Abstract
We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. In particular, we study a smoother which incorporates the inverse of the mass matrix as an iteration matrix, and which we call mass-Richardson smoother. We perform a rigorous analysis in a model setting and perform some numerical experiments to confirm the theoretical results.
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Acknowledgments
This work was supported by the National Research Network “Geometry + Simulation” (NFN S117, 2012–2016), funded by the Austrian Science Fund (FWF).
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Hofreither, C., Zulehner, W. (2015). Mass Smoothers in Geometric Multigrid for Isogeometric Analysis. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_20
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DOI: https://doi.org/10.1007/978-3-319-22804-4_20
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