A Block Solver for the Exponentially Fitted IIPG-0 method

We consider an exponentially fitted discontinuous Galerkin method and propose a robust block solver for the resulting linear systems.Comment: 8 pages, 2 figures, 2 table

Space Decompositions and Solvers for Discontinuous Galerkin Methods

We present a brief overview of the different domain and space decomposition techniques that enter in developing and analyzing solvers for discontinuous Galerkin methods. Emphasis is given to the novel and distinct features that arise when considering DG discretizations over conforming methods. Connections and differences with the conforming approaches are emphasized.Comment: 2 pages 2 figures no table

A block solver for the exponentally fitted IIPG-0 method

We consider an exponentially fitted discontinuous Galerkin method for advection dominated problems and propose a block solver for the resulting linear systems. In the case of strong advection the solver is robust with respect to the advection direction and the number of unknowns

A Spectral Discontinuous Galerkin method for incompressible flow with Applications to turbulence

In this thesis we develop a numerical solution method for the instationary incompressible Navier-Stokes equations. The approach is based on projection methods for discretization in time and a higher order discontinuous Galerkin discretization in space. We propose an upwind scheme for the convective term that chooses the direction of flux across cell interfaces by the mean value of the velocity and has favorable properties in the context of DG. We present new variants of solenoidal projection operators in the Helmholtz decomposition which are indeed discrete projection operators. The discretization is accomplished on quadrilateral or hexahedral meshes where sum-factorization in tensor product finite elements can be exploited. Sum-factorization significantly reduces algorithmic complexity during assembling. In this thesis we thereby build efficient scalable matrix-free solvers and preconditioners to tackle the arising subproblems in the discretization. Conservation properties of the numerical method are demonstrated for both problems with exact solution and turbulent flows. Finally, the presented DG solver enables long time stable direct numerical simulations of the Navier-Stokes equations. As an application we perform computations on a model of the atmospheric boundary layer and demonstrate the existence of surface renewal

A block solver for the exponentially fitted IIPG--0 method

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