A Mesh-Adaptive Metric-Based Full-Multigrid for the Poisson problem

This paper studies the combination of the Full-Multi-Grid (FMG) algorithm with an anisotropic metric-based mesh adaption algorithm. For the sake of sim-plicity, the case of an elliptic two-dimentional Partial Differential Equation (PDE) is studied. Meshes are unstructured and non-embedded, defined through the metric-based parametrisation. A rather classical MG preconditionner is applied, in com-bination with a quasi-Newton fixed point. An anisotropic metric-based mesh adaptation loop is introduced inside the FMG algorithm. FMG convergence stop-ping test is re-visited. Applications to a few 2D continuous and discontinuous-coefficient elliptic model problems show the efficiency of this combination