Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems

We present a new algebraic multigrid (AMG) algorithm for the solution of linear systems arising from discontinuous Galerkin 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. For the construction of the linear systems on the subsequent coarser levels non-smoothed aggregation AMG techniques are used. In a series of numerical experiments we establish the efficiency and robustness of the proposed method for various symmetric and non-symmetric interior penalty discontinuous Galerkin methods, including several model problems with complicated, high-contrast jumps in the coefficients. The solver is robust with respect to an increase in the polynomial degree of the discontinuous Galerkin approximation space (at least up to degree 6), computationally efficient, and it is affected only mildly by the coefficient jumps and by the mesh size h (i.e. O(log h−1) number of iterations). Copyright c © 0000 John Wiley & Sons, Ltd.

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