Numerical approximation of the logarithmic capacity

The logarithmic capacity of compact sets in R2 plays an important role in various fields of applied mathematics. Its value can be computed analytically for a few simple sets. In this paper a new algorithm is presented that numerically approximates the logarithmic capacity for more involved sets. The algorithm requires the solution of a boundary integral equation with Dirichlet boundary data. The boundary integral equation is solved by a collocation approach or a Galerkin approach. We illustrate the effectiveness of the algorithm for a number of examples.