Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods

For a truly meshfree technique, Galerkin meshfree methods rely chiefly on nodal integration of the weak form. In the case of Strong Form Collocation meshfree methods, direct collocation at the nodes can be employed. In this paper, performance of these node-based Galerkin and collocation meshfree methods is compared in terms of accuracy, efficiency, and stability. Considering both accuracy and efficiency, the overall effectiveness in terms of CPU time versus error is also assessed. Based on the numerical experiments, nodally integrated Galerkin meshfree methods with smoothed gradients and variationally consistent integration yield the most effective solution technique, while direct collocation of the strong form at nodal locations has comparable effectiveness.