PARALLELIZATION IN CHOOSE THE CENTERS AND COMPUTE THE WEIGHT VECTORS FOR THE MESHLESS RBF-FD TO SOLVE POISSON EQUATION

Abstract

In recent years, the RBF-FD (Radial Basis Function - Finite difference) method of solving partial differential equation has been researched by many scientists. This method is effective for problems with complex geometry, large fluctuations function or multidimensional space, due to the flexibility of RBF interpolation. However, the biggest problem of this method is that the time for choosing center and computing weight vector is quite high. To overcome this situation, we introduced a method of parallelizing the selection stencil algorithm and computation the weight vector for the RBF-FD method to solve the Poisson equation. Numerical results show that when the data of the problem increases, the parallelization of the selection stencil algorithm and the computation weighted vector has significantly improved computational time.