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Abstract
We present a new algebraic multigrid (AMG) algorithm for the solution of linear systems arising from discontinuous Galerkin (DG) discretizations of heterogeneous elliptic problems. The algorithm is based on the idea of subspace corrections, and the first coarse level space is the subspace spanned by continuous linear basis functions. The linear system associated with this space is constructed algebraically using a Galerkin approach with the natural embedding as the prolongation operator. This embedding operator needs to be provided, which means that the approach is not fully algebraic. For the construction of the linear systems on the subsequent coarser levels, nonsmoothed aggregation AMG techniques are used. In a series of numerical experiments, we establish for the first time the efficiency and robustness of an AMG method for various symmetric and nonsymmetric interior penalty DG methods (including the higherorder cases) on problems with complicated, high contrast jumps in the coefficients. The solver is robust with respect to an increase in the polynomial degree of the DG approximation space (at least up to degree 6), computationally efficient, and affected only mildly by the coefficient jumps and by the mesh size h (i.e., number?of?iterations?=?O(log h1)).
Original language  English 

Pages (fromto)  367388 
Number of pages  22 
Journal  Numerical Linear Algebra with Applications 
Volume  19 
Issue number  2 
DOIs  
Publication status  Published  Mar 2012 
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Dive into the research topics of 'Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems'. Together they form a unique fingerprint.Projects
 2 Finished

Scalability of Elliptic Solvers in Weather and Climate Modelling
Scheichl, R.
Natural Environment Research Council
7/09/11 → 6/11/13
Project: Research council

Multilevel Monte Carlo Methods for Elliptic Problems
Scheichl, R.
Engineering and Physical Sciences Research Council
1/07/11 → 30/06/14
Project: Research council