Parallel and Matrix-Free Implementation of the Non-Nested Multigrid Method
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Traditionally, the geometric multigrid method is applied with a sequence of nested levels. However, the construction of a suitable hierarchy for very fine and unstructured grids is, in general, highly non-trivial. In this scenario, a non-nested multigrid method could be exploited in order to handle the burden of hierarchy generation, allowing some flexibility on the choice of the levels. We present a parallel and matrix-free implementation of the non-nested multigrid method for continuous Lagrange finite elements, where each level may consist of independently partitioned triangulations. In addition, we enable the combination with polynomial multigrid. In order to show the robustness and the performance of the method, we present several 2D and 3D numerical experiments using different polynomial degrees and geometries, coming for instance from CAD models and meshed with external mesh generators. Our implementation is part of the multigrid framework of the C++ Finite Element library deal.II.
