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Preconditioning operators and Sobolevgradients for nonlinear elliptic problems

Authors:

I. FaragóAuthors Info & Claims

Computers & Mathematics with Applications, Volume 50, Issue 7

Pages 1077 - 1092

https://doi.org/10.1016/j.camwa.2005.08.010

Published: 01 October 2005 Publication History

Abstract

A preconditioning framework is presented for the iterative solution of nonlinear elliptic problems based on the preconditioning operator approach. Various fixed preconditioning operators are used in the iteration, which can be interpreted as a weighted Sobolev gradient method.

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Cited By

Raza NSial SButt A(2014)Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradientsComputers & Mathematics with Applications10.1016/j.camwa.2013.11.00667:1(210-216)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.camwa.2013.11.006
Martin TJoshi PBergou MCarr N(2013)Efficient Non-linear Optimization via Multi-scale Gradient FilteringComputer Graphics Forum10.1111/cgf.1201932:6(89-100)Online publication date: 1-Sep-2013
https://dl.acm.org/doi/10.1111/cgf.12019
Renka R(2013)Nonlinear least squares and Sobolev gradientsApplied Numerical Mathematics10.1016/j.apnum.2012.12.00265(91-104)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.apnum.2012.12.002
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Preconditioning operators and Sobolevgradients for nonlinear elliptic problems
1. Mathematics of computing
  1. Mathematical analysis
2. Theory of computation

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cover image Computers & Mathematics with Applications

Computers & Mathematics with Applications Volume 50, Issue 7

October, 2005

201 pages

ISSN:0898-1221

Issue’s Table of Contents

Copyright © Elsevier Ltd. © 2005.

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Pergamon Press, Inc.

United States

Publication History

Published: 01 October 2005

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Cited By

Raza NSial SButt A(2014)Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradientsComputers & Mathematics with Applications10.1016/j.camwa.2013.11.00667:1(210-216)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.camwa.2013.11.006
Martin TJoshi PBergou MCarr N(2013)Efficient Non-linear Optimization via Multi-scale Gradient FilteringComputer Graphics Forum10.1111/cgf.1201932:6(89-100)Online publication date: 1-Sep-2013
https://dl.acm.org/doi/10.1111/cgf.12019
Renka R(2013)Nonlinear least squares and Sobolev gradientsApplied Numerical Mathematics10.1016/j.apnum.2012.12.00265(91-104)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.apnum.2012.12.002
Majid ASial S(2011)Approximate solutions to Poisson-Boltzmann systems with Sobolev gradientsJournal of Computational Physics10.1016/j.jcp.2011.03.056230:14(5732-5738)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1016/j.jcp.2011.03.056
Raza NSial SSiddiqi S(2010)Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element settingJournal of Computational Physics10.1016/j.jcp.2009.10.048229:5(1621-1625)Online publication date: 1-Mar-2010
https://dl.acm.org/doi/10.1016/j.jcp.2009.10.048
Raza NSial SSiddiqi S(2009)Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionalsJournal of Computational Physics10.1016/j.jcp.2008.12.017228:7(2566-2571)Online publication date: 1-Apr-2009
https://dl.acm.org/doi/10.1016/j.jcp.2008.12.017
Raza NSial SSiddiqi SLookman T(2009)Energy minimization related to the nonlinear Schrödinger equationJournal of Computational Physics10.1016/j.jcp.2008.12.016228:7(2572-2577)Online publication date: 1-Apr-2009
https://dl.acm.org/doi/10.1016/j.jcp.2008.12.016
Mujeeb DNeuberger JSial S(2008)Recursive form of Sobolev gradient method for ODEs on long intervalsInternational Journal of Computer Mathematics10.1080/0020716070155846585:11(1727-1740)Online publication date: 1-Nov-2008
https://dl.acm.org/doi/10.1080/00207160701558465

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