A stable computation on local boundary-domain integral method for elliptic PDEs

PONZELLINI MARINELLI LUCIANO; CARUSO NAHUEL DOMINGO; PORTAPILA MAGARITA ISABEL

MATHEMATICS AND COMPUTERS IN SIMULATION

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2021 vol. 180 p. 379 - 400

0378-4754

Many local integral methods are based on an integral formulation over small andheavily overlapping stencils with local Radial Basis Functions (RBFs) interpolations.These functions have become an extremely effective tool for interpolation on scatterednode sets, however the ill-conditioning of the interpolation matrix -when the RBF shapeparameter tends to zero corresponding to best accuracy- is a major drawback. Severalstabilizing methods have been developed to deal with this near flat RBFs in globalapproaches but there are not many applications to local integral methods. In this paperwe present a new method called Stabilized Local Boundary Domain Integral Method(LBDIM-St) with a stable calculation of the local RBF approximation for small shapeparameter that stabilizes the numerical error. We present accuracy results for somePartial Differential Equations (PDEs) such Poisson, convection-diffusion, thermalboundary layer and an elliptic equation with variable coefficients.