Algebraic Multigrid for Discontinuous Galerkin Methods Using Local Transformations
In this paper we present an algebraic multigrid for discontinuous Galerkin methods. Coarser grid levels are created by applying a semi-coarsening approach based on an edge-coloring of the matrix-graph. The grid-transfer uses local basis transformations between the polynomial bases of neighboring elements. Along the coarsening process, the implicit block structure of the linear system is preserved. High frequency errors are reduced by applying an overlapping block smoother. The overlapping patches are constructed and locally weighted depending on the problem type. As model problems serve the Poisson and Stokes equations. The multigrid method is implemented in C++ using the DUNE framework.
KeywordsAlgebraic multigrid Discontinuous Galerkin Local transformations
This work was supported by the “German Academic Exchange Service” (DAAD) with the project 54570350 of the “German-Norwegian collaborative research support scheme”.
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