Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients

Blanca Ayuso De Dios, Michael Holst, Yunrong Zhu, Ludmil Zikatanov

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality with respect to the number of degrees of freedom.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XX
EditorsRandolph Bank, Michael Holst, Jinchao Xu, Olof Widlund
Pages183-190
Number of pages8
DOIs
StatePublished - Jul 25 2013

Publication series

NameLecture Notes in Computational Science and Engineering
Volume91
ISSN (Print)1439-7358

Fingerprint

Preconditioner
Elliptic Problems
Linear systems
Jump
Discretization
Second-order Elliptic Problems
Coefficient
Piecewise Linear
Optimality
Degree of freedom
Linear Systems
Subspace
Robustness
Standards

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

De Dios, B. A., Holst, M., Zhu, Y., & Zikatanov, L. (2013). Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. In R. Bank, M. Holst, J. Xu, & O. Widlund (Eds.), Domain Decomposition Methods in Science and Engineering XX (pp. 183-190). (Lecture Notes in Computational Science and Engineering; Vol. 91). https://doi.org/10.1007/978-3-642-35275-1_20
De Dios, Blanca Ayuso ; Holst, Michael ; Zhu, Yunrong ; Zikatanov, Ludmil. / Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. Domain Decomposition Methods in Science and Engineering XX. editor / Randolph Bank ; Michael Holst ; Jinchao Xu ; Olof Widlund. 2013. pp. 183-190 (Lecture Notes in Computational Science and Engineering).
@inbook{d693ae16c0c94f579b759a9939c71625,
title = "Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients",
abstract = "In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality with respect to the number of degrees of freedom.",
author = "{De Dios}, {Blanca Ayuso} and Michael Holst and Yunrong Zhu and Ludmil Zikatanov",
year = "2013",
month = "7",
day = "25",
doi = "10.1007/978-3-642-35275-1_20",
language = "English (US)",
isbn = "9783642352744",
series = "Lecture Notes in Computational Science and Engineering",
pages = "183--190",
editor = "Randolph Bank and Michael Holst and Jinchao Xu and Olof Widlund",
booktitle = "Domain Decomposition Methods in Science and Engineering XX",

}

De Dios, BA, Holst, M, Zhu, Y & Zikatanov, L 2013, Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. in R Bank, M Holst, J Xu & O Widlund (eds), Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol. 91, pp. 183-190. https://doi.org/10.1007/978-3-642-35275-1_20

Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. / De Dios, Blanca Ayuso; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil.

Domain Decomposition Methods in Science and Engineering XX. ed. / Randolph Bank; Michael Holst; Jinchao Xu; Olof Widlund. 2013. p. 183-190 (Lecture Notes in Computational Science and Engineering; Vol. 91).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients

AU - De Dios, Blanca Ayuso

AU - Holst, Michael

AU - Zhu, Yunrong

AU - Zikatanov, Ludmil

PY - 2013/7/25

Y1 - 2013/7/25

N2 - In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality with respect to the number of degrees of freedom.

AB - In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality with respect to the number of degrees of freedom.

UR - http://www.scopus.com/inward/record.url?scp=84880453473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880453473&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-35275-1_20

DO - 10.1007/978-3-642-35275-1_20

M3 - Chapter

AN - SCOPUS:84880453473

SN - 9783642352744

T3 - Lecture Notes in Computational Science and Engineering

SP - 183

EP - 190

BT - Domain Decomposition Methods in Science and Engineering XX

A2 - Bank, Randolph

A2 - Holst, Michael

A2 - Xu, Jinchao

A2 - Widlund, Olof

ER -

De Dios BA, Holst M, Zhu Y, Zikatanov L. Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. In Bank R, Holst M, Xu J, Widlund O, editors, Domain Decomposition Methods in Science and Engineering XX. 2013. p. 183-190. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-35275-1_20