Numerical Stability of the Localized Regular Dual Reciprocity Method using RBF-QR

PORTAPILA MAGARITA ISABEL; PONZELLINI MARINELLI LUCIANO; CARUSO NAHUEL DOMINGO

Providence

Workshop; ?Localized Kernel-Based Meshless Methods for Partial Differential Equations; 2017

Institute for Computational and Experimental Research in Mathematics (ICERM)

The Localized Regular Dual Reciprocity Method (LRDRM) is based on an integral formulation with local RBF interpolations. These functions are a very powerful tool for interpolation in meshless methods. However, the ill-conditioning of the interpolation matrix -when the RBF shape parameter tends to zero- is a practical obstacle. To avoid this problem, in cases of arbitrarily small shape parameters, the RBF-QR method can be used to stabilize the solution of the systems. In thisposter, we show some results achieved by applying the RBF-QR method to the local interpolations of the LRDRM. Numerical results are shown for some elliptic PDE in order to study the stability of the L2 -Error when the shape parameter ε → 0 (i.e. combining integral methods with RBF stability methods).