  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.
