Discrete least square method for nonmatching mesh problems

This research presents a novel algorithm designed to address nonmatching mesh problems. The key feature of the algorithm is its explicit definition of an interface force on nonmatching interfaces. The displacement at the nonmatching mesh is formulated as a function of the interface force, which is determined through the implementation of displacement continuity conditions using the least square method. Notably, this method offers simplicity and robustness, as it eliminates the necessity for integration at the nonmatching mesh. Numerical examples are provided to assess the algorithm’s performance, demonstrating its potential applicability to a wide array of problems involving nonmatching meshes, including domain decomposition and parallel computation.