On the automatic construction of interface coupling operators for non-matching meshes by optimization methods

We propose a novel optimization technique for the automatic construction of interface operators for coupling non-matching 3D meshes. The core of the method lies in the use of localized Lagrange multipliers and least-squares approximation to find the optimal location of additional interface nodes, allowing the problem to be solved without modifying the meshes of the coupled subdomains and passing the patch test. Although many techniques exist in the literature for coupling incompatible meshes, such as the widely accepted Mortar method, which solves the problem exactly, the proposed method brings two crucial advantages: first, it eliminates the need to compute complex surface integrals on the intersection of the boundary meshes (thanks to the use of techniques adapted from the existing method of localized Lagrange multipliers); and second, and more importantly, we achieve this passing the patch test with comparable accuracy to Mortar. The efficiency and accuracy of the proposed coupling technique is demonstrated by comparing its results with other coupling methods and by solving various theoretical and practical examples with exact and experimental solutions in statics and dynamics.