Part/component-based large-scale finite element analysis; Discontinuous meshes stitching up

Tian, R.

In many situations, using a non-matching mesh is convenient even indispensable. However, conventional finite element interpolation fails when meshes do not match and a gluing algorithm is required to enforce inter-mesh continuity. In this paper, a gluing algorithm is developed based on a meshless interpolation. A continuous function is constructed across two non-matching and discontinuous meshes by a meshless interpolation using nodes from both sides to perform the stitch-up. The original meshes are used for such purposes as the integration of weak form and construction of mass matrix in dynamic analyses etc. In this study, a compactly supported radial basis function interpolation is employed. The gluing algorithm developed is tested in static and wave propagation problems. Some numerical evaluation in three dimensions are also provided. Through the numerical samples, superior performance in both accuracy and convergence over traditional approaches are demonstrated. Compared with other gluing algorithms, for example, the Lagrange multipliers, the current algorithm offers (1) straightforward implementation in any dimensions, and (2) banded, positive and definite system matrices, posing no difficulty in equation solvers.