A hybrid meshless local Petrov–Galerkin method for unbounded domains

Meshless methods have gained popularity in recent years. However, like the finite element method, they do not handle unbounded domains well. Coupling with other techniques more suited to performing this task is problematic, since nodal values on the boundary are fictitious rather than actual. The scaled boundary finite element method is a semi-analytical approach to computational mechanics ideally suited to modelling unbounded domains. Recently a meshless version of the scaled boundary method based on the local Petrov–Galerkin approach has been developed. This paper couples the meshless scaled boundary method, used to model the far field, with conventional meshless local Petrov–Galerkin modelling of the near field. The coupling method is general, and could be applied to other techniques of modelling the far field, such as the infinite element method.