Analysis, improvement and limits of the multiscale Latin method

This work studies the convergence properties of the mixed non-overlapping domain decomposition method (DDM) commonly named “Latin method”. As all DDM, the Latin method is sensitive to near-interface heterogeneity and irregularity. Using a simple yet fresh point of view, we analyze the role of the Robin parameters as well as of the second level (coarse space) correction — which are a characteristic of the method. In particular, we show how to build a spectrum-motivated coarse space aiming at ensuring fast convergence. 2D and 3D linear elasticity problems involving highly heterogeneous materials confirm the robustness of the spectral coarse space and provide evidence of the scalability of the multiscale Latin method.