Hybrid multigrid methods for high-order discontinuous Galerkin discretizations

Multigrid algorithms for high order discontinuous Galerkin methods

I n this paper we study the performance of hand p-multigrid algorithms for high order Discontinuous Galerkin discretizations of elliptic problems. We test the performance of the multigrid schemes employing a wide class of smoothers and considering both twoand three-dimensional test cases.

Algebraic Multigrid for Discontinuous Galerkin Discretizations

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 algebra...

High-Order Discontinuous Galerkin Methods using a Spectral Multigrid Approach

Multigrid algorithms for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations on unstructured meshes. The algorithms are based on coupling both pand h-multigrid (ph-multigrid) methods which are used in non-linear or linear forms, and either directly as solvers or as preconditioners to a Newton-Krylov method. The perform...

Multigrid Solution for High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations

A high-order discontinuous Galerkin finite element discretization and p-multigrid solution procedure for the compressible Navier-Stokes equations are presented. The discretization has an element-compact stencil such that only elements sharing a face are coupled, regardless of the solution space. This limited coupling maximizes the effectiveness of the p-multigrid solver, which relies on an elem...