Agglomeration-based geometric multigrid solvers for compact discontinuous Galerkin discretizations on unstructured meshes. (English) Zbl 1515.65279
Summary: We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interior Penalty method. We demonstrate excellent solver performance for Poisson’s equation, provided a flux formulation is used for the operator coarsening and a suitable switch function chosen for the numerical fluxes.
MSC:
| 65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
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