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

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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)

Original language	English
Pages (from-to)	229-255
Number of pages	27
Journal	IN: PROC. 3RD. INT. CONF. ON FINITE ELEMENTS IN FLOW PROBLEMS, , D.H. NORRIE (ED.)
Volume	2 , Calgary, Canada, Calgary Univ., no date
Issue number	(Banff, Canada: Jun. 10-13, 1980)
Publication status	Published - 1980

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Engineering(all)

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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: PROC. 3RD. INT. CONF. ON FINITE ELEMENTS IN FLOW PROBLEMS, , D.H. NORRIE (ED.), 2 , Calgary, Canada, Calgary Univ., no date((Banff, Canada: Jun. 10-13, 1980)), 229-255.

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. In: IN: PROC. 3RD. INT. CONF. ON FINITE ELEMENTS IN FLOW PROBLEMS, , D.H. NORRIE (ED.). 1980 ; Vol. 2 , Calgary, Canada, Calgary Univ., no date, No. (Banff, Canada: Jun. 10-13, 1980). pp. 229-255.

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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: PROC. 3RD. INT. CONF. ON FINITE ELEMENTS IN FLOW PROBLEMS, , D.H. NORRIE (ED.), vol. 2 , Calgary, Canada, Calgary Univ., no date, no. (Banff, Canada: Jun. 10-13, 1980), pp. 229-255.

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.

In: IN: PROC. 3RD. INT. CONF. ON FINITE ELEMENTS IN FLOW PROBLEMS, , D.H. NORRIE (ED.), Vol. 2 , Calgary, Canada, Calgary Univ., no date, No. (Banff, Canada: Jun. 10-13, 1980), 1980, p. 229-255.

Research output: Contribution to journal › Article › peer-review

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AU - Pironneau, O.

AU - Mantel, B.

AU - Periaux, J.

AU - Perrier, P.

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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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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: PROC. 3RD. INT. CONF. ON FINITE ELEMENTS IN FLOW PROBLEMS, , D.H. NORRIE (ED.). 1980;2 , Calgary, Canada, Calgary Univ., no date((Banff, Canada: Jun. 10-13, 1980)):229-255.

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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