Application of genetic algorithms for optimal positions of source points in the method of fundamental solutions
Abstract
This paper describes the application of the method of fundamental solutions for 2-D harmonic and biharmonic problems. Also, genetic algorithm is presented as a numerical procedure used for the determination of source points positions. Choosing good locations of source points is crucial in the MFS as it has a great impact on the quality of the solution. Genetic algorithm is applied in order to find such an arrangement of source points, which provides the solution of sufficient accuracy.
Keywords
method of fundamental solutions, gnetic algorithm, multicriteria optimization, Motz problem, biharmonic problem,References
[1] J .T. Chen, C.S. Wu, Y.T. Lee, KH. Chen. On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equation. Comput. Math. Appl., 53: 851-879, 2007.[2] A. Karageorghis, G. Fairweather. The method of fundamental solutions for numerical solution of the biharmonic equation. J. Comput. Phys., 69: 434- 459, 1987.
[3] A. Karageorghis, G. Fairweather. The Almansi method of fundamental solutions for solving biharmonic problems. Int. J. Numer. Methods Engrg., 26: 1668- 1682, 1988.
[4] A. Karageorghis, G. Fairweather. The simple layer potential method of fundamental solutions for certain biharmonic equation. Int. J. Numer. Methods Fluids, 9: 1221- 1234, 1989.
[5] Z-C. Li. Combinations of method of fundamental solutions for Laplace's equation with singularities. Eng. Anal. Boundary Elem., 32: 856- 869, 2008.
[6] Z. Michalewicz. Genetic algorithms + Data Structures = Evolution Programs. Springer, 1998.
[7] P. Mitica, Y.F. Rashedb. Convergence and stability of the method of mesh less fundamental solutions using an array of randomly distributed sources. Eng. Anal. Boundary Elem., 28: 143- 153, 2004.
[8] R. Nishimura, K Nishimori, N. Ishihara. Determining the arrangement of fictitious charges in charge simulation method using genetic algorithms. J. Electrostatics, 49: 95- 105, 2000.
[9] R. Nishimura, K Nishimori, N. Ishihara. Automatic arrangement of fictitious charges and contour points in charge simulation method for polar coordinate system. J. Electrostatics, 51-52: 618-624, 200l.
[10] R. Nishimura, K Nishimori, N. Ishihara. Automatic arrangement of fictitious charges and contour points in charge simulation method for two spherical electrodes. J. Electrostatics, 57: 337-346, 2003.
[11] A. Poullikkas, A. Karageorghis, G. Georgiou. Methods of fundamental solutions for harmonic and biharmonic boundary value problems. Comput. Mech., 21: 416-423, 1998.
[12] J. Wang, J.D. Lavers. On the determination of the locations for the virtual sources in the method offundamental solutions for Eddy current problems. IEEE T. Magn., 31: 3512-3514, 1995.
Published
Jul 19, 2022
How to Cite
JOPEK, Hubert; KOŁODZIEJ, Jan A..
Application of genetic algorithms for optimal positions of source points in the method of fundamental solutions.
Computer Assisted Methods in Engineering and Science, [S.l.], v. 15, n. 3-4, p. 215-224, july 2022.
ISSN 2956-5839.
Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/729>. Date accessed: 23 dec. 2024.
Issue
Section
Articles
