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Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems
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DOI：10.1016/j.cma.2020.113432.png)
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Abstract
En 中文
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. (C) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:
Nonlinear
Nonlinear multigrid
Full approximation scheme
Algebraic multigrid
Local spectral coarsening
Unstructured
Finite volume method
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