We present an algorithm based on the multipole method for harmonic mapping of a class of domains 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 in the () 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.
A.O. Bagapsh (Wed,) studied this question.