The time-domain method of weighted residuals (MWR): Moving from grid-based methods to node-based meshless techniques

This paper presents a framework of the method of weighted residuals that can be used to generalize time-domain numerical methods. Based on it, evolution of the conventional grid-based techniques to the node-based meshless methods is described. Such meshless methods provide the flexibility of modeling curved interfaces and boundaries. Numerical examples show the effectiveness and validity of the methods.