Numerical conformal mapping via the Bergman kernel using the generalized minimum residual method

The Bergman kernel function is known to satisfy a certain boundary integral equation of the second kind. For boundaries that possess symmetrical quali ties, the integral equation can be transformed into another integral equati on that uses only a small part of the original boundary. This paper applies an iterative procedure known as the generalized minimum residual method fo r the computation of the Riemann mapping function via the Bergman kernel. T he complexity of this procedure is O(n(2)), where n is the number of colloc ation points on the boundary of the region. Numerical implementation on som e test regions is also presented. (C) 2000 Elsevier Science Ltd. All rights reserved.