Congrès pour honorer la mémoire de Roland Glowinski
58 juillet 2022, Sorbonne Université, place Jussieu, Paris 5ème
Programme
PROGRAM
Tous les exposés auront lieu
Amphi 44, Campus Pierre et Marie Curie, Sorbonne Université, place Jussieu, Paris 5ème (voir plan)
TUESDAY AFTERNOON, JULY 5, 2022

13:45  14:00
Greeting time

14:00  14:40
Opening session

14:45  15:25
PierreLouis Lions (Collège de France, Paris, France)
Solving numerically (some) PDE's in infinite dimensions via (artificial) neural nets
Abstract:
Joint work with Yves Achdou and JeanMichel Lasry.

15:30  16:00
Coffee break

16:00  16:40
Annalisa Quaini (University of Houston, USA)
Towards the computational design of smart nanocarriers
Abstract:
Membrane fusion is a potentially efficient strategy for the delivery of macromolecular therapeutics into the cell cytoplasm. However, existing nanocarriers formulated to induce membrane fusion suffer from a key limitation: the high concentrations of fusogenic lipids needed to cross cellular membrane barriers lead to toxicity in vivo. To overcome this limitation, we are developing in silico models that will explore the use of membrane phase separation to achieve efficient membrane fusion with minimal concentrations of fusioninducing lipids and therefore reduced toxicity. The models we consider are formulated in terms of partial differential equations posed on evolving surfaces. For the numerical solution, we use a fully Eulerian hybrid (finite difference in time and trace finite element in space) discretization method. The method avoids any triangulation of the surface and uses a surfaceindependent background mesh to discretize the problem. Thus, our method is capable of handling problems posed on implicitly defined surfaces and surfaces undergoing strong deformations and topological transitions.

16:45  17:25
Thomas Ayral (Atos Quantum Lab, Les ClayessousBois, France)
Quantum computer(s): which use cases and applications, and for which platforms?
Abstract:
In this talk, I will present the perspectives of quantum computing in terms of concrete use cases and applications. I will give an overview of the current and midterm capabilities of the different types of processors available, starting from applications close to quantum physics to use cases closer to applied mathematics.
WEDNESDAY MORNING, JULY 6, 2022

09:00  09:15
Greeting time

09:15  09:55
Bertrand Maury (Université ParisSaclay, Orsay, France)
Discrete Laplace operators and crowd motion modeling
Abstract:
The Laplace operator has played a crucial role in most of Roland Glowinski's contributions, together with duality approaches. In the continuation of a collaboration with Roland in the late 90's on fluid / rigid grain mixtures, I shall present a more recent approach to model the motion of dense crowds. The core of the model relies on a pressurelike Lagrange multiplier that handles the nonoverlapping constraint between individuals. Like in the standard Darcy context, eliminating the velocity leads to some sort of Poisson problem on this pressure. Yet, the underlying discrete Laplace operator is different from the one that is obtained from the discretization of the usual Laplacian, it lacks some expected properties, like the maximum principle, and we will illustrate how this defect induces some paradoxical phenomena, like the capacity drop, or the socalled Faster is Slower effect (in the context of building evacuations, an increase in the eagerness of people to egress may decrease the process efficiency).

10:00  10:30
Coffee break

10:30  11:10
Virginie Ehrlacher (Ecole Nationale des Ponts et Chaussées, Marne la Vallée, & Inria de Paris, France)
Moment constrained optimal transport problem: application to quantum chemistry
Abstract:
This work is motivated by applications in quantum chemistry, for the computation of the electronic structure of molecules. The socalled Density Functional Theory (DFT) is a very powerful framework which enables to carry out such computations. Within this theory, a key role is played by the socalled LevyLieb functional, the computation of which remains unaffordable for systems with a large number of electrons. This is why a full zoology of approximate DFT models, relying on the use of various approximations of this LevyLieb functional, have been proposed in the chemistry literature. In this talk, a specific focus will be made on one particular DFT model which makes use of the socalled semiclassical limit of the LévyLieb functional, which happens to read as a symmetric multimarginal optimal transport problem with Coulomb cost, the number of marginals being equal to the number of electrons in the system. In this talk, I will present recent results about a new approach for the resolution of multimarginal optimal transport problems which consists in relaxing the marginal constraints into a finite number of moment constraints. Using Tchakhaloff's theorem, it is possible to prove the existence of minimizers of this relaxed problem and characterize them as discrete measures charging a number of points which scales independently of the number of electrons. This opens the way towards the design of new numerical schemes which can hopefully circumvent the curse of dimensionality for this problem. Preliminary numerical results will be presented.

11:15  11:55
Enrique Zuazua (FriedrichAlexander Universität, Erlangen, Germany)
Glowinski: Control, Numerics and beyond
Abstract:
Roland Glowinski made several contributions that revolutionized the field of numerical analysis and scientific computing for the Control of Partial Differential Equations and other related topics such as inverse problems and dispersive PDEs. This arose, to a large extent, along the longstanding collaboration that he developed in this area with JacquesLouis Lions.
In this lecture we briefly present two of his contributions, describing the posterior impact they had. One of them refers to the unexpected violently oscillatory nature of the controls for heat equations he discovered numerically. The other one, to his fundamental remark on the need of employing bigrid methods to exclude the high frequency spurious numerical solutions that are an impediment for the convergence of numerical methods for the control of wave processes.
WEDNESDAY AFTERNOON AND EVENING, JULY 6, 2022

13:45  14:00
Greeting time

14:00  14:40
Frédéric Hecht (Sorbonne Université & Inria de Paris, France)
About FreeFEM
Abstract:
FreeFEM is a software for numerically solving partial differential equations (PDEs) in volumes, on curves or on surfaces of R2 or R3. It is based on variational formulations, on the finite element method, and on boundary element methods.
When using FreeFEM, the user writes a program in a high level domainspecific language (DSL), or in other words a FreeFEM script which is close to the mathematical formulation of the PDE.
The DSL provides the necessary linear algebra, linear and bilinear forms, interpolation operators, and so on, and then computes the solution.
The DSL also contains an extension of some part of C++.
FreeFEM is a free software and open source. It can be used on Mac, Unix and Windows architecture, and also in parallel with MPI.
Pierre Jolivet has solved a problem with 22 · 109 unknowns on 12000 processors.
FreeFEM can even be used inside a browser on smartphones, pads, and so on (thanks to A. Le Hyaric, see
https://www.ljll.math.upmc.fr/lehyaric/ffjs/).
The success of FreeFEM can be measured by its large number of users and its longevity: the first line of code was written by Olivier Pironneau in pascal on the first Apple Macintosh in 1985.
It is interesting to try to understand why no one has succeeded since in writing a more powerful tool to solve PDEs
(compare with matlab pdetoolbox, pypde, comsol, fenics, on wikipedia:
List of finite_element software_packages), and why,
forty years later, it is not a depreciated product.
A basic equation : The FreeFEM April fish (april 2004, Houston)
Figure 1: Solution of Poisson equation: −∆u = 1 in the fish, u = 2 on the eyes, ∂n u = 0 on the exterior boundary
A more realistic HPC example is the Microwave Imaging of the brain intending to discriminate in real time between ischemic and hemorrhagic Cerebrovascular Accidents (CVA)
(2015, with V. Dolean, P. Jolivet, F. Nataf, and P.H. Tournier). The image is obtained by solving an inverse Maxwell problem to the build of electric permittivity of the brain.
The result is obtained in less than 5 minutes on HPC computer with 500 processors.
Figure 2: Evolution of a CVA, exact sections of a 3D image and their reconstructed images, 10% noise

14:45  15:25
Thierry Poinsot (MFT, CNRS & CERFACS, Toulouse, France)
Simulation numérique : du covid à l'hydrogène
Abstract:
Cette présentation décrira des résultats liés à la simulation numérique en mécanique des fluides impulsée au CERFACS par Roland Glowinski en se concentrant sur des thèmes d'actualité : la propagation de virus, la sécurité des trains à grande vitesse, l'allumage des moteurs de fusées et la combustion de l'hydrogène. On insistera sur l'apport de la simulation haute fidélité sur des ordinateurs massivement parallèles pour analyser les mécanismes contrôlant ces applications et sur la vision apportée par Roland Glowinski dans ce domaine.

15:30  16:00
Coffee break

16:00  16:40
Bruno Després (Sorbonne Université, Paris, France)
Numerical computation by moment methods of solutions of Vlasov equations with magnetic field
Abstract:
The Vlasov equations with magnetic field are central in problems of fusion plasmas, for example in Tokamaks such as ITER. The formidable numerical difficulty is that one should solve transport equations in dimension 3 + 3 while taking into account the presence of the strong magnetic field which ensures the confinement. A method of anisotropic moments with Hermite functions will be presented. The strong field limit shows an alternative to gyrokinetic models. Numerical simulations will allow one to understand the challenges in terms of scientific computation.

16:45  17:25
Mary Wheeler (The University of Texas at Austin, USA)
Multiphysics modeling of CO2 and hydrogen storage in porous media
Abstract:
This presentation is dedicated to Professor Roland Glowinski my visionary friend who taught me to address the big picture.
The interactions of fluid with mineral surfaces can alter interfacial and confined environments with different microstructure, dynamic, and thermodynamic behavior conditions. The injection of gases such as CO2 or H2 will disturb the equilibrium between the reservoir brine and minerals potentially resulting in mineral dissolution or precipitation and consequent changes in rock porosity and permeability. The success of subsurface gas storage depends on our understanding of the rock, mineral compositions, fluid properties, and mineralfluid interactions under in situ conditions. The chemical reactions that occur will depend on the minerals present, the compositions of the formation brine and injected gas, and the reservoir temperature and pressure.
The reactions between H2, brine, and rock system may alter the petrophysical and mechanical properties of the rock. Significant change in permeability and porosity can be attributed to the dissolution of these minerals into hydrogen rich brine. The impact is on the performance of the whole reservoir, while the crucial processes happen on the length scale of pores or nanopores. It is thus crucial to understand the pore scale processes well to assess implications for the whole reservoir. To date there is limited experience with largescale geological hydrogen storage. and there are several important aspects that need to be carefully studied including multiphase thermal reactive flow and transport in fractured porous media to understand the impacts of hydrogen reactions with the subsurface fluid(s) and minerals Similar issues arise in geothermal systems.
To address these multiphysics and multiscale simulations requires preservation of physics, chemistry and biology across spatial and temporal scales. In addition, these algorithms must be able to handle efficiently high performance computing, adaptive mesh refinement and highly nonlinear algebraic systems with rough coefficients.. Additional computational issues include data extraction, optimization, uncertainty quantification and machine learning. In this presentation we discuss two high fidelity approaches that have been introduced for unconventional reservoirs that show promise for modeling reservoir energy production: a posteriori error estimation for coupling of multiphase and geomechanics and space time modeling for multiphase flow

18:00  18:45
Homage to Roland Glowinski

19:00  22:00
Reception
Patio 2515 level SB
(registration to the Conference is mandatory to participate)
THURSDAY MORNING, JULY 7, 2022

09:00  09:15
Greeting time

09:15  09:55
Endre Süli (University of Oxford, UK)
Discrete De GiorgiNashMoser theory and the finite element approximation of chemically reacting nonNewtonian fluids
Abstract:
NonNewtonian fluids play an important role in science and engineering, and the mathematical analysis and approximation of models of nonNewtonian fluids has been an active field of research. Some of the groundbreaking early contributions include Roland Glowinski's work with Jean Céa (1972) on the numerical approximation of viscoplastic (Bingham) fluids. Glowinski's subsequent papers with Americo Marrocco, published in 1974 and 1975, were some of the earliest contributions to the finite element approximation of pLaplace type nonlinear elliptic equations and associated convex energyminimization problems for functionals with pgrowth of the kind that appear in models of steady incompressible quasiNewtonian fluids. Glowinski's work over the past five decades on the Bingham model involved a range of new ideas, including domain decomposition and operator splitting methods, the analysis of qualitative properties of Bingham flows, particularly largetime stabilization and, as recently as in 2021, the numerical solution of the BinghamBratuGelfand problem, a nonsmooth nonlinear eigenvalue problem associated with the total variation integral that includes an additional exponential nonlinearity.
This talk is concerned with the convergence analysis of finite element methods for the approximate solution of a system of nonlinear elliptic partial differential equations that arise in models of chemically reacting viscous incompressible nonNewtonian fluids, such as the synovial fluid found in the cavities of synovial joints. The synovial fluid consists of an ultra filtrate of blood plasma that contains hyaluronic acid, whose concentration influences the shearthinning property and helps to maintain a high viscosity; its function is to reduce friction during movement. The shearstress appearing in the model involves a powerlaw type nonlinearity, where, instead of being a fixed constant, the power lawexponent is a function of a spatially varying nonnegative concentration function, which, in turn, solves a nonlinear convectiondiffusion equation. In order to prove the convergence of the sequence of finite element approximations to a solution of this coupled system of nonlinear PDEs, a uniform Hölder norm bound needs to be derived for the sequence of finite element approximations to the concentration in a setting, where the diffusion coefficient in the convectiondiffusion equation satisfied by the concentration is merely an L^infty function. This necessitates the development of a finite element counterpart of the De GiorgiNashMoser theory. Motivated by an early paper by Aguilera and Caffarelli (1986) in the simpler setting of Laplace's equation, we derive such uniform Hölder norm bounds on the sequence of continuous piecewise linear finite element approximations to the concentration. We then use these to deduce the convergence of the sequence of finite element approximations to a weak solution of the coupled system of nonlinear PDEs under consideration.
The talk is based on joint work with Lars Diening (Bielefeld) and Toni Scharle (Oxford).

10:00  10:30
Coffee break

10:30  11:10
Xiaoming Yuan (The University of Hong Kong, China)
Balanced augmented Lagrangian method
Abstract:
The augmented Lagrangian method (ALM) is classic for solving the canonical convex minimization model with linear constraints. It has inspired various important algorithms including the wellknown alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco in 1975. At each iteration, the ALM needs to solve a subproblem in which the objective function and the coefficient matrix in the constraint should be considered simultaneously. We propose a balanced ALM, where subproblems handle the objective function and the coefficient matrix separately. The balanced ALM has two parameters, while positiveness is their only restriction. When the model has separable structure, various splitting versions of the balanced ALM can be easily designed whose subproblems are even easier than those of the ADMM. The balanced ALM and its splitting versions are particularly efficient for a series of sparsity recovery problems arising in compressive sensing and image processing.

11:15  11:55
Laura Grigori (Sorbonne Université & Inria de Paris, France)
Randomization techniques for numerical linear algebra
Abstract:
In this talk we discuss randomization techniques for solving large scale linear algebra problems. We focus in particular on solving
linear systems of equations and eigenvalue problems and we present a randomized GramSchmidt process for orthogonalizing a set of vectors. We discuss its efficiency and its numerical stability while also using mixed precision. Its usage for solving linear systems of equations and eigenvalue problems is further presented. In the last part of the talk we introduce a robust preconditioner that relies on multilevel domain decomposition techniques and that allows us to accelerate the convergence of iterative methods for linear systems of equations.

12:00  12:15
JeanFrédéric Gerbeau
Roland Glowinski and INRIA
THURSDAY AFTERNOON, JULY 7, 2022

13:45  14:00
Greeting time

14:00  14:40
Tuomo Rossi (Jyväskylän yliopisto, Finland)
On the numerical simulation of BoseEinstein condensates
Abstract:
The quantized vortices in BoseEinstein condensates are modeled by the GrossPitaevskii equation whose numerical time integration is instrumental in the physics studies of such systems. In this talk, we consider a reliable numerical method and its efficient GPUaccelerated implementation for the time integration of the three dimensional GrossPitaevskii equation. The method is based on discrete exterior calculus (DEC) which allows us the usage of more versatile spatial discretization than traditional finite difference and spectral methods are applicable to. We pay attention to the computational performance optimizations of the GPU implementation and measure speedups of up to 152fold when compared to a reference CPU implementation. We parallelize the implementation further to multiple GPUs and show that 92% of the computation time can fully utilize the additional resources. An extension to vectorvalued GrossPitaevskii equation is also considered for the simulation of dynamics of spin1 BoseEinstein condensates. We simulate the creation and decay dynamics of a half quantum vortex ring. We observe the DECmethod to improve both accuracy and computational performance compared to the widely used Fourier spectral method.
The results presented in this lecture are joint work with Markus Kivioja and Sanna Mönkölä.

14:45  15:25
Céline Grandmont (Sorbonne Université & Inria de Paris, France)
Mathematical and numerical analysis of a linearized poromechanical model for incompressible and nearly incompressible media. Application to microcirculation
Abstract:
Most living tissues can be modeled by poromechanical systems in which an elastic skeleton is perfused by a fluid.
In this talk we will analyze a linearized version of the model proposed in [3] and already partially analyzed in [1], [2]. One key feature of this model is that it satisfies an energy balance. After having introduced the fully non linear coupled system we will prove the existence of solutions in the cases of a skeleton which is viscoelastic or elastic, and compressible or incompressible. When there is no dissipation in the media we deal with a parabolichyperbolic coupled system. Moreover, in the incompressible case, we end up with a standard constraint on mixture velocity. The study of the incompressibility limit is crucial when considering living tissues which are nearly incompressible and for developing robust schemes at the limit. Then we present a splitting scheme adapted to the coupled problem, completed with numerical simulations. In particular this model is used to reproduce microcirculation experiments (perfusion of artificial microvessels) obtained by Claire A. Dessalles. These results have been obtained in collaboration with Mathieu Barré and Philippe Moireau (INRIA – LMS, Ecole Polytechnique, CNRS – Institut Polytechnique de Paris).
[1] N. Barnafi, P. Zunino, L. Dedè, A. Quarteroni. Mathematical analysis and numerical approximation of a general linearized porohyperelastic model. CAMWA, 2020.
[2] B. Burtschell, P. Moireau, D. Chapelle. Numerical analysis for an energystable total discretization of a poromechanics model with infsup stability. Acta Mathematicae Applicatae Sinica, English Series, 2019.
[3] D. Chapelle, P. Moireau. General coupling of porous flows and hyperelastic formulations: from thermodynamics principles to energy balance and compatible time schemes. European J. of Mechanics, B/Fluids, 2014.

15:30  16:00
Coffee break

16:00  16:40
Enrique FernándezCara (Universidad de Sevilla, Spain)
Glowinski, splitting and control
Abstract:
This talk is devoted to recall several contributions by R. Glowinski to the numerical solution and control of PDE's. First, I will review several splitting methods primarily used to solve NavierStokes equations. Then, I will recall important contributions by Glowinski, J.L. Lions and others in the context of numerical controllability. In particular, I will mention some work dealing with biobjective control problems. In the final part of the talk, I will describe briefly several advances related to these issues obtained in the last decades.

16:45  17:25
Katharina Schratz (Sorbonne Université, Paris, France)
Resonances as a computational tool
Abstract:
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretisation techniques such as discretising the variation of constants formula (e.g., exponential integrators) or splitting the full equation into a series of simpler subproblems (e.g., splitting methods). In many situations these classical schemes allow a precise and efficient approximation. This, however, drastically changes whenever nonsmooth phenomena enter the scene such as for problems at lowregularity and/or with high oscillations. Classical schemes fail indeed to capture the oscillatory nature of the solution, a fact that leads to severe instabilities and loss of convergence. In this talk I present a new class of resonance based schemes. The key idea in the construction of these new schemes is to tackle and deeply embed the underlying structure of resonances into the numerical discretisation. As in the continuous case, these resonances are central to structure preservation and provide the new schemes with strong geometric properties at low regularity.
I will present the key idea behind resonances as a computational tool, give an outlook on their high order counterpart (via decorated tree series inspired by regularity structures) and extension to a more general class of nonlinear partial differential equations (such as NavierStokes).
FRIDAY MORNING, JULY 8, 2022

09:00  09:15
Greeting time

09:15  09:55
Annalisa Buffa (Ecole Polytechnique Fédérale de Lausanne, Switzerland)
Multiscale design optimization of lattice structures
Abstract:
Using spline compositions leads to a convenient approach for the geometric modeling of (boundaryconforming) lattice structures. With this approach, the global (macro) geometry of the structure is represented employing a standard spline model. Then, reference micromodels are embedded into the macroelements associated to the global geometry by the use of functional compositions.
Interestingly, such multiscale geometric models are suitable for numerical simulation. This means that one unique model can be employed during design optimization. However, there is a need for fast analysis methods in order to reduce the computational costs associated to these highfidelity and highorder geometric models. To do so, we assemble the finite element operators with a multiscale procedure and we built a specific solver based on domain decomposition methods. During both the assembly and the resolution, we exploit the similarities between these subcells via a reduced order modelling approach.
As a result, we end up with fast analysis methods that can be naturally integrated in a design loop. Finally, we perform several design optimization examples of innovative lattice structures in order to show the viability, the performance, and the great flexibility of the developed framework.
These results are joint work with P. Antolin and T. Hirschler.

10:00  10:30
Coffee break

10:30  11:10
Aline LefebvreLepot (Ecole Polytechnique, Palaiseau, France)
Numerical simulation of suspensions and Boundary Element Method
Abstract:
Suspensions composed of macroscopic nonbrownian particles immersed in a viscous fluid are found in many fields, including in everyday life. These include industry (food and cosmetics, concrete, reinforced plastics, paper pulp, etc.), nature (silting of rivers, transport of sediments, sandy coasts, lava, etc.), biology (blood tests, etc.) and even ecological concerns (wastewater treatment, etc.). This wide range of applications has led to a large amount of research. From a numerical point of view, the simulation of such systems amounts to solving the Stokes equations coupled to the rigid motion of the particles.
In this talk, we will show how this can be achieved using a Boundary Element Method (BEM). It should be noted that numerical simulation of suspensions has some features that are not usual in classical application domains of BEMs (such as waves or electromagnetism). The adaptation of existing tools to this new application domain is an active area of research. One of the difficulties is due to the fact that the system consists of several moving solids which may be close to each other and for which the distance is not controlled. In this talk, fast and accurate methods for solving such Stokes problems will be presented, taking into account close inclusions.

11:15  11:55
Patrick Le Tallec (Ecole Polytechnique, Palaiseau, France)
From domain decomposition to model reduction for large nonlinear structures
Abstract:
The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions.
The numerical tests indicate that considerable cost reduction (a factor of 20 to 1000) can be achieved while preserving engineering accuracy.
These results are joint work with Bertrand Leturcq.
Modifié Ven 10 jui 2022 21:44:20 CEST par fh v11