High-order maximum-entropy collocation methods

Author (s): Greco, F.; Arroyo, M.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 367
Date: 2020

This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an optimization procedure and the strong form of the problem is directly imposed at the collocation points, reducing significantly the computational times with respect to the Galerkin formulation. Furthermore, such a method is truly meshfree, since no background integration grid is necessary. The validity of HOLMES collocation is verified with supportive numerical examples, where the expected convergence rates are obtained. This includes the approximation of PDEs on domains bounded by implicit and explicit (NURBS) curves, illustrating a direct integration between geometric modeling and numerical analysis.