Vector field approximation using radial basis functions

Daniel A. Cervantes Cabrera (1) , Pedro Gonzalez-Casanova (1) , Christian Gout (2) , L. Juárez Héctor (3) , Rafael Resendiz (3)

1 UNAM - Instituto de Matematicas
2 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
3 Departamento de Matemáticas - UAM Iztapalapa

In this article, we investigate the performance of RBF-PDE methods for approximating solenoidal fields. It is well known that global RBF collocation methods present a trade-off principle, which means that smoothness implies high convergence order plus ill-conditioning. On the other hand, local methods for solving this problem have recently appeared in the literature. In this paper, we perform a numerical investigation of the differences between RBF global and local methods, in order to investigate the possible advantage of using local methods for the approximation of vector fields. More precisely, we compare the local Hermite interpolation technique using inverse multiquadrics against the non-symmetric collocation method of Kansa.

Domaines: Analyse numérique [math.NA]

Daniel A. Cervantes Cabrera, Pedro Gonzalez-Casanova, Christian Gout, L. Juárez Héctor, Rafael Resendiz. Vector field approximation using radial basis functions. Journal of Computational and Applied Mathematics, 2013, 240, pp.163-173. ⟨10.1016/j.cam.2012.07.003⟩. ⟨hal-01023298⟩