Application of genetic algorithms for optimal positions of source points in the method of fundamental solutions
Keywords:
method of fundamental solutions, gnetic algorithm, multicriteria optimization, Motz problem, biharmonic problemAbstract
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.
References
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[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.
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[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.
[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
2022-07-19
Issue
pp. 215-224
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Jopek, H., & Kołodziej, J. A. (2022). Application of genetic algorithms for optimal positions of source points in the method of fundamental solutions. Computer Assisted Methods in Engineering and Science, 15(3-4), 215-224. https://cames3.ippt.pan.pl/index.php/cames/article/view/729
