DeepAI AI Chat
Log In Sign Up

Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems

by   Chak Shing Lee, et al.

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of freedom and spectral decomposition of reference linear operators associated with the aggregates. For rapid convergence, it is important that the resulting coarse spaces have good approximation properties. In our approach, the approximation quality can be directly improved by including more spectral degrees of freedom in the coarsening process. Further, by exploiting local coarsening and a piecewise-constant approximation when evaluating the nonlinear component, the coarse level problems are assembled and solved without ever re-visiting the fine level, an essential element for multigrid algorithms to achieve optimal scalability. Numerical examples comparing relative performance of the proposed nonlinear multigrid solvers with standard single-level approaches – Picard's and Newton's methods – are presented. Results show that the proposed solver consistently outperforms the single-level methods, both in efficiency and robustness.


An Aggregation-based Nonlinear Multigrid Solver for Two-phase Flow and Transport in Porous Media

A nonlinear multigrid solver for two-phase flow and transport in a mixed...

The Hellan-Herrmann-Johnson and TDNNS method for linear and nonlinear shells

In this paper we extend the recently introduced mixed Hellan-Herrmann-Jo...

Algebraic multigrid methods for metric-perturbed coupled problems

We develop multilevel methods for interface-driven multiphysics problems...

A Trefftz-like coarse space for the two-level Schwarz method on perforated domains

We consider a new coarse space for the ASM and RAS preconditioners to so...

A Matrix-free Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods

In this work, we propose a multigrid preconditioner for Jacobian-free Ne...

Impact of spatial coarsening on Parareal convergence

We study the impact of spatial coarsening on the convergence of the Para...

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-pha...