Publications

2026

• Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces
  
  • Urrea Fernanda
  • Treumún Ernesto
  , 2026. We study a state-constrained Bolza optimal control problem governed by a non-local continuity equation in the Wasserstein space $\sP_2(\R^d)$. We develop a Pontryagin maximum principle for these problems in which both the cost functionals and the constraints are only locally Lipschitz, and the initial measure does not necessarily have compact support. To derive the main result, we introduce a notion of a Clarke-type deterministic subdifferential over $\sP_2(\R^d)$. The proof of the main result combines a careful adaptation of the Lasry-Lions regularization to the Wasserstein space coupled with stability results of the Clarke subdifferential that allow us to recover the first-order information. We also show that, for functionals convex along plans, this subdifferential admits a global supporting characterization and provides a first-order characterization of global minimizers.
• Optimal Control Under Signal Temporal Logic Constraints: A Robust Reformulation via Augmented Dynamics
  
  • Lai En
  • Bonalli Riccardo
  • Girard Antoine
  • Jean Frédéric
  , 2026. This work presents a novel approach for solving optimal control problems under Signal Temporal Logic (STL) constraints. The proposed method reformulates the original problem as a classical continuous-time optimal control problem by augmenting the system dynamics with auxiliary variables that encode STL satisfaction through their evolution and boundary conditions. Introducing a robustness parameter, we also establish the convergence of the reformulated problem to the original one as this parameter tends to zero. The proposed method applies to a fragment of STL, which excludes nestings between the until and release operators, but still captures a broad class of STL specifications used in practice. Numerical simulations are realized to demonstrate the feasibility of our method, highlighting its potential for practical applications.
• Fast SDP certification of neural networks : towards large multi-class datasets
  
  • Boyer Margot
  • Rambour Clément
  • Alès Zacharie
  • Lambert Amélie
  , 2026. <div><p>We present a new quadratic model for the certification problem in adversarial robustness, which simultaneously accounts for all possible target classes. Building on this model, we propose a novel semidefinite programming (SDP) relaxation for incomplete verification. A key advantage of our approach is that it certifies robustness in a single optimization, avoiding the need for a separate resolution per class. This yields a significant computational speed-up and enables scalability to large datasets with many classes. To further improve efficiency, we also propose an effective pruning strategy of active neurons, thus reducing the problem dimensionality and accelerating convergence.</p></div>
• Accelerating the Method of Reflections with Domain Decomposition techniques for Boundary Integral Equations in Multiple Scattering
  
  • Chaillat Stéphanie
  • Darbas Marion
  • Gander Martin J
  • Halpern Laurence
  BIT Numerical Mathematics, Springer Verlag, 2026. The Method of Reflections was historically introduced to obtain approximate solu-tions as series expansions for the motion of particles in suspension. It can however equally well be used for solving multiple scattering problems numerically. We show for Helmholtz multiple scattering problems that the Method of Reflections, whether applied in its alternating or parallel version, suffers from convergence problems when scatterers are close. We use boundary integral equations to formulate the methods, and then identify them as algebraic Schwarz methods, thereby interpreting them as boundary domain decomposition techniques. This connection allows us to introduce remedies such as overlap (which can be partial, covering only the illuminating region of the obstacles) and coarse spaces from domain decomposition into the Method of Reflections. This leads to substantially accelerated variants, and also naturally makes them suitable preconditioners for GMRES. These new approaches are particularly efficient for closeby obstacles. Moreover, numerical experiments show that the number of iterations remains robust with respect to the wavenumber. (10.1007/s10543-026-01151-7)
  DOI : 10.1007/s10543-026-01151-7
• A note on pliability and the openness of the multiexponential map in Carnot groups
  
  • Jean Frédéric
  • Sigalotti Mario
  • Socionovo Alessandro
  Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2026. In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and Whitney extension properties. In this note we compare some of these notions. (10.3842/SIGMA.2026.078)
  DOI : 10.3842/SIGMA.2026.078
• Local Multiple Traces Formulation for Transmission Problems in Linear Elasticity
  
  • Chaillat Stéphanie
  • Darbas Marion
  • Escapil-Inchauspé Paul
  • Jerez-Hanckes Carlos
  Computers & Mathematics with Applications, Elsevier, 2026, 220 (15). We investigate the use of the local Multiple Trace Formulation (MTF) in solving time-harmonic elastic wave transmission problems. Originally devised for heterogeneous acoustic media, MTF recasts the boundary value problem as a well-posed system of first-kind boundary integral equations, naturally amenable to parallelization and preconditioning. The formulation takes independent displacement and traction unknowns per subdomain, enforces Calderón identities locally, and imposes transmission conditions weakly across interfaces. We restrict our analysis to single homogeneous scatterers, representing a foundational step toward the application of MTF techniques in heterogeneous elasticity transmission problems. For the sake of clarity, all derivations in the one-dimensional setting are carried out explicitly, with illustrative examples provided in two dimensions. We analyze the effects of frequency and material contrast on the convergence of the GMRES iterative solver. Finally, we present preliminary results for an elastic Calderón preconditioner and discuss its potential to further accelerate iterative solvers. (10.1016/j.camwa.2026.08.005)
  DOI : 10.1016/j.camwa.2026.08.005
• Tangential and normal traces for extension domains with non-Lipschitz boundaries
  
  • Cervera Romain
  • Ciarlet Patrick
  • Rozanova-Pierrat Anna
  • Teplyaev Alexander
  , 2026. We generalize the classical vector-valued tangential and normal trace theory on Lipschitz domains to the setting of non-Lipschitz $H^1$-extension domains, which includes domains with fractal boundaries such as the Koch snowflake. We define and study these operators based on the surjectivity of the trace operator for elements of $H^1(\Omega)$ and the Hilbert structure of the associated trace space. The normal trace operator is defined on $\Hdiv$ in $\mathbb{R}^n$. A generalized Stokes formula allows us to introduce the tangential trace operator on $\Hcurl$ and $\Hc^1(\Omega)$ in two and three dimensions. Following the approach of Buffa, Costabel and Sheen (2002) for Lipschitz domains, we define two abstract tangential boundary spaces as images of these trace operators, establish their Hilbert structure, and construct an abstract rotation operator linking them, in place of the geometric rotation based on the normal vector. We also extend Costabel's (1991) coercive bilinear form approach for Maxwell's equations to non-Lipschitz domains, yielding a theory that supports the treatment of the Hodge-Dirac operator and Green's formulas and enables the solution of boundary-value problems for the $\rotv \rotv +1$ operator within the $H^1$-extension domains framework.
• Exponential twist of probability measures: drift correction in term of a generalized gradient
  
  • Bourdais Thibaut
  • Oudjane Nadia
  • Russo Francesco
  Stochastic Processes and their Applications, Elsevier, 2026. In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure $\P$. This type of transformation naturally appears in variational representation formulae originating from the theory of large deviations and can be interpreted in some cases, as the solution of a specific stochastic control problem. Under a very general Markovian assumption on $\P$, we fully characterize the exponential twist probability measure as the solution of a martingale problem and prove that it inherits the Markov property of the reference measure. The ''generator'' of the martingale problem shows a drift depending on a {\it generalized gradient} of some suitable {\it value function} $v$. The analysis focuses on the fact that any Markovian probability measure fulfills an {\it intrinsic martingale problem} for which no uniqueness is required. (10.1016/j.spa.2026.105064)
  DOI : 10.1016/j.spa.2026.105064
• A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems
  
  • Rappaport Ari
  • Chaumont-Frelet Théophile
  • Modave Axel
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2026, 48 (4), pp.B629-B650. The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at the element interfaces and the physical unknowns inside the elements are eliminated, resulting in a hybridized system with favorable properties for fast iterative solution. In this paper, we extend the CHDG method, initially studied for the Helmholtz equation, to the time-harmonic Maxwell equations. We prove that the local problems stemming from hybridization are well-posed and that the fixed-point iteration naturally associated to the hybridized system is contractive. We propose a 3D implementation with a discrete scheme based on nodal basis functions. The resulting solver and different iterative strategies are studied with several numerical examples using a high-performance parallel C++ code. (10.1137/25M1756818)
  DOI : 10.1137/25M1756818
• Multi-domain FEM-BEM coupling with several impenetrable obstacles
  
  • Boisneault Antonin
  • Bonazzoli Marcella
  • Claeys Xavier
  • Marchand Pierre
  , 2026. In a recent paper we have analyzed a new formulation of the coupling of finite and boundary element methods (FEM-BEM) for Helmholtz problems, involving several heterogeneous bounded subdomains and one homogeneous unbounded subdomain. This formulation, called Generalized Optimized Schwarz Method (GOSM), is substructured, that is, its unknowns are associated with the subdomains interfaces. To derive the GOSM, the first step was to prove that a solution to the Helmholtz problem satisfies a specific multi-domain variational formulation, which involves one operator for each subdomain, each operator being independent of the others. In the present contribution, we design a variational formulation of that type for a more general geometrical and material configuration: several heterogeneous bounded subdomains, impenetrable obstacles and homogeneous subdomains are allowed. Note that, like in our recent paper, we assume that only one subdomain is unbounded, and that its boundary is bounded. The domain partition can have cross-points, that is, points where at least three subdomains are adjacent. We also prove that a solution to the initial Helmholtz problem can be recovered from a solution to the multi-domain variational formulation. This shows that the GOSM is a general and flexible framework to model acoustic wave propagation, as it can handle both multi-domain FEM-BEM coupling and (weakly imposed) boundary conditions on several obstacles.
• High-order numerical integration on self-affine sets
  
  • Joly Patrick
  • Kachanovska Maryna
  • Moitier Zoïs
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2026, 48 (4), pp.A1870-A1897. We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we characterize algebraically, by exploiting a self-similarity property of the integral. We propose an \( h \)-version and a \( p \)-version of the cubature, present an error analysis and conduct numerical experiments. (10.1137/24M1697141)
  DOI : 10.1137/24M1697141
• High-Resolution Inertial Dynamics with Time-Rescaled Gradients for Nonsmooth Convex Optimization
  
  • Le Manh Hung
  • Simonetto Andrea
  Computational Optimization and Applications, Springer Verlag, 2026. We study nonsmooth convex minimization through a continuous-time dynamical system that can be seen as a high-resolution ODE of Nesterov Accelerated Gradient (NAG) adapted to the nonsmooth case. We apply a time-varying Moreau envelope smoothing to a proper convex lower semicontinuous objective function and introduce a controlled time-rescaling of the gradient, coupled with a Hessian-driven damping term, leading to our proposed inertial dynamic. We provide a well-posedness result for this dynamical system, and construct a Lyapunov energy function capturing the combined effects of inertia, damping, and smoothing. For an appropriate scaling, the energy dissipates and yields fast decay of the objective function and gradient, stabilization of velocities, and weak convergence of trajectories to minimizers under mild assumptions. Conceptually, the system is a nonsmooth high-resolution model of Nesterov's method that clarifies how time-varying smoothing and time rescaling jointly govern acceleration and stability. We further extend the framework to the setting of maximally monotone operators, for which we propose and analyze a corresponding dynamical system and establish analogous convergence results. We also present numerical experiments illustrating the effect of the main parameters and comparing the proposed system with several benchmark dynamics. (10.1007/s10589-026-00805-0)
  DOI : 10.1007/s10589-026-00805-0
• Risk-Averse Control for Continuous-Time Stochastic System Under Signal Temporal Logic Constraints
  
  • Lai En
  • Bonalli Riccardo
  • Girard Antoine
  • Jean Frédéric
  , 2026. Signal Temporal Logic (STL) has become a powerful formalism for specifying complex temporal-spatial behaviors in autonomous systems. Handling STL constraints within stochastic setting has received increasing research interest but still poses challenges. This paper proposes a general framework to efficiently solve continuous-time nonlinear stochastic optimal control problems under chance STL constraints. The STL formulae are implemented through extended dynamics, yielding a more classical chance constraint on the terminal state uniquely that we reliably relax via Conditional Value-at-Risk. The resulting new optimal control problem is then solved using established algorithms from risk--averse control. The efficiency and feasibility of the proposed approach are demonstrated through numerical simulations.
• Transport of dissolved and particulate arsenic in the Orbiel River during minor flood events downstream the historic Salsigne gold mining district, Southern France
  
  • Carrière Lali
  • Resongles Eléonore
  • Heydon Marie
  • Roux Hélène
  • Viers Jérôme
  • Schreck Eva
  • Freydier Rémi
  • Marchand Pierre
  • Domeau Aurélien
  • Horgue Pierre
  • Behra Philippe
  • Casiot Corinne
  Journal of Contaminant Hydrology, Elsevier, 2026, 281, pp.104955. Understanding and quantifying the transport of toxic metals and metalloids during flood events downstream of former mining sites is challenging as these events are transient, highly variable and unpredictable, resulting in a scarcity of observational data across watersheds worldwide. In this study, the concentrations and fluxes of dissolved and particulate arsenic (As) were determined to investigate the dynamic of As transfer during flood events in the Orbiel River catchment, in Southern France. This river drains the former Salsigne mining district, where gold-bearing arsenopyrite mineralization was historically exploited. In this Mediterranean catchment, characterized by long dry periods and episodic rainfall, high-frequency automatic sampling of river water was conducted at four stations during five minor to moderate flood events between 2021 and 2023. Arsenic dynamics during each flood were event-specific and varied according to the antecedent hydrological conditions of the basin and the respective contribution of mine-impacted and non-impacted tributaries, which depend on localized rainfall patterns. Dissolved As concentrations ranged from 10 to 35 μg L-1 at the outlet of the catchment, comparable to baseflow levels, while particulate As varied from 20 to 500 mg kg-1, with enrichment factors up to 29 relative to the local geochemical background. Although these recurring, low-intensity floods did not generate strong As concentration peaks, the total As load (i.e., the sum of dissolved and particulate As) transported during the quick-flow phases of individual flood events ranged from 7.5 to 93.2 kg at the catchment outlet, reaching up to 3.9 times that measured during a 50-day low-flow summer period (24 kg). These results demonstrate that recurring minor floods, which occur several times each year, substantially contribute to As export from the Orbiel River catchment despite their moderate magnitude. These findings highlight the need to account for frequent low-intensity floods in contaminant transport assessments and management of legacy mining areas under climate change. (10.1016/j.jconhyd.2026.104955)
  DOI : 10.1016/j.jconhyd.2026.104955
• Low-thrust Interplanetary Trajectories with Missed Thrust Events: a Numerical Approach
  
  • Carpentier Pierre
  • Chancelier Jean-Philippe
  • Cohen Guy
  • Dargent Thierry
  • Epenoy Richard
  Journal of Guidance, Control, and Dynamics, American Institute of Aeronautics and Astronautics, 2026, pp.1-18. The problem under consideration is to drive a spatial vehicle to a target at a given final time while minimizing fuel consumption. This is a classical optimal control problem in a deterministic setting. However temporary stochastic failures of the engine may prevent reaching the target after the engine usage is recovered. Therefore, a stochastic optimal control problem is formulated under the constraint of ensuring a minimal probability of hitting the target. This problem is modeled, improved and finally solved by dualizing the probability constraint and using an Arrow-Hurwicz stochastic algorithm. Numerical results concerning an interplanetary mission are presented. (10.2514/1.G009777)
  DOI : 10.2514/1.G009777
• A note on the discrete Unmapped Tent Pitching for the heterogeneous wave equation
  
  • Bonazzoli Marcella
  • Ciaramella Gabriele
  • Mazzieri Ilario
  , 2026. The Unmapped Tent Pitching (UTP) algorithm is a space-time domain decomposition method for the parallel solution of wave-type problems. We have recently extended UTP to heterogeneous settings and compared, at the continuous level, the computational cost of different space-time decompositions. In this note, we report discrete-level observations showing that the optimal decomposition strategy may differ from the one predicted by the continuous analysis.
• A doubly reduced approximation for the solution to PDE's based on a domain truncation and a reduced basis method: Application to Navier-Stokes equations
  
  • Grosjean Elise
  • Maday Yvon
  , 2023. This paper focuses on the non-intrusive reduced basis (NIRB) method called the \textit{two grids method}. It is used for the simulation of parametric partial differential equations to reduce the associated computational costs of a High-Fidelity code when such problems must be solved for a large number of parameter values or provide a solution in “real time”. As other reduced basis approaches, the “offline step” relies on the High-Fidelity method with a fine enough grid. On the contrary, the non-intrusiveness of the original \textit{two grids method} is based on the use, in the “online step”, of the same method with a much coarser grid, which considerably reduces the cost of this step. We extend here this idea by further reducing the “online step” and further simplify the High-Fidelity method. As an example of application we consider a classical fluid problem, the 2D Backward Facing Step (BFS). We simplify the model by i) truncating the outflow part of the channel at extreme and ii) using a coarse uniform mesh instead of refining it at the re-entrant corner, both choices that contradict what is required to get a high fidelity representation of the flow. To accomplish this, we create two reduced bases and a deterministic process that allows us to pass from one to the other. Several numerical simulations illustrate the ability of this new approach.
• Comprehensive dataset of continuously monitored hydrodynamic and physico-chemical parameters in various karst systems, France
  
  • Cinkus Guillaume
  • Bondu Raphaël
  • Aliouache Mohammed
  • Jourde Hervé
  • Mazzilli Naomi
  • Arfib Bruno
  • Bailly-Comte Vincent
  • Batiot-Guilhe Christelle
  • Celle Hélène
  • Delbart Célestine
  • Fournier Matthieu
  • Labat David
  • Peyraube Nicolas
  • Steinmann Marc
  • Valdès-Lao Danièle
  • Baudement Cécile
  • Béranger Sandra
  • Binet Stéphane
  • Boetsch Anne
  • Brunet Pascal
  • Carrière Simon Damien
  • Chalikakis Konstantinos
  • Charlier Jean-Baptiste
  • Cousquer Yohann
  • Défarge Christian
  • Ducasse Joshua
  • Emblanch Christophe
  • Fabre Juliette
  • Fleury Perrine
  • Garin Thibaut
  • Huon Julien
  • Jardani Abderrahim
  • Johannet Anne
  • Jouves Johan
  • Jozja Nevila
  • Justy Lucile
  • Ladouche Bernard
  • Lamarque Thierry
  • Lastennet Roland
  • Léonardi Véronique
  • Lobry Olivier
  • Lorette Guillaume
  • Loup Christophe
  • Marchand Pierre
  • Manière Louis
  • Maréchal Jean-Christophe
  • Martin Lucie
  • Muller Rémi
  • Massei Nicolas
  • Naessens Fabien
  • Ollivier Chloé
  • Probst Anne
  • Seidel Jean-Luc
  • Serene Leïla
  • Sivelle Vianney
  • Zappelli Alexandre
  Scientific Data, Nature Publishing Group, 2026. Karst aquifers are a crucial source of water, supplying approximately 10% of the global population and often serving as the sole water resource in certain regions. These aquifers are characterized by highly heterogeneous flow dynamics and exhibit significant temporal variability in both hydrodynamic and physico-chemical conditions. Continuous monitoring of these parameters is essential for advancing our understanding of karst aquifer functioning; however, comprehensive, high-frequency datasets remain limited. We present a comprehensive dataset covering 13 karst springs monitored across nine observatories of the French Karst National Observatory Service (SNO KARST), spanning various hydroclimatic regions (oceanic, mountainous, Mediterranean). The SNO KARST aims to strengthen knowledge-sharing and to promote cross-disciplinary research on karst systems at the national scale. The dataset includes: (1) hydrodynamic data (water level, discharge), and (2) physico-chemical data (water temperature, electric conductivity, pH, dissolved oxygen, turbidity, Total Organic Carbon (TOC), Dissolved Organic Carbon (DOC), nitrate, and organic matter fluorescence). Spanning over a decade of continuous monitoring, such a dataset is required for the analysis of the hydrological and physico-chemical dynamics of karst aquifers, the assessment of their vulnerability to pollution and climate change, and the modeling of hydrodynamic and hydrochemical variables, ultimately aiming to improve the management and preservation of these critical water resources in contrasted contexts. (10.1038/s41597-026-07561-0)
  DOI : 10.1038/s41597-026-07561-0
• An inverse tsunami problem in the time domain: a well-posedness analysis of the forward problem and an inversion strategy based on a mixed formulation of the Tikhonov regularization
  
  • Bourgeois Laurent
  • Moireau Philippe
  • Terrine Raphaël
  , 2026. This contribution concerns an inverse problem related to a tsunami in the ocean, the tsunami being caused by a submarine earthquake. Considering the very beginning of the phenomenon, a simple linear model incorporating both gravity and acoustic waves is proposed. The main objective is to develop a strategy to solve the inverse problem of retrieving the bottom displacement from the induced free surface perturbation. Such strategy is based on a mixed formulation of the Tikhonov regularization in the space/time domain, the regularization parameter being determined by using the Morozov principle by means of duality in optimization. Some numerical experiments in 2D, which rely on a tensorized finite element method, show that our strategy is effective. A secondary objective is to prove existence and uniqueness of both strong and variational solutions to the forward problem.
• No-regret optimization of time-varying bilevel problems
  
  • Mauduit Eliabelle
  • Berthier Eloïse
  • Simonetto Andrea
  , 2026. Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear bilevel programs are strongly NP-hard. In this work, we consider bilevel optimization with a known upper-level objective and an unknown, potentially time-varying lower-level response, accessible only through noisy zeroth-order observations. We propose W-SparQ-BL, a Bayesian optimization framework that models the lower-level mapping using multi-output Gaussian processes and enables efficient optimization under uncertainty. Our approach leverages a sparse, observation-based approximation to control the effect of noise and temporal variability, while requiring only limited access to additional information over time. We establish regularity results linking the lower-level response to standard RKHS assumptions for common kernels, including Matérn and squared exponential. We prove that W-SparQ-BL achieves sublinear dynamic regret in both stationary and time-varying settings. Experiments on representative time-varying game-theoretic problems demonstrate the effectiveness of our approach.
• Numerical analysis of an optimal control approach to solve a tsunami inverse problem
  
  • Bourgeois Laurent
  • Moireau Philippe
  • Terrine Raphaël
  , 2026. This paper concerns the reconstruction of an abrupt bottom displacement of the ocean from the measurement of the induced perturbation of the free surface, which is a severely ill-posed inverse problem. This problem is solved by using an optimal control approach, the physics being governed by a time evolution system based on a simple oceanography model. We firstly recast the problem in an abstract framework, secondly propose an implicit Euler scheme for the time discretization combined with a Finite Element method for the space discretization. The main result is an error estimate between the solution to the discrete control optimal problem and the solution to the continuous optimal problem, which is obtained by considering the discrete and continuous weak mixed formulations that characterize the optimality for these two problems. Some numerical experiments illustrate the efficiency of our approach and the consistency of our error estimate.
• Eigenvalue falls in thin broken quantum strips
  
  • Chesnel Lucas
  • Nazarov Sergei A.
  , 2025. We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in trapezoids of thickness $\varepsilon&gt;0$ small. We give an asymptotic expansion of the first eigenvalues and corresponding eigenfunctions as $\varepsilon$ tends to zero. The new point in this work is to study the dependence with respect to $\alpha$. We highlight a curious phenomenon of diving eigenvalues: when the strip is more and more broken, at certain critical angles, that we characterize, an eigenvalue moves down very rapidly below the pack of other eigenvalues. We prove that this occurs more gently at $\alpha=0$ than at positive critical angles.
• Réduction de modèles pour les interactions fluide-structure : exploitation des fonctions de Green adaptées
  
  • Chaillat Stéphanie
  • Pacaut Louise
  • Mercier Jean-François
  • Serre Gilles
  • Trafny Nicolas
  , 2026. Nous considérons un problème d’interaction fluide-structure sur une géométrie complexe, pour lequel nous souhaitons calculer la réponse à des excitations variables. Pour réduire considérable- ment le coût de calcul de cette étude paramétrique sans sacrifier la précision, nous proposons une ap- proche de réduction de modèle séparant les effets de la géométrie et de la source. La méthode repose sur le calcul d’une fonction de Green adaptée au couplage fluide-structure et à la géométrie complexe. Pour rendre le coût de la phase offline acceptable, nous exploitons des méthodes d’éléments de frontière rapides.
• Méthode d'éléments finis discontinus hybridisée pour la résolution itérative accélérée de problèmes d'ondes en fréquence
  
  • Modave Axel
  • Greffe Roland
  • Geuzaine Christophe
  • Rappaport Ari
  • Chabib Ahmed
  , 2026. La discrétisation de problèmes de propagation d’ondes en régime harmonique par éléments finis conduit à des systèmes linéaires coûteux à résoudre. Nous considérons une méthode d’éléments finis discontinus hybridisée en utilisant des variables de transmission aux interfaces entre les mailles. Cette approche permet d’accélérer la convergence des schémas itératifs et possède une structure algo- rithmique adaptée au calcul parallèle, notamment sur cartes graphiques. Nous présentons et étudions des implémentations de cette méthode au moyen de résultats 3D obtenus avec un code C++ dédié.
• A non-local singular non-linear Fokker-Planck PDE
  
  • Bondi Luca
  • Issoglio Elena
  • Russo Francesco
  , 2026. The focus of this paper is a non-local singular non-linear Fokker-Planck partial differential equation (PDE). The peculiarity of this PDE feature is in its divergence coefficient, which presents a product between a Besov distribution and a non-linearity. The latter involves the convolution between an integrable kernel K and the solution of the PDE, which leads to a non-locality of the first order term in the PDE. We prove existence and uniqueness of a solution to the PDE as well as continuity results on its coefficients. Previous analytical results are then applied to the study of well-posedness in law for a non-local singular McKean stochastic differential equation. As byproduct of that probabilistic representation, we establish mass conservation and positivity preserving for the PDE.