Comptes Rendus Mécanique (CRM)

Michele Girfoglio

Annalisa Quaini

Gianluigi Rozza

A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations

Grégoire Allaire

Jean-Michel Coron

Vivette Girault

Comptes Rendus
Mécanique
Grégoire Allaire, Jean-Michel Coron and Vivette Girault
Foreword to the special issue of Comptes Rendus Mécanique in the memory of
Roland Glowinski
Volume 351, Special Issue S1 (2023), p. 1-3
Online since: 26 January 2024
Part of Special Issue: The scientific legacy of Roland Glowinski
Guest editors: Grégoire Allaire (CMAP, Ecole Polytechnique, Institut Polytechnique de
Paris, Palaiseau, France),
Jean-Michel Coron (Laboratoire Jacques-Louis Lions, Sorbonne Université)
and Vivette Girault (Laboratoire Jacques-Louis Lions, Sorbonne Université)
https://doi.org/10.5802/crmeca.238
This article is licensed under the
Creative Commons Attribution 4.0 International License.
http://creativecommons.org/licenses/by/4.0/
C EN T R E
MER S ENN E
The Comptes Rendus. Mécanique are a member of the
Mersenne Center for open scientific publishing
www.centre-mersenne.org — e-ISSN : 1873-7234
Comptes Rendus
Mécanique
2023, Vol. 351, Special Issue S1, p. 1-3
https://doi.org/10.5802/crmeca.238
The scientific legacy of Roland Glowinski / L’héritage scientifique
de Roland Glowinski
Foreword to the special issue of Comptes
Rendus Mécanique in the memory of Roland
Glowinski
Avant-propos du numéro spécial des Comptes Rendus
Mécanique à la mémoire de Roland Glowinski
Grégoire Allaire ∗,a, Jean-Michel Coron b and Vivette Girault b
a CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
b Laboratoire Jacques-Louis Lions, Sorbonne Université
E-mails: gregoire.allaire@polytechnique.fr (G. Allaire), jean.m.coron@gmail.com
(J.-M. Coron), vivette.girault@sorbonne-universite.fr (V. Girault)
Manuscript received and accepted 11 January 2024.
Our dear colleague, Roland Glowinski, passed away on January 26, 2022, at the age of 84. He
was not only a visionary applied mathematician, famous around the world for his numerical
methods and algorithms, but also a wonderful friend. He was a member of the French Academy
of Sciences and, as such, a member of the editorial board of its journal, Comptes Rendus
Mécanique. The present special issue of the Comptes Rendus Mécanique is dedicated to honor
his memory, his outstanding work and profound impact on our community. The contributions
of this special issue are close to the favorite topics of Roland Glowinski: discretization of linear
and non-linear partial differential equations, complex fluids, scientific computing, control and
optimization algorithms, domain decomposition, operator splitting, modelling and simulation
for mechanical, physical, biological and engineering applications.
Roland Glowinski was an alumni of the Ecole Polytechnique in Paris and held a PhD in
mathematics from Paris VI University (nowadays Sorbonne University), prepared under the
supervision of Jacques-Louis Lions. After an early career at the French Television Network, he
was appointed professor at Paris VI University in 1970 and took over in 1976 the direction of the
scientific computing laboratory of IRIA (now INRIA). He quickly became known worldwide as
the best designer of algorithms for continuum mechanics problems; it earned him numerous
appointments as scientific advisor including a position as director of CERFACS in 1992-1994. In
1985 he moved to the University of Houston where he was a Cullen Professor of Mathematics.
He was an adjunct professor at several universities, including Jyvaskyla University in Finland
∗Corresponding author.
ISSN (electronic) : 1873-7234 https://comptes-rendus.academie-sciences.fr/mecanique/
2 Grégoire Allaire, Jean-Michel Coron and Vivette Girault
Figure 1. Roland Glowinski (Credit: Chris Watts, University of Houston)
and Rice University in Houston. Roland Glowinski was a prolific writer, author of six books
and around 380 articles. He received many awards and honors, including the Seymour Cray
prize, Marcel Dassault prize, the W.T. and Idalia Reid prize, and his membership in the French
Academy of Sciences, the French Academy of Technology and the Academia Europaea. The
spectrum of Roland’s scientific contributions is vast and intricate. Let us try to describe his main
contributions.
His seminal work on domain decomposition algorithms stands as a testament to his pioneer-
ing spirit. He was the first to understand the links between Schwarz algorithms and Lagrange
multipliers and thus propose methods without domain overlap. He is also the first to use the
formalism of mixed formulations for these problems. He created the famous annual conference
Domain Decomposition Methods. He earned the Cray prize in 1988 for this work. Roland was
also instrumental in the development of efficient algorithms for fictitious domain methods in
Lagrangian formulation. Following earlier ideas from the Russian school he proposed an appro-
priate functional framework which allowed him to analyze a convenient finite element discretiza-
tion method to deal with time-dependent geometry problems on a single fixed mesh and prove
error estimates.
In the realm of fluid dynamics, Roland’s ideas led to the development of robust precondi-
tioners for the Navier–Stokes equations, discretized by finite element methods. In his book on
numerical methods for non-linear variational problems Roland Glowinski proposed iterative al-
gorithms (conjugated gradients) with preconditioning for the generalized Stokes problem, thus
opening the way to modern intensive computing as it is practiced today. Roland was the first to
Grégoire Allaire, Jean-Michel Coron and Vivette Girault 3
give a mixed formulation for the biharmonic problem, relying merely on low degree finite ele-
ments, which were at the time the fastest methods for calculating viscous flows. These methods
were implemented at Dassault Aviation and were a model of successful scientific cooperation.
In this same cooperation Roland studied transonic flows for a potential compressible fluid and
proposed one of the first discrete formulations of the entropy condition.
Variational inequalities were a favorite topic of Roland Glowinski who devised several funda-
mental algorithms for their numerical solution. In particular, he advocated the augmented La-
grangian formulation which turned out to be extremely efficient for various applications, includ-
ing free boundary problems, non-linear structural mechanics and fluid mechanics. His work was
extremely innovative in several respects. For example, he proposed a primal-dual iterative algo-
rithm, known as Alternating Direction Method of Multipliers, which became extremely popular,
not only among numerical analysts but also in other communities like optimization, imaging and
learning. One striking application was the numerical simulation of thousands of solid balls sus-
pended in a viscous fluid, discretized in a 3-d unstructured mesh method, still using a Lagrangian
formulation.
Finally, Roland Glowinski made ground-breaking contributions in the numerical methods
for the controllability of hyperbolic problems. Following the lead of Jacques-Louis Lions who
introduced the Hilbert Uniqueness Method, he was the first to point out that standard numerical
schemes do not converge for the controllability problem. Indeed, they do not provide a control
allowing to connect a given initial state to a desired target. Roland gave the explanation (the
appearance in the numerical scheme of spurious high frequencies, which interfere so that the
group velocity of the discrete model may vanish or be small) and powerful remedies (a two-grid
approach and filtering methods). Not only did he solve this hard problem but he also did it with
great elegance and mastery, revealing a deep analogy with the mixed finite element methods for
the Stokes system, a topic in which he was also a pioneer.
We had the great privilege of collaborating with Roland Glowinski, and we are very grateful
to have known him and learned so much from him. This special issue of the Comptes Rendus
Mécanique is a token of appreciation and admiration.


Foreword to the special issue of Comptes Rendus Mécanique in the memory of Roland Glowinski

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Jukka Räbinä

Tuomo Rossi

Time-harmonic electromagnetics with exact controllability and discrete exterior calculus

Denis Beaudouin

L’avènement de la science météorologique du XVII$^{\protect \mathrm{e}}$ au XIX$^{\protect \mathrm{e}}$ siècle

Thierry Fusco

Optique adaptative et telescopes geants

Fatima L. Mota

Luis M. Fabietti

Nathalie Bergeon

Rohit Trivedi

The effect of confinement on thermal convection and longitudinal macrosegregation in directionally solidified dilute succinonitrile–camphor alloy

Martin Genet

Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking

Iheb Chouikh

Chokri Bouraoui

A fatigue-reliability approach using ultrasonic non-destructive inspection

Viktor Kosin

Amélie Fau

Clément Jailin

Benjamin Smaniotto

Thomas Wick

François Hild

A projection-based approach to extend digital volume correlation for 4D spacetime measurements

Gérard Iooss

Convection de Bénard–Rayleigh. Cas libre-libre

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