Publications

2025

• A Newton-type method for non-smooth under-determined systems of equations
  
  • Pinta Titus
  Numerical Algorithms, Springer Verlag, 2025. <div><p>We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semismoothness. The classic notion of Newton differentiability does not suffice for our purpose, due to the existence of multiple zeros and as such we extend it to uniform Newton differentiability. In this context, we can show that the distance between the iterates and the set of zeros of the system decreases super-linearly. For the special case of smooth equations, the assumptions of our algorithm are simplified. Finally, we provide some numerical examples to showcase the behavior of our proposed method. The key example is a toy model of complementarity constraint problems, showing that our method has great application potential across engineering fields.</p></div> (10.1007/s11075-025-02212-8)
  DOI : 10.1007/s11075-025-02212-8
• Spectrum of slip dynamics, scaling and statistical laws emerge from simplified model of fault and damage zone architecture
  
  • Almakari Michelle
  • Kheirdast N.
  • Villafuerte C.
  • Thomas Marion Y.
  • Dubernet P.
  • Cheng J.
  • Gupta A.
  • Romanet P.
  • Chaillat S.
  • Bhat Harsha S.
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2025. <div><p>Seismological and geodetic observations of a fault zone reveal a wide range of slip dynamics, scaling, and statistical laws. However, the underlying physical mechanisms remain unclear. In this study, we show that incorporating an off-fault damage zone-characterized by distributed fractures surrounding a main fault-can reproduce many key features observed in seismic and geodetic data. We model a 2D shear fault zone in which off-fault cracks follow power-law size and density distributions, and are oriented either optimally or parallel to the main fault. All fractures follow the rate-and-state friction law with parameters chosen such that each can host slip instabilities. We do not introduce spatial heterogeneities in the frictional properties of the fault. Using quasi-dynamic boundary integral simulations accelerated by hierarchical matrices, we simulate slip dynamics of this system and analyze the events produced both on and off the main fault. Despite the spatially uniform frictional properties, we observe a natural continuum from slow to fast ruptures, as observed in nature. Our simulations reproduce the Omori law, the inverse Omori law, the Gutenberg-Richter scaling, and the moment-duration scaling. We also observe seismicity localizing toward the main fault when an event is about to nucleate on the main fault. During slow slip events, off-fault seismicity migrates in a pattern resembling a fluid diffusion front, despite the absence of fluids in the model. We also show that tremors, Very Low Frequency Earthquakes (VLFEs), Low Frequency Earthquakes (LFEs), Slow Slip Events (SSEs), and earthquakes (EQs) can all emerge naturally in the ‘digital twin’ framework.</p></div>
• Lot-sizing under decision-dependent uncertainty: A probing-enhanced stochastic programming approach
  
  • Quezada Franco
  • Gicquel Céline
  • Kedad-Sidhoum Safia
  • Pagnoncelli Bernardo
  , 2025. We address the multi-item capacitated lot-sizing problem under decision-dependent uncertainty via a probing-enhanced stochastic programming framework. Demand is correlated with another random vector, and the decision-maker can acquire partial information by probing components of this vector, conditioning decisions on observed covariates. This generalizes classical models by embedding information acquisition into a three-stage framework. We propose a compact reformulation that removes non-anticipativity constraints, yielding stronger relaxations and better tractability. We extend classical inequalities and introduce value-function cuts that capture the link between probing and recourse costs. These are embedded in a branch-and-cut algorithm with a primal heuristic. Results show our method outperforms off-the-shelf solver, reducing optimality gaps by up to 85%, and achieving gaps below 1.5% on average. Results highlight the importance of structured reformulation, valid inequalities, and heuristics in solving decision-dependent stochastic programs.
• Accelerating non-local exchange in generalized optimized Schwarz methods
  
  • Claeys Xavier
  • Delville Atchekzai Roxane
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2025, 11, pp.517-532. The generalized optimised Schwarz method proposed in [Claeys &amp; Parolin, 2022] is a variant of the Després algorithm for solving harmonic wave problems where transmission condition are enforced by means of a non-local exchange operator. We introduce and analyse an acceleration technique that significantly reduces the cost of applying this exchange operator without deteriorating the precision and convergence speed of the overall domain decomposition algorithm. (10.5802/smai-jcm.133)
  DOI : 10.5802/smai-jcm.133
• Portage GPU d'un solveur éléments finis discontinus hybridisé pour les problèmes d'ondes en fréquence
  
  • Chabib Ahmed
  • Greffe Roland
  • Geuzaine Christophe
  • Modave Axel
  , 2025. Dans ce travail, nous nous intéressons à la résolution par éléments finis de problèmes de propagation d'ondes en régime harmonique de très grande taille. L'utilisation de cartes graphiques (GPU) permet d'accélérer les calculs, mais il est difficile d'en exploiter pleinement la puissance. Nous considérons une méthode d'éléments finis discontinus de type Galerkin (DG) avec des flux amonts, hybridisée utilisant des variables de transmission définies aux faces des éléments. L'élimination des variables physiques conduit à un système linéaire adapté pour une résolution itérative et une implémentation parallèle efficace sur GPU. Après une description de la méthode, appelée CHDG, nous présentons quelques stratégies de mise en oeuvre sur GPU et nous comparons et discutons leurs performances.
• User-centered decentralized P2P energy trading model for managing line congestion in Energy Communities
  
  • San Martín Sebastián
  • García-Muñoz Fernando
  • Quezada Franco
  • Dávila Sebastián
  Sustainable Energy, Grids and Networks, Elsevier, 2025. <div><p>This paper presents a user-centered, fully decentralized framework to allow an energy community (EC) to self-manage line congestion issues through peer-to-peer (P2P) energy trading and a flexibility market using the users' distributed energy resources (DERs) assets to take an energy seller (buyer) role when they have a surplus (deficit). A three-stage optimization-based model is introduced to consider the users' preferences and identify line congestion issues using the Distflow model to evaluate the distribution network (DN) limitations.</p><p>In this regard, users maximize their benefits in the first optimization stage by optimizing their DER operation.</p><p>In the second stage, the distribution system operator (DSO) solves an optimal power flow model to identify potential congestion given the users' preferences. If congestion occurs, the third stage activates a P2P energy and flexibility market designed to resolve the issue by minimizing deviations from the users' initial preferences. To achieve full decentralization, a two-step alternating direction method of multipliers (ADMM) algorithm is employed: the first step addresses optimal power flow, while the second manages the P2P and flexibility market. Tests were conducted on a 33-bus DN for different DER penetration levels, showing that the methodology efficiently meets energy requirements while respecting the network's physical constraints and improving information security.</p></div>
• McKean-Vlasov equations with singular coefficients - a review of recent results
  
  • Bondi Luca
  • Issoglio Elena
  • Russo Francesco
  , 2025. This paper focuses on recent works on McKean-Vlasov stochastic differential equations (SDEs) involving singular coefficients. After recalling the classical framework, we review existing recent literature depending on the type of singularities of the coefficients: on the one hand they satisfy some integrability and measurability conditions only, while on the other hand the drift is allowed to be a generalised function. Different types of dependencies on the law of the unknown and different noises will also be considered. McKean-Vlasov SDEs are closely related to non-linear Fokker-Planck equations that are satisfied by the law (or its density) of the unknown. These connections are often established also in this singular setting and will be reviewed here. Important tools for dealing with singular coefficients are also included in the paper, such as Figalli-Trevisan superposition principle, Zvonkin transformation, Markov marginal uniqueness, and stochastic sewing lemma.
• Preconditioning of GMRES for Helmholtz problems with quasimodes
  
  • Dolean Victorita
  • Marchand Pierre
  • Modave Axel
  • Raynaud Timothée
  , 2026, pp.329-336. Finite element methods are effective for Helmholtz problems involving complex geometries and heterogeneous media. However, the resulting linear systems are often large, indefinite, and challenging for iterative solvers, particularly at high wave numbers or near resonant conditions. We derive a GMRES convergence bound that incorporates the nonlinear behavior of the relative residual and relates convergence to harmonic Ritz values. This perspective reveals how small eigenvalues associated with quasimodes can hinder convergence, and when they cease to have an effect. These phenomena occur in domain decomposition, and we illustrate them through numerical experiments. We also combine domain decomposition methods with deflation techniques using (approximate) eigenvectors tailored to resonant regimes. Their impact on GMRES performance is evaluated.
• Isolated Rotor Blade Shape Sensitivity for Aeroacoustic Optimization Using a Discrete Adjoint Framework
  
  • Mohammedi Yacine
  • Daroukh Majd
  • Buszyk Martin
  • Hajczak Antoine
  • Salah El Din Itham
  • Bonnet Marc
  , 2025. A discrete adjoint framework is developed to optimize rotor self-noise from steady fluid simulations in the rotating frame. To this end, a simplified expression of the off-body frequency-domain Ffowcs-Williams and Hawkings (FW-H) equation is derived for far-field observers, following the model of Hanson and Parzych (1993) originally written for on-body surfaces. The latter is implemented and compared against the results given by an established time-domain FW-H solver. Far-field acoustic pressure sensitivities are derived analytically and validated by comparison with second-order accurate finite differences. The sensitivities of any objective function expressed in terms of the acoustic pressure can therefore be reconstructed. Then the discrete adjoint of a Reynolds-averaged Navier-Stokes solver provides the objective function gradients with respect to the blade shape parameters. The complete workflow is validated against finite difference evaluations on an isolated open rotor in cruise conditions. (10.2514/6.2025-3367)
  DOI : 10.2514/6.2025-3367
• Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations
  
  • Faria Luiz
  • Marchand Pierre
  • Montanelli Hadrien
  , 2025. We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency errors introduced by the perturbed bilinear and sesquilinear forms. We illustrate our results with numerical experiments in 3D based on basis functions and curved triangular elements up to order four.
• Attraction of the core and the cohesion flow
  
  • Laplace Mermoud Dylan
  Theory and Decision, Springer Verlag, 2025, 99 (1-2), pp.377-392. We adopt a continuous-time dynamical system approach to study the evolution of the state of a game driven by the willingness to reduce the total dissatisfaction of the coalitions about their payment. Inspired by the work of Grabisch and Sudhölter about core stability, we define a vector field on the set of preimputations from which is defined, for any preimputation, a cohesion curve describing the evolution of the state. We prove that for each preimputation, there exists a unique cohesion curve. Subsequently, we show that, for the cohesion flow of a balanced game, the core is the unique minimal attractor of the flow, the realm of which is the whole preimputation set. These results improve our understanding of the ubiquity of the core in the study of cooperative games with transferable utility. (10.1007/s11238-025-10060-0)
  DOI : 10.1007/s11238-025-10060-0
• $C^{ 0,1}$ -Itô chain rules and generalized solutions of parabolic PDEs
  
  • Ciccarella Carlo
  • Russo Francesco
  Stochastics and Dynamics, World Scientific Publishing, 2025, 25 (03n04). In this paper we first establish an It\^o formula for a finite quadratic variation process $X$ expanding $f(t,X_t),$ when $f$ is of class $C^2$ in space and is absolutely continuous in time. Second, via a Fukushima-Dirichlet decomposition we obtain an explicit chain rule for $f(t,X_t)$, when $X$ is a continuous semimartingale and $f$ is a ``quasi-strong solution'' (in the sense of approximation of classical solutions) of a parabolic PDE. (10.1142/S0219493725500194)
  DOI : 10.1142/S0219493725500194
• The algebraic structures of social organizations: the operad of cooperative games
  
  • Laplace Mermoud Dylan
  • Roca I Lucio Victor
  , 2025. <div><p>The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we start by endowing the collection of all cooperative games with any number of players with an operad structure, and we show that it generalises all the previous notions of sums, products and compositions of games considered by Owen, Shapley, von Neumann and Morgenstern, and many others. Furthermore, we explicitly compute this operad in terms of generators and relations, showing that the Möbius transform map induces a canonical isomorphism between the operad of cooperative games and the operad that encodes commutative triassociative algebras. In other words, we prove that any cooperative game is a linear combination of iterated compositions of the 2-player bargaining game and the 2-player dictator games. We show that many interesting classes of games (simple, balanced, capacities a.k.a fuzzy measures and convex functions, totally monotone, etc) are stable under compositions, and thus form suboperads. In the convex case, this gives by the submodularity theorem a new operad structure on the family of all generalized permutahedra. Finally, we focus on how solution concepts in cooperative game theory behave under composition: we study the core of a composite and describe it in terms of the core of its components, and we give explicit formulas for the Shapley value and the Banzhaf index of a compound game.</p></div>
• On the Formation of Steady Coalitions
  
  • Laplace Mermoud Dylan
  , 2024. This paper studies the formation of the grand coalition of a cooperative game by investigating its possible internal dynamics. Each coalition is capable of forcing all players to reconsider the current state of the game when it does not provide sufficient payoff. Different coalitions may ask for contradictory evolutions, leading to the impossibility of the grand coalition forming. In this paper, we give a characterization of the impossibility, for a given state, of finding a new state dominating the previous one such that each aggrieved coalition has a satisfactory payoff. To do so, we develop new polyhedral tools related to a new family of polyhedra, appearing in numerous situations in cooperative game theory. (10.48550/arXiv.2410.05087)
  DOI : 10.48550/arXiv.2410.05087
• Projection onto the core: An optimal reallocation to correct market failure
  
  • Laplace Mermoud Dylan
  , 2024. This paper provides formulae and algorithms to compute the projection onto the core of a preimputation outside it. The core of a game is described using an exponential number of linear constraints, and we cannot know beforehand which are redundant or defining the polytope. We apply these new results to market games, a class of games in which every game has a nonempty core. Given an initial state of the game represented by a preimputation, it is not guaranteed that the state of the game evolves toward the core following the dynamics induced by the domination relations. Our results identify and compute the most efficient side payment that acts on a given state of the game and yields its closest core allocation. Using this side payment, we propose a way to evaluate the failure of a market to reach a state of the economy belonging to the core, and we propose a new solution concept consisting of preimputations that minimizes this failure. (10.48550/arXiv.2411.11810)
  DOI : 10.48550/arXiv.2411.11810
• Nonlocal vector calculus on the sphere
  
  • Montanelli Hadrien
  • Slevinsky Richard Mikael
  • Du Qiang
  , 2025. (10.48550/arXiv.2505.12372)
  DOI : 10.48550/arXiv.2505.12372
• Two-phase Trajectory Planning Method for Robust Planetary Landing in a Sensor-equipped Area
  
  • Leparoux Clara
  • Hérissé Bruno
  • Jean Frédéric
  , 2025, pp.1296-1301. This article addresses the planetary landing problem by considering uncertainties and leveraging the presence of a detection area where precise measurements are available. The flight consists of two distinct phases: the first phase, subject to a high level of uncertainties, and the second phase, during which the vehicle is feedback controlled to ensure precise landing. We propose a method to compute the optimal control for the initial phase, aiming to minimize fuel consumption for the entire trajectory while satisfying a probabilistic constraint that ensures the vehicle reaches the detection zone with a specified threshold. (10.23919/ECC65951.2025.11186925)
  DOI : 10.23919/ECC65951.2025.11186925
• A few techniques to achieve invisibility in waveguides
  
  • Chesnel Lucas
  , 2025, pp.68. The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more specific, we will be interested in the propagation of acoustic waves in guides which are unbounded in one direction. In general, the diffraction of an incident field in such a structure in presence of an obstacle generates a reflection and a transmission characterized by some scattering coefficients. Our goal will be to play with the geometry, the frequency and/or the index material to control these scattering coefficients. We will explain how to: - develop a continuation method based on the use of shape derivatives to construct invisible defects; - exploit complex resonances located closed to the real axis to hid obstacles; - construct a non self-adjoint operator whose eigenvalues coincide with frequencies such that there are incident fields whose energy is completely transmitted. Our approaches will mainly rely on techniques of asymptotic analysis as well as spectral theory for self-adjoint and non self-adjoint operators. Most of the results will be illustrated by numerical experiments.
• Parametric study of turbulence ingestion noise for marine propellers
  
  • Lavanant Romain
  • Cotté Benjamin
  • Serre Gilles
  • Mercier Jean-François
  , 2025, pp.1851-1858. Hydrodynamic noise is an important component of the overall noise radiated by a ship, particularly at low frequencies where propeller noise could be dominant especially at high speed. This study proposes a simplified analytical solution of the phenomenon of spectral humps of propeller noise due to the interaction between a rotating propeller and an incident turbulent flow. The acoustic radiation is described by the Ffowcs-Williams and Hawkings analogy in the compact approximation. The inflow turbulence field is assumed to be homogeneous and isotropic and is modeled using a von Kármán spectrum. Experimental validation and comparison with more costly analytical solutions demonstrate the ability of the developed model to correctly capture the characteristics of the humps related to turbulence ingestion. From the results obtained, a parametric analysis enables us to define a criterion for the emergence and shape of turbulence ingestion humps according to the propeller advance ratio, improving the criterion proposed by Ffowcs-Williams and Hawkings in 1969. (10.61782/fa.2025.0670)
  DOI : 10.61782/fa.2025.0670
• Fast Boundary Element Methods Beyond Homogeneous Media: Challenges Towards Realistic Wave Propagation Simulations
  
  • Chaillat Stéphanie
  , 2026. <div><p>Boundary Element Methods (BEMs), based on the discretization of boundary integral equations, have proven particularly well-suited for modeling wave propagation in unbounded domains. In recent years, significant advances have made these methods applicable to realistic configurations. Fast algorithms, including the Fast Multipole Method, low-rank approximations, and mesh adaptivity, have significantly mitigated the inherent limitations of BEMs, substantially reducing computational costs and making BEM a competitive tool for large-scale simulations. While fast BEMs are now mature for homogeneous media and simple geometries, their applicability to more complex scenarios requires additional methodological advances. This review highlights recent collaborative efforts that expand BEMs to more challenging problems, including novel FEM-BEM coupling strategies inspired by volumetric domain decomposition methods, preconditioning techniques for multiple-scattering problems, and approaches for piecewise homogeneous media that extend BEM applicability beyond fully homogeneous domains.</p></div>
• Radial perfectly matched layers and infinite elements for the anisotropic wave equation
  
  • Halla Martin
  • Kachanovska Maryna
  • Wess Markus
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2025, 57 (3), pp.3171-3216. We consider the scalar anisotropic wave equation. Recently a convergence analysis for radial perfectly matched layers (PML) in the frequency domain was reported and in the present article we continue this approach into the time domain. First we explain why there is a good hope that radial complex scalings can overcome the instabilities of PML methods caused by anisotropic materials. Next we discuss some sensitive details, which seem like a paradox at the first glance: if the absorbing layer and the inhomogeneities are sufficiently separated, then the solution is indeed stable. However, for more general data the problem becomes unstable. In numerical computations we observe instabilities regardless of the position of the inhomogeneities, although the instabilities arise only for fine enough discretizations. As a remedy we propose a complex frequency shifted scaling and discretizations by Hardy space infinite elements or truncation-free PMLs. We show numerical experiments which confirm the stability and convergence of these methods. (10.1137/24M1636551)
  DOI : 10.1137/24M1636551
• Optimized Schwarz Methods in Time for Discrete Transport Control
  
  • Bui Duc-Quang
  • Delourme Bérangère
  • Halpern Laurence
  • Kwok Felix
  , 2025. We investigate optimized Schwarz domain decomposition methods in time for the control of the 1D transport equation. In the case of an internal control over the whole domain, the optimization problem can be transformed into a system of two coupled PDEs. We then apply the time-domain decomposition (without overlap) strategy on this PDE system as well as on its discretized counterpart. Under Fourier analysis, we analyse three different iterations: the fixed point iteration, the relaxed iteration and the preconditioned GMRES method. For each case, we propose parameters for the transmission conditions that lead to fast convergence of the method. We illustrate our results by numerical examples.
• Homogenization of stable-like operators with random, ergodic coefficients
  
  • Klimsiak Tomasz
  • Komorowski Tomasz
  • Marino Lorenzo
  Journal of Differential Equations, Elsevier, 2025, 430, pp.113183. We show homogenization for a family of R d -valued stable-like processes (X ε;θ t ) t≥0 , ε ∈ (0, 1], whose (random) Fourier symbols equal q ε (x, ξ; θ) = 1 ε α q x ε , εξ; θ , where<p>1 -e iy•ξ + iy • ξ1 {|y|≤1} a(x; θ)y, y |y| d+2+α dy, for (x, ξ, θ) ∈ R 2d × Θ. Here α ∈ (0, 2) and the family (a(x; θ)) x∈R d of d × d symmetric, non-negative definite matrices is a stationary ergodic random field over some probability space (Θ, H, m). We assume that the random field is deterministically bounded and non-degenerate, i.e. |a(x; θ)| ≤ Λ and Tr(a(x; θ)) ≥ λ for some Λ, λ &gt; 0 and all θ ∈ Θ. In addition, we suppose that the field is regular enough so that for any θ ∈ Θ, the operator -q(•, D; θ), defined on the space of compactly supported C 2 functions on R d , is closable in the space of continuous functions vanishing at infinity and its closure generates a Feller semigroup. We prove the weak convergence of the laws of (X ε;θ t ) t≥0 , as ε ↓ 0, in the Skorokhod space, m-a.s. in θ, to an α-stable process whose Fourier symbol q(ξ) is given by q(ξ) = Ω q(0, ξ; θ)Φ * (θ) m(dθ), where Φ * is a strictly positive density w.r.t. measure m. Our result has an analytic interpretation in terms of the convergence, as ε ↓ 0, of the solutions to random integro-differential equations ∂ t u ε (t, x; θ) = -q ε (x, D; θ)u ε (t, x; θ), with the initial condition u ε (0, x; θ) = f (x), where f is a bounded and continuous function on R d .</p> (10.1016/j.jde.2025.02.054)
  DOI : 10.1016/j.jde.2025.02.054
• A multi-objective optimization approach for generalized linear multiplicative programming
  
  • Nguyen Minh Hieu
  • Nguyen Thanh Loan
  , 2026, 1688. Multiplicative programming is a fundamental mathematical optimization problem in which the objective function contains a product of several real-valued functions. This paper deals with a class of multiplicative programming, called generalized linear multiplicative programming (GLMP), in which the objective is to minimize the product of two positive linear functions with general positive powers under linear constraints. Since the objective is a typical non-convex function, GLMP may have multiple local minima, making it computationally challenging. To address this, we propose a multi-objective optimization-based approach. By treating each function as an objective to be minimized, we show that a solution of GLMP is necessarily a non-dominated extreme point located on the vertex of the convex hull of the Pareto front. Then, we use a recursive algorithm to determine the set of all non-dominated extreme points. Notice that the solutions of GLMP can be directly extracted from this set. Furthermore, based on the Weighted Sum Method, it requires only solving one linear program in each iteration. Finally, we provide computational results on a specific instance of GLMP with 0-1 knapsack constraints, indicating that our approach is promising. (10.1007/978-3-032-08381-4_8)
  DOI : 10.1007/978-3-032-08381-4_8
• Convergence analysis of GMRES applied to Helmholtz problems near resonances
  
  • Dolean Victorita
  • Marchand Pierre
  • Modave Axel
  • Raynaud Timothée
  , 2025. The finite element solution of Helmholtz problems near resonant or quasi-resonant frequencies poses significant challenges, as iterative solvers typically suffer from severely degraded convergence. We analyze the convergence behavior of GMRES applied to linear systems arising from such configurations. Theoretical convergence estimates are derived based on harmonic Ritz values, highlighting their proximity to small eigenvalues as a key determining factor. We further examine deflation strategies and their interplay with preconditioning techniques, using the Complex Shifted Laplacian preconditioner as a case study. Numerical experiments on resonant and quasi-resonant test cases validate the theoretical framework and demonstrate the effectiveness of deflation strategies. This study provides new insights and practical guidance for analyzing and improving iterative solvers for time-harmonic problems near resonances.