Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper preconditioning is developed for mixed nonlinearelliptic boundary value problems using Sobolev space background.The approach generalizes the similar results of the authors for Dirichletproblems. Namely, a linear preconditioning operator is found first for theBVP itself on the continuous level, then the projection of this operatorunder the applied discretization will provide a natural preconditioningmatrix. The mixed boundary conditions are incorporated in the preconditionersuch that the derivative of the original boundary conditions isassociated to the preconditioning operator. The paper first provides thetheoretical foundation, then the construction and advantages of the proposedpreconditioners are presented.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages104-112
Number of pages9
Volume2179
ISBN (Print)3540430431
Publication statusPublished - 2001
Event3rd International Conference on Large-Scale Scientific Computing, LSSC 2001 - Sozopol, Bulgaria
Duration: Jun 6 2001Jun 10 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2179
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other3rd International Conference on Large-Scale Scientific Computing, LSSC 2001
CountryBulgaria
CitySozopol
Period6/6/016/10/01

Fingerprint

Nonlinear Elliptic Boundary Value Problem
Sobolev spaces
Preconditioning
Sobolev Spaces
Boundary value problems
Boundary conditions
Mathematical operators
Mixed Boundary Value Problem
Mixed Boundary Conditions
Operator
Derivatives
Discretization
Projection
Derivative
Generalise

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Karátson, J., & Faragó, I. (2001). Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2179, pp. 104-112). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2179). Springer Verlag.

Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems. / Karátson, J.; Faragó, I.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2179 Springer Verlag, 2001. p. 104-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2179).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Karátson, J & Faragó, I 2001, Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2179, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2179, Springer Verlag, pp. 104-112, 3rd International Conference on Large-Scale Scientific Computing, LSSC 2001, Sozopol, Bulgaria, 6/6/01.
Karátson J, Faragó I. Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2179. Springer Verlag. 2001. p. 104-112. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Karátson, J. ; Faragó, I. / Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2179 Springer Verlag, 2001. pp. 104-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{dd42acb6ebfc47688a762511bd2ccb83,
title = "Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems",
abstract = "In this paper preconditioning is developed for mixed nonlinearelliptic boundary value problems using Sobolev space background.The approach generalizes the similar results of the authors for Dirichletproblems. Namely, a linear preconditioning operator is found first for theBVP itself on the continuous level, then the projection of this operatorunder the applied discretization will provide a natural preconditioningmatrix. The mixed boundary conditions are incorporated in the preconditionersuch that the derivative of the original boundary conditions isassociated to the preconditioning operator. The paper first provides thetheoretical foundation, then the construction and advantages of the proposedpreconditioners are presented.",
author = "J. Kar{\'a}tson and I. Farag{\'o}",
year = "2001",
language = "English",
isbn = "3540430431",
volume = "2179",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "104--112",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - Sobolev space preconditioning for mixed nonlinear elliptic boundary value problems

AU - Karátson, J.

AU - Faragó, I.

PY - 2001

Y1 - 2001

N2 - In this paper preconditioning is developed for mixed nonlinearelliptic boundary value problems using Sobolev space background.The approach generalizes the similar results of the authors for Dirichletproblems. Namely, a linear preconditioning operator is found first for theBVP itself on the continuous level, then the projection of this operatorunder the applied discretization will provide a natural preconditioningmatrix. The mixed boundary conditions are incorporated in the preconditionersuch that the derivative of the original boundary conditions isassociated to the preconditioning operator. The paper first provides thetheoretical foundation, then the construction and advantages of the proposedpreconditioners are presented.

AB - In this paper preconditioning is developed for mixed nonlinearelliptic boundary value problems using Sobolev space background.The approach generalizes the similar results of the authors for Dirichletproblems. Namely, a linear preconditioning operator is found first for theBVP itself on the continuous level, then the projection of this operatorunder the applied discretization will provide a natural preconditioningmatrix. The mixed boundary conditions are incorporated in the preconditionersuch that the derivative of the original boundary conditions isassociated to the preconditioning operator. The paper first provides thetheoretical foundation, then the construction and advantages of the proposedpreconditioners are presented.

UR - http://www.scopus.com/inward/record.url?scp=84944904147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944904147&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84944904147

SN - 3540430431

VL - 2179

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 104

EP - 112

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -