Open Access

ARTICLE

Meshless Solution of Potential Problems by Combining Radial Basis Functions and Tensor Product ones

Annamaria Mazzia¹, Flavio Sartoretto²

1 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Italy, mazzia@dmsa.unipd.it
2 Dipartimento di Informatica Università di Venezia, Italy, flavio.sartoretto@unive.it

Computer Modeling in Engineering & Sciences 2010, 68(1), 95-112. https://doi.org/10.3970/cmes.2010.068.095

Abstract

Meshless methods for the solution of Partial Differential Equations receive nowadays increasing attention. Many meshless strategies have been proposed. The majority of meshless variational methods one can find in the literature, use Radial Basis Functions (RBF) as generators of suitable trial and test spaces. One of the main problems encountered when exploiting RBF is performing numerical integrations over circles (when 2D problems are attacked, spheres for 3D ones). We exploit Tensor Product Functions (TPF) as the test function space. This strategy allows one to consider rectangular integration domains, which are much easier to manage. This paper numerically analyzes the effectiveness in solving potential problems of various settings for trial and test functions. Finally, the accuracy of our best choice method is analyzed, when using both uniform and pseudo-random meshes.

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