Algebraic Multigrid Preconditioning of High-Order Spectral Elements for Elliptic Problems on a Simplicial Mesh

Algebraic multigrid is investigated as a solver for linear systems that arise from high-order spectral element discretizations. An algorithm is introduced that utilizes the efficiency of low-order finite elements to precondition the high-order method in a multilevel setting. In particular, the efficacy of this approach is highlighted on simplexes in two and three dimensions with nodal spectral elements up to order n = 11. Additionally, a hybrid preconditioner is also developed for use with discontinuous spectral element methods. The latter approach is verified for the discontinuous Galerkin method on elliptic problems.