Analysis of high order dimension independent RBF-FD solution of Poisson's equation

The RBF-FD solution of a Poisson problem with mixed boundary conditions is analyzed in 1D, 2D and 3D domains discretized with scattered nodes. The results are presented in terms of convergence analyses for different orders of RBF-FD approximation, which are further combined with theoretical complexity analyses and experimental execution time measurements into a study of accuracy vs. execution time trade-off. The study clearly demonstrates regimes of optimal setups for target accuracy ranges. Finally, the dimension independence is demonstrated with a solution of Poisson's equation in an irregular 4D domain.