Subgrid finite volume preconditioner for Discontinuous Galerkin implemented in the DUNE framework

University essay from Lunds universitet/Matematik LTH

Author: Johannes Kasimir; [2021]

Keywords: discontinuous galerkin spectral element method; dune; high performance computing; numerical analysis; numerical methods; fluid dynamics; simulation; multigrid; iterative methods; Technology and Engineering;

Abstract: A Jacobian free multigrid preconditioner for linear problems arising from Implicit Discontinuous Galerkin (DG) discretizations is implemented. The preconditioner is based on a multigrid method for a low order Finite volume (FV) discretization on a subcellgrid. L2-projections are introduced as a strategy to translate between the discretizations. Numerical tests on advection dominated linear advection diffusion in two dimensions, performed using the DUNE framework, shows there is potential in this approach when the FV problem can be solved efficiently to low error

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