Numerical Conformal Mapping onto the Unit Disk with Concentric Circular Slits by the Charge Simulation Method

摘要

We present a method of numerical conformal mapping of multiply-connected domains with closed boundary Jordan curves onto the unit disk with concentric circular slits. It is a basic problem of conformal mapping of multiply-connected domains. If the domain is bounded by a single closed Jordan curve, the problem is identified as Riemann's mapping theorem. We reduce the mapping problem to a Dirichlet problem with a pair of conjugate harmonic functions and apply the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. We here give an explicit form of approximate mapping function which is continuous using the principal value of logarithmic function.