The use of conformal transformations for the numerical solution of elliptic boundary value problems with boundary singularities
Ημερομηνία
1979Source
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)Volume
23Issue
1Pages
73-87Google Scholar check
Metadata
Εμφάνιση πλήρους εγγραφήςΕπιτομή
onto. Ω¯ A conformal transformation method is described for the numerical solution of a class of two-dimensional elliptic boundary value problems which have curved boundaries or contain boundary singularities. The method maps the region . Ω¯ of the problem conformally onto a rectangle . Ω¯ , thus transforming the original problem into a computationally simpler problem in . Ω¯ .The transformation of . Ω¯ is achieved by means of three successive conformal transformations the first of which is, in certain cases, performed numerically. The basic details of the method, for application to harmonic problems, have been described in earlier papers. For this reason the emphasis here is on the modifications needed for performing the first transformation numerically and for applying the method to more general elliptic boundary value problems. © 1978, by Academic Press Inc. (London) Ltd.