Meshless Solution of Potential Problems by Combining Radial Basis Functions and Tensor Product ones
Annamaria Mazzia; Flavio Sartoretto

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 68, No. 1, pp. 95-112, 2010
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Keywords Meshless Methods, Poisson Problem, Mixed Boundary Conditions, Moving Least Squares, Radial Basis Functions, Tensor Product Functions.
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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