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

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 ...

Two - Level Algebraic Multigrid

Convergence of the multigrid-reduction-in-time algorithm for the linear elasticity equations

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction ...

Algebraic Two-Level Convergence Theory for Singular Systems

We consider the algebraic convergence theory that gives its theoretical foundations to classical algebraic multigrid methods. All the main results constitutive of the approach are properly extended to singular compatible systems, including the recent sharp convergence estimates for both symmetric and nonsymmetric systems. On the other hand, issues associated with singular coarse grid matrices a...

Part-level Sequence Dependent Setup Time Reduction in CMS

This paper presents the idea of creating cells while reducing part-level sequence-dependent setup time in general cellular manufacturing systems (CMS). Setup time reduction in CMS has gained modest attention in the literature. This could be attributed to the fact that the fundamental problem in cell formation in CMS has been mainly related to material handling and machine utilization while setu...