p-refined RBF-FD solution of a Poisson problem

Abstract

Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined. In this work, we employ RBF-FD approximation method with polyharmonic splines augmented with monomials and study the numerical properties of p-refined solutions, such as convergence orders and execution time. To fully exploit the refinement advantages, the numerical performance is studied on a Poisson problem with a strong source within the domain.

References in corpus (1)

• Monomial augmentation guidelines for RBF-FD from accuracy vs. computational time perspective

Cited by in corpus (1)

• Stability analysis of RBF-FD and WLS based local strong form meshless methods on scattered nodes