Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement
Abstract
In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with hp-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work, we extend to the hp-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh h, and the degree of the polynomial approximation p. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Furthermore, numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).
- Authors:
-
[1];
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1823212
- Report Number(s):
- LLNL-JRNL-814157
Journal ID: ISSN 2096-6385; 1022610
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Communications on Applied Mathematics and Computation
- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 2; Journal ID: ISSN 2096-6385
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Discontinuous Galerkin; Preconditioners; Domain decomposition; hp-refinement
Citation Formats
Pazner, Will, and Kolev, Tzanio. Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement. United States: N. p., 2021.
Web. doi:10.1007/s42967-021-00136-3.
Pazner, Will, & Kolev, Tzanio. Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement. United States. https://doi.org/10.1007/s42967-021-00136-3
Pazner, Will, and Kolev, Tzanio. Fri .
"Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement". United States. https://doi.org/10.1007/s42967-021-00136-3. https://www.osti.gov/servlets/purl/1823212.
@article{osti_1823212,
title = {Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement},
author = {Pazner, Will and Kolev, Tzanio},
abstractNote = {In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with hp-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work, we extend to the hp-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh h, and the degree of the polynomial approximation p. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Furthermore, numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).},
doi = {10.1007/s42967-021-00136-3},
journal = {Communications on Applied Mathematics and Computation},
number = 2,
volume = 4,
place = {United States},
year = {Fri Jul 09 00:00:00 EDT 2021},
month = {Fri Jul 09 00:00:00 EDT 2021}
}
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