The Accuracy Improvement of Numerical Conformal Mapping using Pade Approximation by Arnoldi method(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

In this paper, we consider a method for computation of numerical conformal mappings using Pade approximation. This method calculates the poles of the denominator of a Pade approximation as charge points, using the results obtained by the charge simulation method proposed by Amano et al. Although good accuracy of numerical conformal mapping can be obtained using a few charge points, the accuracy is degraded when a certain number of charge points is exceeded. In order to improve the accuracy of this method, we reduce calculations of charge points by Pade approximation to a generalized eigenvalue problem. Moreover, we construct a highly accurate unitary matrix to appear in this generalized eigenvalue problem using the Arnoldi method. Some numerical examples illustrate the efficiency of the improved method.