The Localized Regular Dual Reciprocity Method (LRDRM) for PDE initial value problems

CARUSO NAHUEL DOMINGO; PORTAPILA MAGARITA ISABEL

Rio de Janeiro

Congreso; International Congress of Mathematicians; 2018

The Localized Regular Dual Reciprocity Method (LRDRM) is an integral domain decomposition method that uses a Radial Basis Functions (RBF) interpolantion with two distinguishing features, the boundary conditions are imposed at the local interpolation level and all the calculated integrals are regular. In addition an enhancement of the LRDRM enforcesthe interpolation functions to satisfy the stationary Partial Differential Equation to be solved. Different kernels can be considered in order to eliminate the contribution of the single layer potential.In this work we present an extension of the LRDRM for non-stationary PDE initial value problems. Different time schemes are considered. The new formulation is tasted for time-dependent convection-diffusion equations. The numerical solutions show an accurate behaviour of the method for these problems.