Comptes Rendus
The Legacy of Roland Glowinski
Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 73-88.

Roland Glowinski published 8 books and more than 300 articles. He was also an editor of many very well cited proceedings. Hence this attempt to summarize his scientific work is not likely to do justice to his work. Nevertheless, we will try to extract his major contributions, such as the augmented Lagrangian algorithm, various domain decomposition and fictitious methods and their performance on the Navier–Stokes equations in a moving domain. Roland has created a school of applied mathematicians remarkable by their rigor and efficiency for industrial applications. He marked his time and his books will be authorities as long as computer architectures are similar to their present structures.

Roland Glowinski a publié 8 livres et plus de 300 articles. Il a également été rédacteur en chef de nombreux actes très bien cités. Il est donc peu probable que cette tentative de résumer son travail scientifique rende justice à son œuvre. Néanmoins, nous essaierons d’extraire ses principales contributions, telles que l’algorithme du Lagrangien augmenté, diverses méthodes de décomposition de domaines et méthodes de domaines fictifs et leurs performances sur les équations de Navier–Stokes dans un domaine mobile. Roland a créé une école de mathématiciens appliqués remarquables par leur rigueur et leur efficacité pour les applications industrielles. Il a marqué son temps et ses livres feront autorités tant que la structure des ordinateurs restera ce qu’elle est actuellement.

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DOI: 10.5802/crmeca.169
Keywords: Finite Element Method, Conjugate Gradient, Navier–Stokes equations, non-Newtonian fluid, fictitious domain, domain decomposition
Mot clés : Méthode des éléments finis, gradient conjugiué, équations de Navier–Stokes, fluide non-newtonien, domaine fictif, décomposition de domaine

Alain Bensoussan 1, 2; Olivier Pironneau 3

1 Lars Magnus Ericsson Chair, University of Texas at Dallas, 800 W Campbell Rd, Richardson, TX 75080, USA
2 Chair Professor of Risk and Decision Analysis, City University Hong Kong. 83 Tat Chee Ave, Kowloon Tong, Hong Kong, China
3 LJLL, Boite 187, Sorbonne Université, 75005 Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Alain Bensoussan; Olivier Pironneau. The Legacy of Roland Glowinski. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 73-88. doi : 10.5802/crmeca.169. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.169/

[1] Roland Glowinski Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, Springer, 1984 | DOI | Zbl

[2] Roland Glowinski Etude et approximation de quelques problèmes intégraux et intégro-differentiels, Ph. D. Thesis, Université Paris VI, Paris, France (1970)

[3] Roland Glowinski Resolution numérique d’un probleme non classique de calcul des variations, Symposium on Optimization, Nice 1969 (A. V. Balakrisnan, ed.) (Lecture Notes in Mathematics), Volume 132, Springer (1970), pp. 108-129 | Zbl

[4] Philippe G. Ciarlet The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications, 4, North-Holland, 1978 | Zbl

[5] Jean Cea; Roland Glowinski Sur des méthode d’optimisation par relaxation, Rev. Franc. Automat. Inform. Rech. Operat., Volume 7 (1973) no. R-3, pp. 5-32 | Zbl

[6] Kazufumi Ito; Karl Kunisch Semi-smooth Newton methods for variational inequalities of the first kind, M2AN, Math. Model. Numer. Anal., Volume 37 (2003) no. 1, pp. 41-62 | Numdam | MR | Zbl

[7] Jean-François Bourgat Numerical study of a dual iterative method for solving a finite element approximation of the biharmonic equation, Computer Methods appl. Mech. Engin., Volume 9 (1976), pp. 203-218 | DOI | MR | Zbl

[8] Marie-Odile Bristeau; Roland Glowinski Finite Element Analysis of the unsteady flow of a visco-plastic fluid in a cylindrical pipe, Finite Element Methods in Flow Problems (J. T. Oden; O. C. Zienkiewicz; R. H. Gallagher; C. Taylor, eds.), University of Alabama Press, Huntsville (1974), pp. 471-488

[9] Roland Glowinski; Americo Marrocco Analyse numérique du champs magnétique d’un alternateur par éléments finis, Comput. Methods Appl. Mech. Engin., Volume 3 (1974) no. 1, pp. 55-85 | DOI | Zbl

[10] D. Begis; Roland Glowinski Dual numerical techniques, application to an optimal control problem, Techniques in Optimization (A. V. Balakrishnan, ed.) (1972), pp. 159-174

[11] Roland Glowinski; Olivier Pironneau Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem, SIAM Rev., Volume 21 (1979) no. 2, pp. 167-212 | DOI | MR | Zbl

[12] Jérôme Lemoine; Arnaud Munch Resolution of the implicit Euler scheme for the Navier–Stokes equation through a least-squares method (To appear in Numerisch Mathematik, https://hal.archives-ouvertes.fr/hal-01996429/)

[13] Marie-Odile Bristeau; Roland Glowinski; Jacques F. Periaux; Pierre C. Perrier; Olivier Pironneau; Gérard Poirier Application of Optimal Control and Finite Element Methods to the Calculation of Transonic Flows and Incompressible Viscous Flows, Numerical methods in applied fluid dynamics (Reading, 1978), Academic Press Inc., 1980, pp. 203-320 | Zbl

[14] M. Fortin; Roland Glowinski Méthodes de lagrangien augmenté: applications à la résolution numérique de problèmes aux limites, Méthodes mathématiques de l’Informatique, 9, Dunod; North-Holland, 1982

[15] Roland Glowinski; Jacques-Louis Lions; Raymond Trémolière Analyse Numérique des inéquation variationnelles, Méthodes Mathématiques de l’Informatique, 5, Bordas-Dunod, 1976 | Zbl

[16] Roland Glowinski Finite Element Methods for Incompressible Viscous Flow, Numerical methods for fluids (Part 3) (P. G. Ciarlet; J. L. Lions, eds.) (Handbook of Numerical Analysis), Volume 9, North-Holland, 2003, pp. 1-1083 | Zbl

[17] Roland Glowinski; Tsorng-Whay Pan Numerical simulation of incompressible viscous flow, De Gruyter Series in Applied and Numerical Mathematics, 7, Walter de Gruyter, 2022 | DOI | Zbl

[18] Vivette Girault; Roland Glowinski Error analysis of a fictitious domain method ap- plied to a Dirichlet problem, Japan J. Ind. Appl. Math., Volume 12 (1995) no. 3, pp. 487-514 | DOI | Zbl

[19] Roland Glowinski; Patrick Le Tallec Augmented Lagrangians and Operator Splitting Methods in Nonlinear Mechanics, SIAM Studies in Applied Mathematics, 9, Society for Industrial and Applied Mathematics, 1989 | DOI | Zbl

[20] Roland Glowinski; Jacques F. Periaux Numerical Methods for Nonlinear Problems in Fluid Dynamics, Supercomputing (A. Lichnewsky; C. Saguez, eds.), North-Holland (1987), pp. 381-479 | Zbl

[21] Bertrand Maury; Roland Glowinski Fluid-particle flow: a symmetric formulation, C. R. Math. Acad. Sci. Paris, Volume 324 (1997) no. 9, pp. 1079-1084 | DOI | MR | Zbl

[22] Shev MacNamara; Gilbert Strang Operator Splitting, Splitting Methods in Communication, Imaging, Science, and Engineering (Scientific Computation), Springer, 2016, pp. 95-114 | DOI | Zbl

[23] Yurii A. Kuznetsov Efficient iterative solvers for elliptic finite element problems on nonmatching grids, Russ. J. Numer. Anal. Math. Model., Volume 10 (1995) no. 3, pp. 187-211 | MR | Zbl

[24] Roland Glowinski; Yurii A. Kuznetsov; T. Rossi; J. Toivanen A fictitious domain method with Lagrange multipliers, ENUMATH 99. Numerical mathematics and advanced applications. Proceedings of the 3rd European conference, Jyväskylä, Finland, July 26-30, 1999 (Neittaanmaki; T. Tiihonen; P. Tarvainen, eds.), World Scientific (2000), pp. 733-742 | Zbl

[25] Guriĭ I. Marchuk; Yurii A. Kuznetsov; A. M. Matsokin Fictitious domain and domain decomposition methods, Sov. J. Numer. Anal. Math. Model., Volume 1 (1986) no. 1, pp. 3-35 | MR | Zbl

[26] Patrick Le Tallec; Yann-Hervé de Roeck; Marina Vidrascu Domain decomposition methods for large linearly elliptic three dimensional problems (1990) no. RR-1182 (https://hal.inria.fr/inria-00075376) (Technical report)

[27] Roland Glowinski; Tsorng-Whay Pan; Todd I. Hesla; Daniel D. Joseph; Jacques F. Periaux A distributed Lagrange multiplier/fictitious domain method for flow around moving rigid bodies: Application to particulate flow, Int. J. Numer. Methods Fluids, Volume 30 (1999) no. 8, pp. 1043-1066 | DOI | Zbl

[28] Roland Glowinski; Tsorng-Whay Pan; Todd I. Hesla; Daniel D. Joseph A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, Volume 25 (1999) no. 5, pp. 755-794 | DOI | MR | Zbl

[29] Shang-Huan Chiu; Tsorng-Whay Pan; Roland Glowinski A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids, Comput. Fluids, Volume 172 (2018), pp. 661-673 | DOI | MR | Zbl

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