Domain decomposition by radial basis functions for time dependent partial differential equations

In the last years, there has been an increased investigation of efficient algorithms to solve problems of great scale. The main restriction of the traditional methods, like finite difference methods and finite element methods, is the mesh generation. In this work, we investigate the overlapping domain decomposition method applied to time dependent partial differential equations with unsymmetric radial basis function collocation method. Numerical experiments performed with thin-plate splines as kernel function, for an evolutionary problem in two dimensions, show a drastic time reduction as we increase the number of subdomains, high numerical accuracy and lower numerical diffusion. The numerical results suggest that the scheme proposed can be useful to tackle large scale time dependent problems.