The condition number of the BEM-matrix arising from Laplace's equation

We investigate the condition number of the matrices that appear in the boundary element method. In particular we consider the Laplace equation with mixed boundary conditions. For Dirichlet boundary conditions, the condition number of the system matrix increases linearly with the number of boundary elements. We extend the research and search for a relation between the condition number and the number of elements in the case of mixed boundary conditions. In the case of a circular domain, we derive an estimate for the condition number of the system matrix. This matrix consists of two blocks, each block originating from a well-conditioned matrix. We show that the block matrix is also well-conditioned.