Numerical conformal mappings of bounded multiply connected domains by the charge simulation method

We present here a simple method of numerical conformal mappings from bounded multiply connected domains onto the bounded canonical slit domains of Nehari, i.e., a disk with concentric circular slits, and an annulus with concentric circular slits. In this method, we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. Some numerical examples show the effectiveness of the method.