Abstract:
We present an algorithm based on the multipole method for harmonic mapping of a class of domains $\mathfrak{g}$ with a curvilinear boundary containing incoming arc angles and narrow isthmuses. Results of a numerical implementation of this algorithm are given for two such domains. The use of several hundred approximation functions (multipoles) ensured an accuracy of the order of 10$^{-4}$ in the $C(\bar{\mathfrak{g}})$ norm. In a previous work, the authors presented a similar conformal mapping algorithm for the same domains, based on this method, along with a corresponding numerical implementation that demonstrated the same accuracy. A comparison of these previous results with those obtained in this work provides material for analyzing the quality of computational grids obtained using conformal and harmonic mappings.
