On Hybrid Multigrid-Schwarz Algorithms
Journal of Scientific Computing
Preconditioning on high-order element methods using Chebyshev--Gauss--Lobatto nodes
Applied Numerical Mathematics
Journal of Computational Physics
Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D
Journal of Scientific Computing
International Journal of High Performance Computing Applications
Horizontal Large Eddy Simulation of Stratified Mixing in a Lock-Exchange System
Journal of Scientific Computing
Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes
Journal of Computational Physics
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We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz methods based on restrictions of the originating SE matrices converge faster than FE-based methods and that weighting the Schwarz matrices by the inverse of the diagonal counting matrix is essential to effective Schwarz smoothing. Several of the methods considered achieve convergence rates comparable to those attained by classic multigrid on regular grids.