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Title: Space-time discretizations using constrained first-order system least squares (CFOSLS)

Abstract

This work studies finite element discretizations for three types of time-dependent PDEs, namely heat equation, scalar conservation law and wave equation, which we reformulate as first order systems in a least-squares setting, subject to a space-time conservation constraint (coming from the original PDE). Available piecewise polynomial finite element spaces in (n + 1)-dimensions for functional spaces from the (n + 1)-dimensional de Rham sequence for n = 2, 3 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multigrid preconditioners are presented for the discrete CFOSLS system. The results are obtained from a parallel implementation of the methods for which we report reasonable scalability.

Authors:
 [1];  [2];  [3];  [1];  [4]
  1. Portland State Univ., OR (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Johannes Kepler Univ. Linz (Austria)
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Portland State Univ., OR (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); US Army Research Office (ARO); National Science Foundation (NSF)
OSTI Identifier:
1670550
Alternate Identifier(s):
OSTI ID: 1564346
Report Number(s):
LLNL-JRNL-750662
Journal ID: ISSN 0021-9991; 936013
Grant/Contract Number:  
AC52-07NA27344; W911NF-15-1-0590; W911NF-16-1-0307; DMS-1624776
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 373; Journal Issue: na; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; CFOSLS; Space-time; Multigrid; Finite element method; 4D de Rham sequence

Citation Formats

Voronin, Kirill, Lee, Chak Shing, Neumüller, Martin, Sepulveda, Paulina, and Vassilevski, Panayot S. Space-time discretizations using constrained first-order system least squares (CFOSLS). United States: N. p., 2018. Web. https://doi.org/10.1016/j.jcp.2018.07.024.
Voronin, Kirill, Lee, Chak Shing, Neumüller, Martin, Sepulveda, Paulina, & Vassilevski, Panayot S. Space-time discretizations using constrained first-order system least squares (CFOSLS). United States. https://doi.org/10.1016/j.jcp.2018.07.024
Voronin, Kirill, Lee, Chak Shing, Neumüller, Martin, Sepulveda, Paulina, and Vassilevski, Panayot S. Tue . "Space-time discretizations using constrained first-order system least squares (CFOSLS)". United States. https://doi.org/10.1016/j.jcp.2018.07.024. https://www.osti.gov/servlets/purl/1670550.
@article{osti_1670550,
title = {Space-time discretizations using constrained first-order system least squares (CFOSLS)},
author = {Voronin, Kirill and Lee, Chak Shing and Neumüller, Martin and Sepulveda, Paulina and Vassilevski, Panayot S.},
abstractNote = {This work studies finite element discretizations for three types of time-dependent PDEs, namely heat equation, scalar conservation law and wave equation, which we reformulate as first order systems in a least-squares setting, subject to a space-time conservation constraint (coming from the original PDE). Available piecewise polynomial finite element spaces in (n + 1)-dimensions for functional spaces from the (n + 1)-dimensional de Rham sequence for n = 2, 3 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multigrid preconditioners are presented for the discrete CFOSLS system. The results are obtained from a parallel implementation of the methods for which we report reasonable scalability.},
doi = {10.1016/j.jcp.2018.07.024},
journal = {Journal of Computational Physics},
number = na,
volume = 373,
place = {United States},
year = {2018},
month = {7}
}

Journal Article:

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Cited by: 2 works
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Figures / Tables:

Table 1 Table 1: Definitions of $\mathcal{L}$x(u), $\mathcal{L}_{t}$(u), and tr(u) for different PDEs.

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