Published In

Computer Methods in Applied Mechanics and Engineering

Document Type

Article

Publication Date

12-2020

Subjects

Mathematical -- Nonlinear equations

Abstract

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.

Rights

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

10.1016/j.cma.2020.113432

Persistent Identifier

https://archives.pdx.edu/ds/psu/34512

Included in

Mathematics Commons

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