Publications

2026

• Optimization-based numerical methods for the two-and three-dimensional time harmonic Maxwell problem with sign-changing coefficients
  
  • Chaaban Farah
  • Ciarlet Patrick
  • Rihani Mahran
  , 2026. We study the two-and three-dimensional time-harmonic Maxwell equations in a medium composed of a classical material and a metamaterial. The problem is modeled as an interface problem with sign-changing coefficients, with the electric field as the main vector-valued unknown. To carry out the theoretical and numerical analyses, we only require that the problem has a unique solution. We then construct a convergent numerical approximation, with the help of Nédélec finite elements and prove its convergence in the strong H(curl)-norm. At the discrete level, we consider two approaches. The first directly adapts the arguments used for the continuous problem, while the second uses the extra regularity of the tangential traces of discrete fields. Finally, numerical experiments illustrate the theoretical results.
• 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 $\boldsymbol{H}({\rm div},\Omega)$ in $\mathbb{R}^n$. A generalized Stokes formula allows us to introduce the tangential trace operator on $\boldsymbol{H}({\bf curl},\Omega)$ and $\boldsymbol{H}^1(\Omega)$ 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 $\operatorname{\textbf{curl}}\operatorname{\textbf{curl}}+\textbf{I}$ operator within the $H^1$-extension domains framework.
• Diffraction of waves by finite thin coatings : asymptotic expansion and effective models
  
  • Baudet Cédric
  , 2026. We consider the Helmholtz equation in a Dirichlet angular sector (which may be locally perturbed) covered on one side by a thin homogeneous layer. First, we propose an asymptotic expansion of the solution at any order and for any angle when the thickness of the layer tends to 0, using a matched asymptotic expansion. This consists in introducing different asymptotic expansions in three subdomains – the vicinity of the corner, the layer and the rest of the domain – that are linked through matching conditions. The presence of the corner makes these matching conditions delicate to derive because the fields have complex singular behaviors. We overcome this difficulty using a novel system of algebraic tools, including formal series and operators on these series. Moreover, we justify the asymptotic expansion with error estimates and provide details on the form of the expansion depending on the angle.We numerically validate this expansion up to order 5 for several angles. This requires computing the behavior at infinity of some corner profiles. To do this, we introduce a Galerkin-type method enriched by complements at infinity. These complements are known functions that appear in the behavior at infinity of the corner profiles with coefficients that become unknowns of the system.Finally, we propose effective models of order 3, resp. 5 where, far from the corner, the layer is replaced with an effective Robin, resp. Ventcel, boundary condition and, near the corner, an artificial boundary is introduced and a Dirichlet-to-Neumann (DtN) type condition is imposed. The DtN map relies on a modal decomposition of the truncated asymptotic expansion at order 3, resp. 5. The modes take into account the singular behavior of the expansion terms, the corner profiles and some algebraic matching coefficients. We show that our effective models are well-posed when the layer is thin enough, and rigorously justify these models with error estimates. These results are illustrated by numerical simulations.
• OPTEC (Optimized Parallelized Task Execution in C++)
  
  • Baudet Cédric
  , 2026. OPTEC (Optimized Parallelized Task Execution in C++) is a C++ library. Its main features are as follows: – Optimized parallel execution of a task list: each process is handed a new task as soon as it finishes the previous one, until the task list is exhausted. – Data communication between tasks through a simple send/request interface. – Estimation of the remaining computation time, based on the tasks' time complexity or their completion percentage (also useful for non-parallelized computations). – Memory (RAM) resource management, with automatic pausing of some processes to avoid saturating the RAM. More advanced features: task-order optimization, computation of undetermined constants appearing in the complexity formula, sending of custom types between processes, compatibility with the FEM-BEM library XLiFE++, etc.
• 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
• 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
• 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
• 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
• 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.
• 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.
• Influence of aerodynamic-acoustic trade-off on weighted-sum optimization of an open rotor and mulitpoint optimization using a discrete adjoint framework
  
  • Mohammedi Yacine
  • Daroukh Majd
  • Buszyk Martin
  • Hajczak Antoine
  • Bonnet Marc
  • Salah El-Din Itham
  , 2026. Weighted-sum aeroacoustic optimizations are conducted on an isolated open rotor under cruise and take-off conditions to investigate the influence of aerodynamic-acoustic trade-off within the objective function. The composite objective function combines torque and acoustic power level at the Blade Passing Frequency (BPF), while thrust is imposed as a constraint. To this end, a discrete adjoint framework is employed to calculate and provide gradients of the objective function and constraints. A mesh deformation tool modifies the geometry based on updated values of design parameters provided by the optimizer. The acoustic metric is evaluated using a simplified expression of the off-body frequency-domain Ffowcs-Williams and Hawkings (FW-H) equation derived for far-field observers, following the model of Hanson and Parzych (1993) originally written for on-body surfaces. Aerodynamic performance is quantified through axial and tangential forces. The sensitivities of the aerodynamic and acoustic metrics are obtained by analytically differentiating their expressions. Then, the discrete adjoint of a Reynolds-averaged Navier-Stokes solver supplies gradients of the objective and constraint functions relative to blade shape parameters. These values and their gradients are then used by a gradient-based optimizer to guide the aeroacoustic design optimization process. Analysis of the resulting optimal geometries reveals that scenarios accounting for combined contributions of torque and acoustic power at the BPF provide the most favorable trade-offs, with reduced shock intensity associated with dihedral effects at cruise, and delayed flow detachment linked to sweepback effects at take-off, thereby maintaining favorable aerodynamic loading distributions across operating conditions. (10.2514/6.2026-3353)
  DOI : 10.2514/6.2026-3353
• Theoretical Study of Turbulence Ingestion Noise for Propellers in Nonuniform Flows
  
  • Lavanant Romain
  • Cotté Benjamin
  • Serre Gilles
  • Mercier Jean-François
  , 2026. This paper presents an analytical model for predicting the broadband noise radiated by a propeller ingesting a spatially nonuniform turbulent flow. The formulation, derived from Goldstein's acoustic analogy, expresses the far-field power spectral density through azimuthal Fourier decompositions of the incident heterogeneous turbulence spectrum, thereby retaining inter-strip and blade-to-blade correlations along the blade span. The spatially varying turbulence parameters (integral length scale and turbulence intensity) that serve as inputs to the spectrum models are derived analytically from Prandtl's mixing-length shear-production approach. Two turbulence spectrum formulations are considered: a heterogeneous isotropic von Kármán spectrum and a heterogeneous anisotropic Kerschen-Gliebe spectrum. A comparison with experimental data for a rotor ingesting a turbulent boundary layer highlights the respective roles of anisotropy and heterogeneity. On the one hand, an isotropic turbulence description fails to reproduce the measured spectral humps (haystacks) at blade passing frequency harmonics; anisotropy with a stretched streamwise length scale is required. On the other hand, the heterogeneous model captures the progressive attenuation of higher-order haystacks through destructive interference between contributions of varying eddy sizes across the propeller disk, an effect that homogeneous models systematically overpredict. (10.2514/6.2026-3517)
  DOI : 10.2514/6.2026-3517
• 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.
• Poisson-type problems with transmission conditions at boundaries of infinite metric trees
  
  • Kachanovska Maryna
  • Naderi Kiyan
  • Pankrashkin Konstantin
  Journal of Mathematical Analysis and Applications, Elsevier, 2026, 557 (1), pp.130261. The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching along a compact surface (interface). The lower-dimensional piece is a so-called infinite metric tree (one-dimensional branching structure), and the key ingredient of the study is a rigorous definition of the gluing conditions between the two components. These constructions are based on the recent concept of embedded trace maps and some abstract machineries derived from a suitable Green-type formula. The problem is then reduced to the study of Fredholm properties of a linear combination of Dirichlet-to-Neumann maps for the tree and the Euclidean domain, which yields desired existence and uniqueness results. One also shows that large finite sections of the tree can be used for an efficient approximation of solutions (10.1016/j.jmaa.2025.130261)
  DOI : 10.1016/j.jmaa.2025.130261
• Fault Volume Digital Twin to Reproduce the Full Slip Spectrum, Scaling, and Statistical Laws
  
  • Almakari Michelle
  • Kheirdast Navid
  • Villafuerte Carlos
  • Thomas M.
  • Dubernet Pierpaolo
  • Cheng Jinhui
  • Gupta Ankit
  • Romanet P.
  • Chaillat S.
  • Bhat H.
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2026, 131 (5), pp.e2025JB032915. Seismological and geodetic observations of fault zones reveal diverse slip dynamics, scaling, and statistical laws. Existing mechanisms explain some but not all of these behaviors. 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 rate‐and‐state friction with parameters enabling slip instabilities. We do not introduce spatial heterogeneities in frictional properties. Using quasi‐dynamic boundary integral simulations accelerated by hierarchical matrices, we simulate slip dynamics and analyze events produced both on and off the main fault. Despite spatially uniform frictional properties, we observe a natural continuum from slow to fast ruptures, as seen in nature. Our simulations reproduce the Omori law, inverse Omori law, Gutenberg‐Richter scaling, and moment‐duration scaling. We observe seismicity localizing toward the main fault before nucleation of main‐fault events. During slow slip events (SSEs), off‐fault seismicity migrates in patterns resembling fluid diffusion fronts, despite the absence of fluids. We show that tremors, very low‐frequency earthquakes, low frequency earthquakes, SSEs, and earthquakes can all emerge naturally within this fault volume framework, making it an ideal digital twin for testing hypotheses, performing ground‐truth inversions, and probing mechanical properties inaccessible with natural observations. (10.1029/2025JB032915)
  DOI : 10.1029/2025JB032915
• A Rellich-type theorem for the Helmholtz equation in a junction of stratified media
  
  • Al Humaikani Sarah
  • Bonnet-Ben Dhia Anne-Sophie
  • Fliss Sonia
  • Hazard Christophe
  , 2026. <div><p>We prove that there are no non-zero square-integrable solutions to a two-dimensional Helmholtz equation in some unbounded inhomogeneous domains which represent junctions of stratified media. More precisely, we consider domains that are unions of three half-planes, where each half-plane is stratified in the direction orthogonal to its boundary. As for the well-known Rellich uniqueness theorem for a homogeneous exterior domain, our result does not require any boundary condition. Our proof is based on half-plane representations of the solution which are derived through a generalization of the Fourier transform adapted to stratified media. A byproduct of our result is the absence of trapped modes at the junction of open waveguides as soon as the angles between branches are greater than π/2.</p></div>
• Stability of time stepping methods for discontinuous Galerkin discretizations of Friedrichs' systems
  
  • Imperiale Sébastien
  • Joly Patrick
  • Rodríguez Jerónimo
  , 2025. In this work we study new various energy-based theoretical results on the stability of s-stages, s-th order explicit Runge-Kutta integrators as well as a modified leap-frog scheme applied to discontinuous Galerkin discretizations of transient linear symmetric hyperbolic Friedrichs' systems. We restrict the present study to conservative systems and Cauchy problems.
• A posteriori error estimates for mixed finite element discretization of the multigroup Neutron Simplified Transport equations with Robin boundary condition
  
  • Ciarlet Patrick
  • Do Minh-Hieu
  • Gervais Mario
  • Madiot François
  , 2026. We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) equations, in the case where a Robin (or Fourier type) boundary condition is imposed on the boundary. This boundary condition is of particular importance in neutronics, since it corresponds to the well-known vacuum boundary condition. We provide guaranteed and locally efficient estimators. In particular, a specific estimator is designed to handle the Robin boundary condition. We also develop the theory in the case of mixed imposed boundary conditions, of Dirichlet, Neumann or Fourier type. The approach is further extended to a Domain Decomposition Method, the so-called DD+L 2 jumps method. In this framework, the adaptive mesh refinement strategy is implemented for a discretization using Cartesian meshes on each subdomain. Numerical experiments illustrate the theory.
• Analysis of a two-level domain decomposition preconditioner for the time-harmonic Maxwell equations in anisotropic media
  
  • Bonazzoli Marcella
  • Ciarlet Patrick
  • Modave Axel
  • Rappaport Ari
  , 2026. We analyze a domain decomposition preconditioner, namely a two-level additive Schwarz method, for the time-harmonic Maxwell equations in anisotropic media. The material law is described by a tensor-valued electric permittivity ε, magnetic permeability µ and conductivity σ which are assumed to be uniformly symmetric positive definite in the physical domain. Convergence estimates for the preconditioned GMRES solver are obtained through bounds on the norm and the field-of-values (FOV) of the preconditioned operator. Our purpose is to extend the convergence analysis available for scalar and constant coefficients established in Bonazzoli et al. [5] to this tensorial setting. While the overall argument follows the additive Schwarz framework therein, the anisotropic case requires substantial new ingredients. Among these are a coefficient-weighted discrete Helmholtz decomposition, regularity estimates adapted to the anisotropic setting, and a stronger "high frequency regime" assumption. The latter allows control of unsigned terms that vanish via orthogonality in the scalar case. These tools are crucial for the main technical result: bounding the FOV away from the origin through estimates explicit in the frequency and anisotropy parameters, under suitable resolution assumptions.
• Fluid-structure Green's functions via BEM/BEM coupling for flow induced noise in arbitrary elastic geometries
  
  • Pacaut Louise
  • Chaillat Stéphanie
  • Mercier Jean-François
  • Serre Gilles
  , 2026. We address the challenge of efficiently simulating the noise generated by the interaction of a turbulent flow noise with complex elastic structures, a coupled fluid/structure interaction (FSI) problem. Current approaches typically separate vibro-acoustic and hydro-acoustic contributions, limiting the accuracy of hydrodynamic noise predictions. To overcome this limitation, we develop a numerical method for computing a Green's function tailored to the coupled FSI problem, enabling a monolithic prediction of the radiated noise without separating the two components. This approach not only improves the accuracy of hydrodynamic noise simulations but also significantly reduces computational costs. The Green's function is constructed using a novel integral formulation and solved numerically via a coupled fast BEM/ BEM solver.
• Asymptotic models for time-domain scattering by small particles
  
  • Savchuk Adrian
  , 2026. In this manuscript, we address the problem of time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that achieves a higher convergence rate compared to existing models. Our method relies on a boundary integral formulation, semi-discretized in space using a Galerkin approach, where the main challenge lies in choosing appropriate basis functions for the Galerkin space. We show that using equilibrium densities as basis functions yields a cubic-convergent asymptotic model that ensures a priori stability in the time domain due to the coercivity properties of the single-layer boundary integral operator. Unlike the case of spheres, where entries can be computed explicitly, the generalized method requires double integration, which becomes computationally expensive as the number of particles increases. To address this, we derive a simplified model that preserves the stability and convergence properties of the original formulation, alongside a lower-order but computationally advantageous Born model, providing a rigorous theoretical error analysis for both. When the distance between obstacles decreases with the small parameter, the cubic convergence of the scattered field can no longer be guaranteed. To overcome this limitation, we derive high-order asymptotic models by enriching the basis functions in the Galerkin space to maintain accuracy even for closely clustered particles. Finally, the proposed framework is applied to more complex interactions between a large obstacle and multiple small particles, and is further extended to time-domain electromagnetic scattering by small spheres. Numerical experiments validate the theoretical stability and performance across all proposed models.