Genetic algorithms applied to optimal arrangement of collocation points in 3D potential boundary-value problems

  • Eugeniusz Zieniuk
  • Krzysztof Szerszeń
  • Agnieszka Bołtuć


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.

Key words

Boundary integral equation Parametric Integral Equation System (PIES) Bézier surfaces Coons surfaces collocation method genetic algorithms 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Eugeniusz Zieniuk
    • 1
  • Krzysztof Szerszeń
    • 1
  • Agnieszka Bołtuć
    • 1
  1. 1.Faculty of Mathematics and Physics Institute of Computer ScienceUniversity of BialystokBialystokPoland

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