The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs

In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The benefits from direct discretization approach called the “direct RBF (D-RBF-PU)” method. Thanks to avoiding all derivatives PU weight functions as well lower local approximants, faster simpler than standard RBF-PU Besides, discontinuous can now be utilized develop in more efficient less expensive way. Alternatively, an RBF-generated finite difference (RBF-FD) setting which much some situations accurate original RBF-FD. polyharmonic splines are used approximations, error stability issues considered. Some numerical experiments irregular two- three-dimensional domains, cost comparison tests, performed support theoretical analysis show efficiency