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

Abstract : This paper studies the combination of the Full-Multi-Grid (FMG) algorithm with an anisotropic metric- based mesh adaptation algorithm. For the sake of simplicity, 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 combination with a quasi-Newton fixed point. An anisotropic metric-based mesh adaptation loop is introduced inside the FMG algorithm. FMG convergence stopping test is re-visited. Applications to a few 2D continuous and discontinuous-coefficient elliptic model problems show the efficiency of this combination.
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Gautier Brethes, Olivier Allain, Alain Dervieux. A Mesh-Adaptive Metric-Based Full-Multigrid for the Poisson problem. International Journal for Numerical Methods in Fluids, Wiley, 2015, 79 (1), pp.30-53. ⟨10.1002/fld.4042⟩. ⟨hal-01255500⟩

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