Abstract
Laplace's equation with any boundary conditions can be solved by means of the Parametric Integral Equation System (PIES). For modelling of the boundary geometry in 3D problems Bézier and Coons surfaces are used. A numerical solution of the PIES requires no boundary discretization and is reduced only to the approximation of boundary functions. For its solving a collocation method with Chebyshev polynomials was used. An arrangement of collocation points has high influence on the accuracy of obtained results. Genetic algorithms are applied for searching most optimal arrangement of collocation points.
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Zieniuk, E., Szerszeń, K., Bołtuć, A. (2005). Genetic algorithms applied to optimal arrangement of collocation points in 3D potential boundary-value problems. In: Saeed, K., Pejaś, J. (eds) Information Processing and Security Systems. Springer, Boston, MA. https://doi.org/10.1007/0-387-26325-X_12
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DOI: https://doi.org/10.1007/0-387-26325-X_12
Publisher Name: Springer, Boston, MA
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