Single-level multigrid

Two - Level Algebraic Multigrid

Multigrid Methods with Constraint Level Decomposition for Variational Inequalities∗

In this paper we introduce four multigrid algorithms for the constrained minimization of non-quadratic functionals. These algorithms are combinations of additive or multiplicative iterations on levels with additive or multiplicative ones over the levels. The convex set is decomposed as a sum of convex level subsets, and consequently, the algorithms have an optimal computing complexity. The meth...

Two-level Algebraic Multigrid for the Helmholtz Problem

An algebraic multigrid method with two levels is applied to the solution of the Helmholtz equation in a first order least squares formulation, discretized by Q1 finite elements with reduced integration. Smoothed plane waves in a fixed set of directions are used as coarse level basis functions. The method is used to investigate numerically the sensitivity of the scattering problem to a change of...

Two-Level Convergence Theory for Multigrid Reduction in Time (MGRIT)

Abstract. In this paper we develop a two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), as it is implemented in the open-source XBraid package [25]. MGRIT is a scalable and multi-level approach to parallel-in-time simulations that non-intrusively uses existing time-stepping schemes, and that in a specific two-level setting is equivalent to ...

An Additive Standpoint in Parallel Two-Level Multigrid Algorithms