Non-matching mesh gluing by meshless interpolation - an alternative to Lagrange multipliers

Rewards of using non-matching meshes are great in many aspects: sub-meshing a complex structure in a sub-structure-wise manner separately and/or in parallel; selective local refinement; unlimited scalability guarantee for generating meshes in increasingly large-scale finite element simulation, etc. However, when meshes do not match, a gluing algorithm is required to enforce inter-domain continuity. ‘Non-matching’ terminologically originates from mesh discretization in nature, and the non-matching mesh issue is therefore avoidable or does not exist in a node-based or meshless discretization in meshless methods. Motivated by this, a gluing algorithm is developed based on meshless interpolation. The gluing is accomplished by continuous trial and test functions across non-matching meshes constructed using nodes only. The developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions. It is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one-piece conforming mesh. Compared with Lagrange multiplier gluing—one of the most common approaches—the current algorithm has two significant benefits: (1) easier implementation in any dimension and (2) positive definite banded system matrices, not acting against equation solvers, and hence better suited for large-scale finite element analysis. Copyright q 2006 John Wiley & Sons, Ltd