Multilevel Method Based on Non-nested Meshes
نویسندگان
چکیده
Partial differential equations in complex domains are very flexibly discretized by 7 finite elements with unstructured meshes. For such problems, the challenging task to construct 8 coarse level spaces for efficient multilevel preconditioners can in many cases be solved by a 9 semi-geometric approach, which is based on a hierarchy of non-nested meshes. In this paper, 10 we investigate the connection between the resulting semi-geometric multigrid methods and the 11 truly geometric variant more closely. This is done by considering a sufficiently simple com12 putational domain and treating the geometric multigrid method as a special case in a family of 13 almost nested settings. We study perturbations of the meshes and analyze how efficiency and 14 robustness depend on a truncation of the interlevel transfer. This gives a precise idea of which 15 results can be achieved in the general unstructured case. 16
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