An H-Multigrid Method for Hybrid High-Order Discretizations

Di Pietro DA, Hülsemann F, Matalon P, Mycek P, Rüde U, Ruiz D (2021)

Publication Type: Journal article, Original article

Publication year: 2021

Journal

SIAM Journal on Scientific Computing Society for Industrial and Applied Mathematics

Original Authors: Daniele A. Di Pietro, Frank Hülsemann, Pierre Matalon, Paul Mycek, Ulrich Rüde, Daniel Ruiz

Pages Range: S839-S861

DOI: 10.1137/20M1342471

Abstract

We consider a second-order elliptic PDE discretized by the hybrid high-order method, for which globally coupled unknowns are located at faces. To efficiently solve the resulting linear system, we propose a geometric multigrid algorithm that keeps the degrees of freedom on the faces at every grid level. The core of the algorithm lies in the design of the prolongation operator that passes information from coarse to fine faces through the reconstruction of an intermediary polynomial of higher degree on the cells. High orders are natively handled by the use of the same polynomial degree at every grid level. The proposed algorithm requires a hierarchy of nested meshes, such that the faces (and not only the elements) are successively coarsened. Numerical tests on homogeneous and heterogeneous diffusion problems show fast convergence, scalability in the mesh size and polynomial order, and robustness with respect to heterogeneity of the diffusion coefficient.

Authors with CRIS profile

Pierre Matalon Lehrstuhl für Informatik 10 (Systemsimulation) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation)

Additional Organisation(s)

Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

University of Montpellier / Université Montpellier FR France (FR) Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) FR France (FR)

How to cite

APA:

Di Pietro, D.A., Hülsemann, F., Matalon, P., Mycek, P., Rüde, U., & Ruiz, D. (2021). An H-Multigrid Method for Hybrid High-Order Discretizations. SIAM Journal on Scientific Computing, S839-S861. https://dx.doi.org/10.1137/20M1342471

MLA:

Di Pietro, Daniele A., et al. "An H-Multigrid Method for Hybrid High-Order Discretizations." SIAM Journal on Scientific Computing (2021): S839-S861.

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