Publications

2024

• Modeling fluid injection effects in dynamic fault rupture using Fast Boundary Element Methods
  
  • Bagur Laura
  , 2024. Earthquakes due to either natural or anthropogenic sources cause important human and material damage. In both cases, the presence of pore fluids influences the triggering of seismic instabilities.A new and timely question in the community is to show that the earthquake instability could be mitigated by active control of the fluid pressure. In this work, we study the ability of Fast Boundary Element Methods (Fast BEMs) to provide a multi-physic large-scale robust solver required for modeling earthquake processes, human induced seismicity and their mitigation.In a first part, a Fast BEM solver with different temporal integration algorithms is used. We assess the performances of various possible adaptive time-step methods on the basis of 2D seismic cycle benchmarks available for planar faults. We design an analytical aseismic solution to perform convergence studies and provide a rigorous comparison of the capacities of the different solving methods in addition to the seismic cycles benchmarks tested. We show that a hybrid prediction-correction / adaptive time-step Runge-Kutta method allows not only for an accurate solving but also to incorporate both inertial effects and hydro-mechanical couplings in dynamic fault rupture simulations.In a second part, once the numerical tools are developed for standard fault configurations, our objective is to take into account fluid injection effects on the seismic slip. We choose the poroelastodynamic framework to incorporate injection effects on the earthquake instability. A complete poroelastodynamic model would require non-negligible computational costs or approximations. We justify rigorously which predominant fluid effects are at stake during an earthquake or a seismic cycle. To this aim, we perform a dimensional analysis of the equations, and illustrate the results using a simplified 1D poroelastodynamic problem. We formally show that at the timescale of the earthquake instability, inertial effects are predominant whereas a combination of diffusion and elastic deformation due to pore pressure change should be privileged at the timescale of the seismic cycle, instead of the diffusion model mainly used in the literature.
• Méthodes d'inversion de type one-shot et décomposition de domaine
  
  • Vu Tuan Anh
  , 2024. Notre objectif principal est d’analyser la convergence d’une méthode d’optimisation basée sur le gradient, pour résoudre des problèmes inverses d’identification de paramètres, dans laquelle les problèmes directs et adjoints correspondants sont résolus par un solveur itératif. Le couplage des itérations pour les trois inconnues (le paramètre du problème inverse, la solution du problème direct et la solution du problème adjoint) donne ce que l’on appelle les méthodes d’inversion de type one-shot. De nombreux tests numériques ont montré que l’utilisation de très peu d’itérations internes pour les problèmes directs et adjoints peut néanmoins conduire à une bonne convergence pour le problème inverse. Cela nous motive à développer une théorie de convergence rigoureuse pour les méthodes de type one-shot en utilisant un petit nombre fixe d’itérations internes, avec un schéma semi-implicite pour la mise à jour du paramètre et une fonction de coût régularisée. Notre théorie couvre une classe générale de problèmes inverses linéaires dans le cadre discret de dimension finie, pour lesquels les problèmes directs et adjoints sont résolus par des méthodes génériques d’itération de point fixe. En étudiant le rayon spectral de la matrice par blocs des itérations couplées, nous prouvons que pour des pas de descente suffisamment petits, les méthodes de type one-shot (semi-implicites) convergent. En particulier, dans le cas scalaire, où les inconnues appartiennent à des espaces à une dimension, nous établissons des conditions de convergence suffisantes et même nécessaires sur le pas de descente. Ensuite, nous appliquons des méthodes de type one-shot aux problèmes inverses de conductivité (linéarisés et puis non linéaires), et résolvons les problèmes directs et adjoints par des méthodes de décomposition de domaines, plus spécifiquement des méthodes de Schwarz optimisées sans recouvrement. Nous analysons un algorithme de décomposition de domaine qui calcule simultanément les solutions directe et adjointe pour une conductivité donnée. En combinant cet algorithme avec la mise à jour du paramètre par descente de gradient, nous obtenons une méthode one-shot de décomposition de domaine qui résout le problème inverse. Nous proposons deux versions discrétisées de l’algorithme couplé, dont la seconde (dans le cas du problème inverse de conductivité linéarisé) s’inscrit dans le cadre abstrait de notre théorie de convergence. Enfin, plusieurs expériences numériques sont fournies pour illustrer les performances des méthodes de type one-shot, en comparaison avec la méthode de descente de gradient classique dans laquelle les problèmes directs et adjoints sont résolus par des solveurs directs. En particulier, nous observons que, même dans le cas de données bruitées, très peu d’itérations internes peuvent toujours garantir une bonne convergence des méthodes de type one-shot.
• A Markovian characterization of the exponential twist of probability measures
  
  • Bourdais Thibaut
  • Oudjane Nadia
  • Russo Francesco
  , 2024. 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 "generalized gradient" of some suitable "value function" $v$.
• Whispering Gallery Modes and Frequency Combs: Two excursions in the world of photonic resonators
  
  • Dauge Monique
  • Balac Stéphane
  • Caloz Gabriel
  • Moitier Zoïs
  , 2024. In photonics, resonators are versatile elements designed with the aim of guiding light. They encompass various orders of magnitude for their sizes and the power of their laser sources. Accordingly some effects can be considered as negligible, leading to simplified mathematical models. We will focus on two such models: one related to Whispering Gallery Mode resonators and the other to ring/Fabry-Perot resonators. In the first case the retained model leads to a two-dimensional linear Helmholtz equation in the whole space with material laws having a jump along a bounded interface. The set of complex resonances is analyzed close to the real axis, corresponding to modes concentrated close to the interface. In the second case a one-dimensional model with cubic nonlinearity based on the LugiatoLefever equation is considered. Branches of stationary solutions issued from flat solutions are highlighted, providing frequency comb solutions. (10.17617/3.MBE4AA)
  DOI : 10.17617/3.MBE4AA
• Evaluation of two boundary integral formulations for the Eddy current nondestructive testing of metal structures
  
  • Demaldent Edouard
  • Bakry Marc
  • Merlini Adrien
  • Andriulli Francesco
  • Bonnet Marc
  , 2024, pp.87-88. We investigate two bounary integral formulations for the resolution of the Maxwell equations in the Eddy Current (EC) regime in a context of nondestructive testing (NdT). The first one, based on an approximation of the Maxwell equations, requires a loop-star decomposition of the surface currents and the global loops are constructed manually for non-simply connected domains. The second formulation is stabilized by using quasi-Helmholtz projectors, thus avoiding the definition of global loops. (10.17617/3.MBE4AA)
  DOI : 10.17617/3.MBE4AA
• Computation of a fluid-structure Green's function using a BEM-BEM coupling
  
  • Pacaut Louise
  • Mercier Jean-François
  • Chaillat Stéphanie
  • Serre Gilles
  , 2024. In order to determine the elasto-acoustic noise produced by a boat hull excited by a turbulent boundary layer, we propose a numerical method to compute the acoustic scattering by an elastic body surrounded by a fluid. To reduce the computational costs a Boundary Element Method (BEM) is used. Since the turbulent flow along the hull is known only statistically, a formulation combining the free field acoustic and elastic Green's functions is not adequate. A better suited choice is to determine a global Green's function satisfying the transmission conditions of the fluid-structure problem. The boundary integral representation of the scattered pressure is then simplified. This so-called tailored Green's function is determined by solving an acoustic/elastic coupled problem with a BEM. Here we focus on a particular difficulty: when the source is close to the surface, the numerical accuracy of the Green's function deteriorates. We describe a method to regularize our BEM scheme in this context. We validate the method for the problem of an elastic sphere in water.
• Construction of transparent conditions for electromagnetic waveguides
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Fliss Sonia
  • Parigaux Aurélien
  , 2024. We are interested in the numerical resolution of diffraction problems in closed electromagnetic waveguides by means of finite elements methods. To proceed, we need to truncate the domain and design adapted transparent conditions on the artificial boundary to avoid spurious reflections. When the guide is homogeneous in the transverse section, this can be done by writing an Electric-to-Magnetic condition based on a modal decomposition of the field. The latter takes a rather simple form thanks to the orthogonality of transverse modes. For guides that are heterogeneous in the transverse section, the transverse modes are no longer orthogonal but satisfy bi-orthogonality relations linked to the Poynting energy flux. Modal decompositions are more delicate to derive and it may happen that certain modes have phase and group velocities of different sign, which prevents the use of Perfectly Matched Layers. Adapting techniques already developed in elasticity, we derive a new transparent condition based on a Poynting-to-Magnetic operator with overlap. To illustrate the method, we present numerical results obtained with Nédélec finite elements using the XLiFE++ library.
• Fast and accurate boundary integral equation methods for the multi-layer transmission problem
  
  • Cortes Elsie A
  • Carvalho Camille
  • Chaillat Stéphanie
  • Tsogka Chrysoula
  , 2024. We consider a multi-layer transmission problem, which can be used for example to describe the light scattering in meta-materials (assemblings of various concentric penetrable materials). Our goal is to solve the multi-layer problem accurately with optimal discretization. Generally, the costs to solve this problem grow as more layers are introduced - solving this problem is thus particularly challenging for 3D models. For this reason, we use boundary integral equation (BIE) methods: they reduce the dimensionality of the problem and can provide high order accuracy. However, BIE methods suffer from the so-called close evaluation problem. We address it using modified representations. We further examine how to improve the speed of our method by optimizing the accuracy over number of discretization points ratio. In particular, we investigate whether the usual rule of thumb to mesh interfaces, based on the most constraining material, is necessary for the multi-layer transmission problem. (10.17617/3.MBE4AA)
  DOI : 10.17617/3.MBE4AA
• Substructuring based FEM-BEM coupling for Helmholtz problems
  
  • Boisneault Antonin
  • Bonazzoli Marcella
  • Claeys Xavier
  • Marchand Pierre
  , 2024. This talk concerns the solution of the Helmholtz equation in a medium composed of a bounded heterogeneous domain and an unbounded homogeneous one. Such problems can be expressed using classical FEM-BEM coupling techniques. We solve these coupled formulations using iterative solvers based on substructuring Domain Decomposition Methods (DDM), and aim to develop a convergence theory, with fast and guaranteed convergence. A recent article of Xavier Claeys proposed a substructuring Optimized Schwarz Method, with a nonlocal exchange operator, for Helmholtz problems on a bounded domain with classical conditions on its boundary (Dirichlet, Neumann, Robin). The variational formulation of the problem can be written as a bilinear application associated with the volume and another with the surface, for which, under certain sufficient assumptions, convergence of the DDM strategy is guaranteed. In this presentation we show how some specific FEM-BEM coupling methods fit, or not, the previous framework, in which we consider Boundary Integral Equations (BIEs) instead of classical boundary conditions. In particular, we prove that the symmetric Costabel coupling satisfies the framework assumptions, implying that the convergence is guaranteed. (10.17617/3.MBE4AA)
  DOI : 10.17617/3.MBE4AA
• High-Resolution Seismic Imaging for Dam-Rock Interface using Full-Waveform Inversion
  
  • Aziz Boukraa Mohamed
  • Audibert Lorenzo
  • Bonazzoli Marcella
  • Haddar Houssem
  • Vautrin Denis
  , 2024. We are interested in imaging the interface between the concrete structure of the hydroelectric dam and the underlying rock using non-destructive seismic waves. Our method, combining "Full Waveform Inversion" with shape optimization, produces high-resolution images. Numerical results from realistic synthetic data demonstrate the method ability to accurately recover the interface with a limited number of measurements. (10.17617/3.MBE4AA)
  DOI : 10.17617/3.MBE4AA
• Efficient methods for the solution of boundary integral equations on fractal antennas
  
  • Joly Patrick
  • Kachanovska Maryna
  • Moitier Zoïs
  , 2024. This work focuses on construction of efficient numerical methods for wave scattering by fractal antennas, see [3]. It builds on the theoretical basis proposed in the recent work [1], which establishes boundary integral (BIE) formulations for solving sound-soft Helmholtz scattering problems on fractal screens. An important feature of such formulations is the use of the Hausdorff measure on fractals instead of the standard Lebesgue’s measure. This adds an extra dimension to the two classical difficulties encountered with numerical BEM simulations, namely the evaluation of boundary integrals and the fact that the underlying matrices are dense. Our idea is to exploit the Hausdorff measure’s self-similar structure in order to deal with these difficulties. (10.17617/3.MBE4AA)
  DOI : 10.17617/3.MBE4AA
• Crouzeix-Raviart elements on simplicial meshes in $d$ dimensions
  
  • Bohne Nis-Erik
  • Ciarlet Patrick
  • Sauter Stefan
  , 2024. In this paper we introduce Crouzeix-Raviart elements of general polynomial order $k$ and spatial dimension $d\geq2$ for simplicial finite element meshes. We give explicit representations of the non-conforming basis functions and prove that the conforming companion space, i.e., the conforming finite element space of polynomial order $k$ is contained in the Crouzeix-Raviart space. We prove a direct sum decomposition of the Crouzeix-Raviart space into (a subspace of) the conforming companion space and the span of the non-conforming basis functions. Degrees of freedom are introduced which are bidual to the basis functions and give rise to the definition of a local approximation/interpolation operator. In two dimensions or for $k=1$, these freedoms can be split into simplex and $(d-1)$ dimensional facet integrals in such a way that, in a basis representation of Crouzeix-Raviart functions, all coefficients which belong to basis functions related to lower-dimensional faces in the mesh are determined by these facet integrals. It will also be shown that such a set of degrees of freedom does not exist in higher space dimension and $k>1$.
• Multistage stochastic optimization of a mono-site hydrogen infrastructure by decomposition techniques
  
  • Lefgoum Raian
  • Afsar Sezin
  • Carpentier Pierre
  • Chancelier Jean-Philippe
  • de Lara Michel
  Journal of Optimization Theory and Applications, Springer Verlag, 2024, 207 (3), pp.49. The development of hydrogen infrastructures requires to reduce their costs. In this paper, we develop a multistage stochastic optimization model for the management of a hydrogen infrastructure which consists of an electrolyser, a compressor and a storage to serve a transportation demand. This infrastructure is powered by three different sources: on-site photovoltaic panels (PV), renewable energy through a power purchase agreement (PPA) and the power grid. We consider uncertainties affecting on-site photovoltaic production and hydrogen demand. Renewable energy sources are emphasized in the hydrogen production process to ensure eligibility for a subsidy, which is awarded if the proportion of nonrenewable electricity usage stays under a predetermined threshold. We solve the multistage stochastic optimization problem using a decomposition method based on Lagrange duality. The numerical results indicate that the solution to this problem, formulated as a policy, achieves a small duality gap, thus proving the effectiveness of this approach. (10.1007/s10957-025-02795-1)
  DOI : 10.1007/s10957-025-02795-1
• Contributions to Efficient Finite Element Solvers for Time-Harmonic Wave Propagation Problems
  
  • Modave Axel
  , 2024. The numerical simulation of wave propagation phenomena is of paramount importance in many scientific and engineering disciplines. Many time-harmonic problems can be solved with finite elements in theory, but the computational cost is a strong constraint that limits the size of the problems and the accuracy of the solutions in practice. Ideally, solution techniques should provide the best accuracy at minimal computational cost for real-world problems. They should take advantage of the power of modern parallel computers, and they should be as easy as possible to use for the end user. In this HDR thesis, contributions are presented on three topics: the improvement of domain truncation techniques (i.e. high-order absorbing boundary conditions and perfectly matched layers), the acceleration of substructuring and preconditioning techniques based on domain decomposition methods (i.e. non-overlapping domain decomposition methods with interface conditions based on domain truncation techniques), and the design of a new hybridization approach for efficient discontinuous finite element solvers.
• Imaging a dam-rock interface with inversion of a full elastic-acoustic model
  
  • Boukraa Mohamed Aziz
  • Bonazzoli Marcella
  • Haddar Houssem
  • Audibert Lorenzo
  • Vautrin Denis
  , 2024. We are interested in imaging the interface between the concrete structure of hydroelectric dams and the rock foundation using non-destructive seismic waves. We present a geophysical technique for processing seismic measurements to obtain an image of the interface with metric resolution. The proposed technique is based on "Full Waveform Inversion" with a shape optimization approach. Numerical results using synthetic measurements demonstrate the method ability to accurately recover the interface with a limited number of measurement points and in the presence of noise.
• Inverse optimal control problem in the non autonomous linear-quadratic case
  
  • Jean Frédéric
  • Maslovskaya Sofya
  , 2024. Inverse optimal control problem emerges in different practical applications, where the goal is to design a cost function in order to approximate given optimal strategies of an expert. Typical application is in robotics for generation of human motions. In this paper we analyze a general class of non autonomous inverse linear quadratic problems. This class of problems is of particular interest because it arises as a linearization of a nonlinear problem around an optimal trajectory. The addressed questions are the injectivity of the inverse problem and the reconstruction. We show that the nonlinear problem admits the same characterization of the injectivity as the autonomous one. In the autonomous case we show moreover that the injectivity property is generic in the considered class. We also provide a numerical test of the reconstruction algorithm in the autonomous setting.
• Heat and momentum losses in H 2 –O2 –N 2/Ar detonations: on the existence of set-valued solutions with detailed thermochemistry
  
  • Veiga-López F.
  • Faria Luiz
  • Melguizo-Gavilanes J.
  Shock Waves, Springer Verlag, 2024, 34 (3), pp.273-283. The effect of heat and momentum losses on the steady solutions admitted by the reactive Euler equations with sink/source terms is examined for stoichiometric hydrogen–oxygen mixtures. Varying degrees of nitrogen and argon dilution are considered in order to access a wide range of effective activation energies, $$E_{\textrm{a,eff}}/R_{\textrm{u}}T_{0}$$ E a,eff / R u T 0 , when using detailed thermochemistry. The main results of the study are discussed via detonation velocity-friction coefficient ( D – $$c_{\textrm{f}}$$ c f ) curves. The influence of the mixture composition is assessed, and classical scaling for the prediction of the velocity deficits, $$D(c_{\textrm{f,crit}})/D_{\textrm{CJ}}$$ D ( c f,crit ) / D CJ , as a function of the effective activation energy, $${E}_{\textrm{a,eff}}/R_{\textrm{u}} T_{0}$$ E a,eff / R u T 0 , is revisited. Notably, a map outlining the regions where set-valued solutions exist in the $$E_{\textrm{a,eff}}/R_{\textrm{u}}T_{0}\text {--}{\alpha }$$ E a,eff / R u T 0 -- α space is provided, with $$\alpha $$ α denoting the momentum–heat loss similarity factor, a free parameter in the current study. (10.1007/s00193-024-01182-5)
  DOI : 10.1007/s00193-024-01182-5
• An algorithm for computing scattering poles based on dual characterization to interior eigenvalues
  
  • Cakoni Fioralba
  • Haddar Houssem
  • Zilberberg Dana
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2024, 480 (2292). We present an algorithm for the computation of scattering poles for an impenetrable obstacle with Dirichlet or Robin boundary conditions in acoustic scattering. This paper builds upon the previous work of Cakoni et al . (2020) titled ‘A duality between scattering poles and transmission eigenvalues in scattering theory’ (Cakoni et al . 2020 Proc. A. 476 , 20200612 ( doi:10.1098/rspa.2020.0612 )), where the authors developed a conceptually unified approach for characterizing the scattering poles and interior eigenvalues corresponding to a scattering problem. This approach views scattering poles as dual to interior eigenvalues by interchanging the roles of incident and scattered fields. In this framework, both sets are linked to the kernel of the relative scattering operator that maps incident fields to scattered fields. This mapping corresponds to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Leveraging this dual characterization and inspired by the generalized linear sampling method for computing the interior eigenvalues, we present a novel numerical algorithm for computing scattering poles without relying on an iterative scheme. Preliminary numerical examples showcase the effectiveness of this computational approach. (10.1098/rspa.2024.0015)
  DOI : 10.1098/rspa.2024.0015
• Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control
  
  • Berret Bastien
  • Verdel Dorian
  • Burdet Etienne
  • Jean Frédéric
  PLoS Computational Biology, PLOS, 2024, 20 (11), pp.e1012598. Despite our environment is often uncertain, we generally manage to generate stable motor behaviors. While reactive control plays a major role in this achievement, proactive control is critical to cope with the substantial noise and delays that affect neuromusculoskeletal systems. In particular, muscle co-contraction is exploited to robustify feedforward motor commands against internal sensorimotor noise as was revealed by stochastic optimal open-loop control modeling. Here, we extend this framework to neuromusculoskeletal systems subjected to random disturbances originating from the environment. The analytical derivation and numerical simulations predict a singular relationship between the degree of uncertainty in the task at hand and the optimal level of anticipatory co-contraction. This prediction is confirmed through a single-joint pointing task experiment where an external torque is applied to the wrist near the end of the reaching movement with varying probabilities across blocks of trials. We conclude that uncertainty calls for impedance control via proactive muscle co-contraction to stabilize behaviors when reactive control is insufficient for task success. (10.1101/2024.06.17.599269)
  DOI : 10.1101/2024.06.17.599269
• New computable algorithms for smooth multiobjective optimization problems
  
  • Grad Sorin-Mihai
  • Illés Tibor
  • Rigó Petra Renáta
  , 2024. We propose new practical algorithms for solving smooth multiobjective optimization problems based on determining joint decreasing directions via suitable linear programming problems. The presented iterative method is specialized for unconstrained, sign constrained and linearly constrained multiobjective optimization problems. In all cases we show that the objective function values sequence is decreasing with respect to the considered nonnegative orthant while the iterates are feasible. Furthermore, we prove that every accumulation point of the sequence generated by the algorithm, if any, is a substationary point to the considered multiobjective optimization problem, and, under convexity assumptions, it is actually a weakly Pareto efficient (also known as weakly Pareto-optimal) point. Different to similar algorithms from the literature, the ones proposed in this work involve joint decreasing directions that are easily computable in polynomial time by solving linear programming problems. The computational performance of our algorithms has been illustrated on convex unconstrained and convex linearly constrained multiobjective optimization problems.
• Generalized impedance boundary conditions with vanishing or sign-changing impedance
  
  • Bourgeois Laurent
  • Chesnel Lucas
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2024, 56 (3), pp.4223-4251. We consider a Laplace type problem with a generalized impedance boundary condition of the form ∂_νu = −∂_x(g∂_xu) on a flat part Γ of the boundary. Here ν is the outward unit normal vector to ∂Ω, g is the impedance function and x is the coordinate along Γ. Such problems appear for example in the modelling of small perturbations of the boundary. In the literature, the cases g=1 or g=−1 have been investigated. In this work, we address situations where Γ contains the origin and g(x)=1_{x>0}(x)x^\alpha or g(x)=−sign(x)|x|^\alpha with \alpha≥ 0. In other words, we study cases where g vanishes at the origin and changes its sign. The main message is that the well-posedness in the Fredholm sense of the corresponding problems depends on the value of \alpha. For \alpha∈ [0,1), we show that the associated operators are Fredholm of index zero while it is not the case when \alpha=1. The proof of the first results is based on the reformulation as 1D problems combined with the derivation of compact embedding results for the functional spaces involved in the analysis. The proof of the second results relies on the computation of singularities and the construction of Weyl's sequences. We also discuss the equivalence between the strong and weak formulations, which is not straightforward. Finally, we provide simple numerical experiments which seem to corroborate the theorems. (10.1137/23M1604217)
  DOI : 10.1137/23M1604217
• Time Consistency for Multistage Stochastic Optimization Problems under Constraints in Expectation
  
  • Carpentier Pierre
  • Chancelier Jean-Philippe
  • de Lara Michel
  SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2024, 34 (2), pp.1909-1936. We consider sequences-indexed by time (discrete stages)-of families of multistage stochastic optimization problems. At each time, the optimization problems in a family are parameterized by some quantities (initial states, constraint levels.. .). In this framework, we introduce an adapted notion of time consistent optimal solutions, that is, solutions that remain optimal after truncation of the past and that are optimal for any values of the parameters. We link this time consistency notion with the concept of state variable in Markov Decision Processes for a class of multistage stochastic optimization problems incorporating state constraints at the final time, either formulated in expectation or in probability. For such problems, when the primitive noise random process is stagewise independent and takes a finite number of values, we show that time consistent solutions can be obtained by considering a finite dimensional state variable. We illustrate our results on a simple dam management problem. (10.1137/22M151830X)
  DOI : 10.1137/22M151830X
• Optimal computation of integrals in the Half-Space Matching method for modal simulation of SHM/NDE in 3D elastic plate
  
  • Allouko Amond
  • Bonnet-Ben Dhia Anne-Sophie
  • Lhémery Alain
  • Baronian Vahan
  Journal of Physics: Conference Series, IOP Science, 2024, 2768, pp.012004. Simulating structural health monitoring (SHM) or nondestructive evaluation (NDE) methods based on elastic guided waves (GW) is very helpful to handle their complexity (co-existence of several GW modes, frequency dependence of wavespeed) and to further design optimal methods of inspection offering high sensitivity to the sought flaws. The half-space matching (HSM) method has been established for the development of a model that hybridizes local finite element (FE) computations for GW scattering by a flaw, with a modal semi-analytical model for GW radiation and propagation in flawless plate-like structures. Highly oscillatory Integral formulae appear in the HSM method that radiate the scattered field away from the FE zone as the superimposition of modal contributions, which computation can be time-consuming. The present work is concerned with their optimal computation. Integral of this form can be efficiently computed under the far-field approximation but this classical technique fails at predicting accurately wavefields at relatively short distances (small number of wavelengths). The method developed herein relies on the complexification of the integrals to be computed and on specific deformation of integration paths in the complex plane, as detailed in the paper. It allows the evaluation of the integrals without approximation other than that of numerical quadratures, ensuring high accuracy while offering high computing performances. It indifferently applies in the far-field and in the near-field. The method of computation is validated by comparing its predictions with a reference solution of GW scattering. Its computational performances are also demonstrated, compared to those of the standard computation of the HSM integral formulae to be computed and on specific deformation of integration paths in the complex plane, as detailed in the paper. It allows the evaluation of the integrals without approximation other than that of numerical quadratures, ensuring high accuracy while offering high computing performances. It indifferently applies in the far-field and in the near-field. The method of computation is validated by comparing its predictions with a reference solution of GW scattering. Its computational performances are also demonstrated, compared to those of the standard computation of the HSM integral formulae. (10.1088/1742-6596/2768/1/012004)
  DOI : 10.1088/1742-6596/2768/1/012004
• Automated far-field sound field estimation combining robotized acoustic measurements and the boundary elements method
  
  • Pascal Caroline
  • Marchand Pierre
  • Chapoutot Alexandre
  • Doaré Olivier
  , 2024. The identification and reconstruction of acoustic fields radiated by unknown structures isusually performed using either Sound Field Estimation (SFE) or Near-field Acoustic Holog-raphy (NAH) techniques. The latter turns out to be especially useful when data is onlyavailable close to the source, but information throughout the whole space is needed.Yet, the lack of amendable and efficient implementations of state-of-the-art solutions, aswell as the laborious and often lengthy deployment of acoustic measurements continue to besignificant obstacles to the practical application of such methods.The purpose of this work is to address both problems. First, a completely automated metrol-ogy setup is proposed, in which a robotic arm is used to gather extensive, yet accurate ge-ometric and acoustic data without any human intervention. The impact of the robot onacoustic pressure measurements has been cautiously estimated, and proved to remain negli-gible within a defined validity frequency range.The sound field prediction is then tackled using the Boundary Element Method (BEM), andimplemented using the FreeFEM++ BEM library. Numerically simulated measurements haveallowed us to assess the method accuracy, which matches theoretically expected results, androbustness against positioning inaccuracies, provided that the robot is carefully calibrated.The overall solution has been successfully tested using actual robotized measurements of anunknown loudspeaker, with a reconstruction error of less than 30 % on the previously definedvalidity frequency range
• Multidomain FEM-BEM coupling for acoustic scattering
  
  • Bonazzoli Marcella
  • Claeys Xavier
  Journal of Integral Equations and Applications, Rocky Mountain Mathematics Consortium, 2024, 36 (2), pp.129-167. We model time-harmonic acoustic scattering by an object composed of piece-wise homogeneous parts and an arbitrarily heterogeneous part. We propose and analyze new formulations that couple, adopting a Costabel-type approach, boundary integral equations for the homogeneous subdomains with volume variational formulations for the heterogeneous subdomain. This is an extension of the Costabel FEM-BEM coupling to a multi-domain configuration, with cross-points allowed, i.e. points where three or more subdomains are adjacent. While generally just the exterior unbounded subdomain is treated with the BEM, here we wish to exploit the advantages of BEM whenever it is applicable, that is, for all the homogeneous parts of the scattering object. Our formulation is based on the multi-trace formalism, which initially was introduced for acoustic scattering by piece-wise homogeneous objects. Instead, here we allow the wavenumber to vary arbitrarily in a part of the domain. We prove that the bilinear form associated with the proposed formulation satisfies a Gårding coercivity inequality, which ensures stability of the variational problem if it is uniquely solvable. We identify conditions for injectivity and construct modified versions immune to spurious resonances. (10.1216/jie.2024.36.129)
  DOI : 10.1216/jie.2024.36.129