A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

Tomas Johansson, Daniel Lesnic

Research output: Contribution to journalArticle

Abstract

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.
Original languageEnglish
Pages (from-to)1327-1341
Number of pages15
JournalApplicable Analysis
Volume85
Issue number11
DOIs
Publication statusPublished - Nov 2006

Fingerprint

Conjugate gradient method
Conjugate Gradient Method
Viscous flow
Viscous Flow
Stokes Operator
Discrepancy Principle
Fluid
Stopping Criterion
Fluids
Hydrostatics
Conjugate Gradient
Stokes Flow
Iterative Procedure
Viscous Fluid
Boundary Elements
Bounded Domain
Cauchy Problem
Boundary Value Problem
Numerical Solution
Boundary element method

Keywords

  • boundary element method
  • cauchy problem
  • conjugate gradient
  • inverse problem
  • regularization
  • Stokes flow

Cite this

Johansson, Tomas ; Lesnic, Daniel. / A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow. In: Applicable Analysis. 2006 ; Vol. 85, No. 11. pp. 1327-1341.
@article{39e2ebfec7c2440eb4fd28bb9b68abcf,
title = "A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow",
abstract = "The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.",
keywords = "boundary element method, cauchy problem, conjugate gradient , inverse problem, regularization, Stokes flow",
author = "Tomas Johansson and Daniel Lesnic",
year = "2006",
month = "11",
doi = "10.1080/00036810600841928",
language = "English",
volume = "85",
pages = "1327--1341",
journal = "Applicable Analysis",
issn = "0003-6811",
publisher = "Taylor & Francis",
number = "11",

}

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow. / Johansson, Tomas; Lesnic, Daniel.

In: Applicable Analysis, Vol. 85, No. 11, 11.2006, p. 1327-1341.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

AU - Johansson, Tomas

AU - Lesnic, Daniel

PY - 2006/11

Y1 - 2006/11

N2 - The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

AB - The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

KW - boundary element method

KW - cauchy problem

KW - conjugate gradient

KW - inverse problem

KW - regularization

KW - Stokes flow

UR - http://www.tandfonline.com/10.1080/00036810600841928

U2 - 10.1080/00036810600841928

DO - 10.1080/00036810600841928

M3 - Article

VL - 85

SP - 1327

EP - 1341

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 11

ER -