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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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An Effective Realization of the High Accurate Block-Grid Method in Solving Laplace's Equation on Polygons
by
Suzan Cival
Department of Mathematics, Eastern Mediterranean University, Northern Cyprus
Coauthors: A.A. Dosiyev(Department of Mathematics, Eastern Mediterranean University, Northern Cyprus)

As shown in [1], the high accurate Block-Grid method in solving Laplace's equation on polygons the sixth order matching operator (S6) is used for gluing the subsystems. The construction of S6 requires to approximate the solution at point which belong to cell of grids, we need the values of solution at 31 net points around it. Because of this property realization of Block-Grid equations becomes ineffective in terms of time and storage efficiency.

In this paper we propose an effective realization of Block-Grid  method by using discrete Fourier representation of exact solution of finite difference equations instead of S6u, i.e., extending this representation at any interior point of rectangles. The numerical experiments show the effectiveness of this approach.

[1] A.A. Dosiyev, A Block-Grid method for increased accuracy for solving Drichlet's problem for Laplace's equation on polygons.Comp. Maths Math. Phys., Vol.34, No.5 (1994), 591-604.

Date received: March 6, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-87.