Non-matching mesh gluing by meshless interpolation; An Alternative to Lagrange multipliers

Tian, R.; Yagawa, Genki

Rewards of using non-matching meshes are great in many aspects: sub-meshing a complex structure in a sub-structure-wise manner separately; selective local refinement; unlimited scalability guarantee for generating meshes, etc. However, when meshes do not match, a gluing algorithm is required to enforce inter-domain continuity. The non-matching mesh issue is 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. 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.