can be treated and we include code snippets within the text to indicate implementation details. We compare the performance and accuracy to previous results in the cases when numerical data is available and also in the case of several model problems where exact results are available.
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