A quasi-linear technique applied to the method of fundamental solution

• Autores: Kamal Shanazari, Mahmoud Fallahi
• Localización: Engineering analysis with boundary elements, ISSN 0955-7997, Vol. 34, Nº. 4, 2010, págs. 388-392
• Idioma: inglés
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• Resumen

  • This paper proposes the use of a quasi-linear technique for the method of fundamental solution (MFS) to treat the non-linear Poisson-type equations. The MFS, which is a fully meshless method, often deals with the linear and non-linear poisson equations by approximating a particular solution via employing radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. The current work suggests a linearization scheme for the non-homogeneous term in terms of the dependent variable resulting in Helmholtz-type equations whose fundamental solutions are available. Consequently, the MFS can be directly applied to the new linearized equation. The numerical examples illustrate the effectiveness of the presented method.