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Robust Multigrid for Cartesian Interior Penalty DG Formulations of the Poisson Equation in 3D

  • Jörg StillerEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered subdomains. The MG method reaches superior convergence rates corresponding to residual reductions of about two orders of magnitude within a single V(1,1) cycle. It is robust with respect to the mesh size and the ansatz order, at least up to P = 32. Rigorous exploitation of tensor-product factorization yields a computational complexity of O(PN) for N unknowns, whereas numerical experiments indicate even linear runtime scaling. Moreover, by allowing adjustable subdomain overlaps and adding Krylov acceleration, the method proved feasible for anisotropic grids with element aspect ratios up to 48.

Notes

Acknowledgements

Funding by German Research Foundation (DFG) in frame of the project STI 157/4-1 is gratefully acknowledged.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Fluid Mechanics and Center of Advancing Electronics Dresden (cfaed), TU DresdenDresdenGermany

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