|Title:|| Algebraic multigrid schemes for high-order discontinuous Galerkin methods|
|Date:|| Sunday 29th July 2018|
|Author(s) :|| Antonietti, P.f.; Melas, L.|
|Abstract:|| We present algebraic multigrid (AMG) methods for the efficient solution of the linear system of equations stemming from high-order discontinuous Galerkin discretizations of second-order elliptic problems.
For discontinuous Galerkin methods standard multigrid approaches cannot be employed because of redundancy of the degrees of freedom associated to the same grid point. We present new aggregation procedures and test them on extensive two-dimensional numerical experiments that demonstrate that the proposed AMG method is uniformly convergent with respect to all the discretization parameters, namely the mesh-size and the polynomial approximation degree.|