On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods.

Roland Glowinski; O. Pironneau; B. Mantel; J. Periaux; P. Perrier

On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods.

Roland Glowinski, O. Pironneau, B. Mantel, J. Periaux, P. Perrier

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

1 Citation (Scopus)

Abstract

The authors consider the solution of large nonlinear problems in Fluid Dynamics by functional least square formulation and conjugate gradient algorithms with scaling. A new technique for the incomplete Choleski factorization of large, sparse symmetric positive definite matrices is presented. Then the special properties of the associated auxiliary operators allow the calculation of efficient incore solutions of the Navier-Stokes equations for incompressible fluids. To illustrate the possibility of the method, a 2-D unsteady separated flow in and around an air intake at large incidence (40 degrees) and fairly high Reynolds number (750) is simulated; the results of the numerical experiments are displayed and analyzed. (A)

Original language	English
Title of host publication	Proceedings of the Third International Conference on Finite Elements in Flow Problems
Editors	D. H. Norrie
Publisher	University of Calgary
Pages	229-255
Number of pages	27
Volume	2
Publication status	Published - Jun 1980
Event	Third International Conference on Finite Elements in Flow Problems - Banff, Canada Duration: 10 Jun 1980 → 13 Jun 1980

Publication series

Name	Proceedings of the International Conference on Finite Elements in Flow Problems

Conference

Conference	Third International Conference on Finite Elements in Flow Problems
Country/Territory	Canada
City	Banff
Period	10/06/80 → 13/06/80

Cite this

Glowinski, R., Pironneau, O., Mantel, B., Periaux, J., & Perrier, P. (1980). On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods. In D. H. Norrie (Ed.), Proceedings of the Third International Conference on Finite Elements in Flow Problems (Vol. 2, pp. 229-255). (Proceedings of the International Conference on Finite Elements in Flow Problems). University of Calgary.

Glowinski, Roland ; Pironneau, O. ; Mantel, B. et al. / On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods. Proceedings of the Third International Conference on Finite Elements in Flow Problems. editor / D. H. Norrie. Vol. 2 University of Calgary, 1980. pp. 229-255 (Proceedings of the International Conference on Finite Elements in Flow Problems).

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abstract = "The authors consider the solution of large nonlinear problems in Fluid Dynamics by functional least square formulation and conjugate gradient algorithms with scaling. A new technique for the incomplete Choleski factorization of large, sparse symmetric positive definite matrices is presented. Then the special properties of the associated auxiliary operators allow the calculation of efficient incore solutions of the Navier-Stokes equations for incompressible fluids. To illustrate the possibility of the method, a 2-D unsteady separated flow in and around an air intake at large incidence (40 degrees) and fairly high Reynolds number (750) is simulated; the results of the numerical experiments are displayed and analyzed. (A)",

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Glowinski, R, Pironneau, O, Mantel, B, Periaux, J & Perrier, P 1980, On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods. in DH Norrie (ed.), Proceedings of the Third International Conference on Finite Elements in Flow Problems. vol. 2, Proceedings of the International Conference on Finite Elements in Flow Problems, University of Calgary, pp. 229-255, Third International Conference on Finite Elements in Flow Problems, Banff, Canada, 10/06/80.

On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods. / Glowinski, Roland; Pironneau, O.; Mantel, B. et al.
Proceedings of the Third International Conference on Finite Elements in Flow Problems. ed. / D. H. Norrie. Vol. 2 University of Calgary, 1980. p. 229-255 (Proceedings of the International Conference on Finite Elements in Flow Problems).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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T1 - On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods.

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AU - Pironneau, O.

AU - Mantel, B.

AU - Periaux, J.

AU - Perrier, P.

PY - 1980/6

Y1 - 1980/6

N2 - The authors consider the solution of large nonlinear problems in Fluid Dynamics by functional least square formulation and conjugate gradient algorithms with scaling. A new technique for the incomplete Choleski factorization of large, sparse symmetric positive definite matrices is presented. Then the special properties of the associated auxiliary operators allow the calculation of efficient incore solutions of the Navier-Stokes equations for incompressible fluids. To illustrate the possibility of the method, a 2-D unsteady separated flow in and around an air intake at large incidence (40 degrees) and fairly high Reynolds number (750) is simulated; the results of the numerical experiments are displayed and analyzed. (A)

AB - The authors consider the solution of large nonlinear problems in Fluid Dynamics by functional least square formulation and conjugate gradient algorithms with scaling. A new technique for the incomplete Choleski factorization of large, sparse symmetric positive definite matrices is presented. Then the special properties of the associated auxiliary operators allow the calculation of efficient incore solutions of the Navier-Stokes equations for incompressible fluids. To illustrate the possibility of the method, a 2-D unsteady separated flow in and around an air intake at large incidence (40 degrees) and fairly high Reynolds number (750) is simulated; the results of the numerical experiments are displayed and analyzed. (A)

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AN - SCOPUS:0018952492

VL - 2

T3 - Proceedings of the International Conference on Finite Elements in Flow Problems

SP - 229

EP - 255

BT - Proceedings of the Third International Conference on Finite Elements in Flow Problems

A2 - Norrie, D. H.

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T2 - Third International Conference on Finite Elements in Flow Problems

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ER -

Glowinski R, Pironneau O, Mantel B, Periaux J, Perrier P. On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods. In Norrie DH, editor, Proceedings of the Third International Conference on Finite Elements in Flow Problems. Vol. 2. University of Calgary. 1980. p. 229-255. (Proceedings of the International Conference on Finite Elements in Flow Problems).

On an efficient new preconditioned conjugate gradient method. Application to the incore solution of the Navier-Stokes equations via nonlinear least squares and finite element methods.

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