Extending the local radial basis function collocation methods for solving semi-linear partial differential equations

G. Gutierrez, O. R. Baquero, J. M. Valencia, W. F. Florez

    Resultado de la investigación: Capítulo del libro/informe/acta de congresoContribución a la conferenciarevisión exhaustiva

    2 Citas (Scopus)

    Resumen

    This work addresses local radial basis function (RBF) collocation methods for solving a major class of non-linear boundary value problems, i.e., Lu = f(x, u) being f a non-linear function of u. This class of problems has been largely analyzed in the BEM community. To our knowledge, few works are reported where the local RBF collocation methods (LRBFCM) based on the generalized Hermite RBF interpolation (double collocation) have been extended successfully to solve semi-linear problems even when extending to more complex nonlinear cases are not reported yet. The studied schemes are based on a strong-form approach of the PDE and an overlapping multi-domain procedure combining with standard iterative schemes. At each sub-domain, a locally meshless approximation solution by a standard or Hermite RBF expansion can be constructed.We studied also the performance respect to the shape parameter of RBF. It is confirmed that the local RBF double collocation can improve greatly the accuracy order. Some 2D benchmark problems with mixed boundary conditions showing the accuracy, convergence property and implementation issues of LRBFCM are presented.

    Idioma originalInglés
    Título de la publicación alojadaMesh Reduction Methods
    Subtítulo de la publicación alojadaBEM/MRM XXXI
    Páginas117-128
    Número de páginas12
    DOI
    EstadoPublicada - 2009
    Evento31st International Conference on Boundary Elements and Other Mesh Reduction Methods, BEM/MRM 31 - New Forest, Reino Unido
    Duración: 2 sept. 20094 sept. 2009

    Serie de la publicación

    NombreWIT Transactions on Modelling and Simulation
    Volumen49
    ISSN (versión impresa)1743-355X

    Conferencia

    Conferencia31st International Conference on Boundary Elements and Other Mesh Reduction Methods, BEM/MRM 31
    País/TerritorioReino Unido
    CiudadNew Forest
    Período2/09/094/09/09

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