6.1.1 Coupled iterations of domain decomposition and gradient descent methods for inverse problems solution

L. Audibert, M. Bonazzoli, H. Haddar, T. A. Vu

The aim of this work is to analyze the convergence of the gradient descent method to solve inverse problems, where the corresponding forward problem is solved iteratively, by fixed point or Krylov subspace methods, preconditioned with domain decomposition techniques. In particular, we are interested in the case where the inner iterations are incomplete, i.e. stopped before achieving convergence. One-shot methods, which iterate at the same time on the forward problem solution and on the inverse problem unknown, have been studied in the optimization literature where strong convexity is usually assumed to ensure convergence. In the framework of inverse problems such assumptions are not verified in general. As a first step, the analysis is being performed on the case of linear inverse problems.

6.1.2 Qualitative indicator functions for imaging crack networks using acoustic waves

L. Audibert, L. Chesnel, H. Haddar, K. Napal

We consider the problem of imaging a crack network embedded in some homogeneous background from measured multi-static far field data generated by acoustic plane waves. We propose two novel approaches that can be seen as extensions of linear sampling-type methods and that provide indicator functions which are sensitive to local cracks densities. The first approach uses multiple frequencies data to compute spectral signatures associated with artificially embedded localized obstacles. The second approach also exploits the idea of incorporating an artificial background but uses data for a single frequency. The indicator function is built using a similar concept as for differential sampling methods: compare the solution of the interior transmission problem for healthy inclusion with the one with embedded cracks. The performance of the methods is tested and discussed on synthetic examples and the numerical results are compared with the ones obtained using the classical factorization method. 1

6.1.3 Differential tomography of micromechanical evolution in elastic materials of unknown micro/macrostructure

H. Haddar and F. Pourahmadian

Differential evolution indicators are introduced for 3D spatiotemporal imaging of micromechanical processes in complex materials where progressive variations due to manufacturing and/or aging are housed in a highly scattering background of a-priori unknown or uncertain structure. In this vein, a three-tier imaging platform is established where: (1) the domain is periodically (or continuously) subject to illumination and sensing in an arbitrary configuration; (2) sequential sets of measured data are deployed to distill segment-wise scattering signatures of the domain's internal structure through carefully constructed, non-iterative solutions to the scattering equation; and (3) the resulting solution sequence is then used to rigorously construct an imaging functional carrying appropriate invariance with respect to the unknown stationary components of the background e.g., pre-existing interstitial boundaries and bubbles. This gives birth to differential indicators that specifically recover the 3D support of micromechanical evolution within a network of unknown scatterers. The direct scattering problem is formulated in the frequency domain where the background is comprised of a random distribution of monolithic fragments. The constituents are connected via highly heterogeneous interfaces of unknown elasticity and dissipation which are subject to spatiotemporal evolution. The support of internal boundaries are sequentially illuminated by a set of incident waves and thusinduced scattered fields are captured over a generic observation surface. The performance of the proposed imaging indicator is illustrated through a set of numerical experiments for spatiotemporal reconstruction of progressive damage zones featuring randomly distributed cracks and bubbles 19.

6.1.4 A Factorization Method for Inverse Time Domain Obstacles with Impedance Boundary Conditions

H. Haddar and X. Liu

We develop a factorization method to obtain explicit characterization of a (possibly non-convex) impedance scattering object from measurements of time-dependent causal scattered waves in the far field regime. In particular, we prove that far fields of solutions to the wave equation due to particularly modified incident waves, characterize the obstacle by a range criterion involving the square root of the time derivative of the corresponding far field operator. Our analysis makes essential use of a coercivity property of the solution of the initial boundary value problem for the wave equation in the Laplace domain. This forces us to consider this particular modification of the far field operator. The latter in fact, can be chosen arbitrarily close to the true far field operator given in terms of physical measurements. We provide validating numerical examples in 2D on synthetic data. The latter is generated using a FDTD solver with PML 15.

6.1.5 Factorization Method for Imaging a Local Perturbation in Inhomogeneous Periodic Layers from Far Field Measurements

H. Haddar and A. Konschin

We analyze the Factorization method to reconstruct the geometry of a local defect in a periodic absorbing layer using almost only incident plane waves at a fixed frequency. A crucial part of our analysis relies on the consideration of the range of a carefully designed far field operator, which characterizes the geometry of the defect. We further provide some validating numerical results in a two dimensional setting 14.

6.1.6 Shape reconstruction of deposits inside a steam generator using eddy current measurements

L. Audibert, H. Girardon and H. Haddar

Non-destructive testing is an essential tool to assess the safety of the facilities within nuclear plants. In particular, conductive deposits on U-tubes in steam generators constitute a major danger as they may block the cooling loop. To detect these deposits, eddy-current probes are introduced inside the U-tubes to generate currents and measuring back an impedance signal. Based on earlier work on this subject, we develop a shape optimization technique with regularized gradient descent to invert these measurements and recover the deposit shape. To deal with the unknown, and possibly complex, topological nature of the latter, we propose to model it using a level set function. The methodology is first validated on synthetic axisymmetric configurations and fast convergence in ensured by careful adaptation of the gradient steps and regularization parameters. We then consider a more realistic modeling that incorporates the support plate and the presence of imperfections on the tube interior section. We employ in particular an asymptotic model to take into account these imperfections and treat them as additional unknowns in our inverse problem. A multi-objective optimization strategy, based on the use of different operating frequencies, is then developed to solve this problem. Various numerical experimentation with synthetic data demonstrated the viability of our approach. The approach is also successfully validated against experimental data 25. The approach is then extended to the full 3D eddy current model where various HPC techniques have been incorporated to make the inversion time plausible for industrial test cases 24.

6.1.7 On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates

L. Bourgeois, L. Chesnel

We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a small parameter $\epsilon >0$. In this context, in order to prove convergence of finite elements methods, it is necessary to get regularity results of the solutions to these regularized problems which hold uniformly in $\epsilon$. In the present work, we obtain these results in smooth domains and in 2D polygonal geometries. In presence of corners, due the particular structure of the regularized problems, classical techniques à la Grisvard do not work and instead, we apply the Kondratiev approach. We describe the procedure in detail to keep track of the dependence in $\epsilon$ in all the estimates. The main originality of this study lies in the fact that the limit problem is ill-posed in any framework 4.

6.1.8 Data Completion Method For the Helmholtz Equation Via Surface Potentials for Partial Cauchy Data

M. Aussal, Y. Boukari and H. Haddar

We propose and study a data completion algorithm for recovering missing data from the knowledge of Cauchy data on parts of the same boundary. The algorithm is based on surface representation of the solution and is presented for the Helmholtz equation. This work is an extension of the data completion algorithm proposed by the two last authors where the case of data available of a closed boundary was studied. The proposed method is a direct inversion method robust with respect to noisy incompatible data. Classical regularization methods with discrepancy selection principles can be employed and automatically lead to a convergent schemes as the noise level goes to zero. We conduct 3D numerical investigations to validate our method on various synthetic examples 2.

6.2.1 A duality between scattering poles and transmission eigenvalues in scattering theory

F. Cakoni, D. Colton, H. Haddar

We develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields, corresponding to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Our discussion includes the scattering problem for a Dirichlet obstacle where duality is between scattering poles and Dirichlet eigenvalues, and the inhomogeneous scattering problem where the duality is between scattering poles and transmission eigenvalues. Our new characterization of the scattering poles suggests a numerical method for their computation in terms of scattering data for the corresponding interior scattering problem 6.

6.2.2 A continuation method for building invisible obstacles in waveguides

A. Bera, A.-S. Bonnet-Ben Dhia, L. Chesnel

We consider the propagation of acoustic waves at a given wavenumber in a waveguide which is unbounded in one direction. We explain how to construct penetrable obstacles characterized by a physical coefficient $\rho$ which are invisible in various ways. In particular, we focus our attention on invisibility in reflection (the reflection matrix is zero), invisibility in reflection and transmission (the scattering matrix is the same as if there were no obstacle) and relative invisibility (two different obstacles have the same scattering matrix). To study these problems, we use a continuation method which requires to compute the scattering matrix $𝕊\left(\rho \right)$ as well as its differential with respect to the material index $d𝕊\left(\rho \right)$. The justification of the method also needs for the proof of abstract results of ontoness of well-chosen functionals constructed from the terms of $d𝕊\left(\rho \right)$. We provide a complete proof of the results in monomode regime when the wavenumber is such that only one mode can propagate. And we give all the ingredients to implement the method in multimoderegime. We also present numerical results to illustrate the analysis. 3

6.2.3 Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides

L. Chesnel, S.A. Nazarov

We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid variation for real frequencies in a vicinity of a complex resonance located close to the real axis. This is the so-called Fano resonance phenomenon. And when the geometry presents certain properties of symmetry, there are two different real frequencies such that we have either $R=0$ or $T=0$, where $R$ and $T$ denote the reflection and transmission coefficients. In this work, we prove that without the assumption of symmetry of the geometry, quite surprisingly, there is always one real frequency for which we have $T=0$. In this situation, all the energy sent in the waveguide is backscattered. However in general, we do not have $R=0$ in the process. We provide numerical results to illustrate our theorems. 7

6.2.4 Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater topography

L. Chesnel, S.A. Nazarov, J. Taskinen

We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an arbitrary prescribed wave number. To proceed, we compute asymptotic expansions of the diffraction solutions with respect to the small parameter of the geometry taking into account the existence of boundary layer phenomena. We establish error estimates to validate the expansions using advances techniques of weighted spaces with detached asymptotics. In the process, we show the absence of trapped surface waves for perturbations small enough. This analysis furnishes asymptotic formulas for the scattering matrix and we use them to determine underwater topographies which are non-reflecting. Theoretical and numerical examples are given. 8

6.3.1 Domain decomposition preconditioners for non-self-adjoint or indefinite problems

M. Bonazzoli, X. Claeys, F. Nataf, P.-H. Tournier

In this work we analyze the convergence of the one-level overlapping domain decomposition preconditioner SORAS (Symmetrized Optimized Restricted Additive Schwarz) applied to a generic linear system whose matrix is not necessarily symmetric/self-adjoint nor positive definite. By generalizing the theory for the Helmholtz equation developed in [I.G. Graham, E.A. Spence, and J. Zou, SIAM J.Numer.Anal., 2020], we identify a list of assumptions and estimates that are sufficient to obtain an upper bound on the norm of the preconditioned matrix, and a lower bound on the distance of its field of values from the origin. We stress that our theory is general in the sense that it is not specific to one particular boundary value problem. Moreover, it does not rely on a coarse mesh whose elements are sufficiently small. As an illustration of this framework, we prove new estimates for overlapping domain decomposition methods with Robin-type transmission conditions for the heterogeneous reaction-convection-diffusion equation. An article on this topic has been submitted 26.

6.3.2 Multi-Trace FEM-BEM formulation for acoustic scattering by composite objects

M. Bonazzoli, X. Claeys

This work is about the scattering of an acoustic wave by an object composed of piecewise homogenous parts and an arbitrarily heterogeneous part. We propose and analyze a formulation that couples, adopting a Costabel-type approach, boundary integral equations for the homogeneous subdomains with domain variational formulations for the heterogenous subdomain. This is an extension of Costabel FEM-BEM coupling to a multi-domain configuration, with junctions points allowed, i.e. points where three or more subdomains abut. Usually just the exterior unbounded subdomain is treated with the BEM; here we wish to exploit the BEM whenever it is applicable, that is for all the homogenous parts of the scattering object, since it yields a reduction in the number of unknowns compared to the FEM. Our formulation is based on the multi-trace formalism for acoustic scattering by piecewise homogeneous objects; 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. An article on this topic will be submitted soon.

6.4.1 Design of an acoustic energy distributor using thin resonant slits

L. Chesnel, S.A. Nazarov

We consider the propagation of time harmonic acoustic waves in a device with three channels. The wave number is chosen such that only the piston mode can propagate. The main goal of this work is to present a geometry which can serve as an energy distributor. More precisely, the geometry is first designed so that for an incident wave coming from one channel, the energy is almost completely transmitted in the two other channels. Additionally, tuning a bit two geometrical parameters, we can control the ratio of energy transmitted in the two channels. The approach is based on asymptotic analysis for thin slits around resonance lengths. We also provide numerical results to illustrate the theory. 30

6.4.2 Abnormal acoustic transmission in a waveguide with perforated screens

L. Chesnel, S.A. Nazarov

We consider the propagation of the piston mode in an acoustic waveguide obstructed by two screens with small holes. In general, due to the features of the geometry, almost no energy of the incident wave is transmitted through the structure. The goal of this article is to show that tuning carefully the distance between the two screens, which form a resonator, one can get almost complete transmission. We obtain an explicit criterion, not so obvious to intuit, for this phenomenonto happen. Numerical experiments illustrate the analysis. 29

6.5.1 Maxwell's equations with hypersingularities at a conical plasmonic tip

A.-S. Bonnet-Ben Dhia, L. Chesnel, M. Rihani

In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic field exhibits strongly oscillating singularities at the tip which have infinite energy. Consequently Maxwell's equations are not well-posed inthe classical $L^2$ framework. The goal of the present work is to provide an appropriate functional setting for 3D Maxwell's equations when the dielectric permittivity (but not the magnetic permeability) takes critical values. Following what has been done for the 2D scalar case, the idea is to work in weighted Sobolev spaces, adding to the space the so-called outgoing propagating singularities. The analysis requires new results of scalar and vector potential representations of singular fields. The outgoing behaviour is selected via the limiting absorption principle. 27

6.5.2 Homogenization of Maxwell's equations and related scalar problems with sign-changing coefficients

R. Bunoiu, L. Chesnel, K. Ramdani, M. Rihani

In this work, we are interested in the homogenization of time-harmonic Maxwell's equations in a composite medium with periodically distributed small inclusions of a negative material. Here a negative material is a material modelled by negative permittivity and permeability. Due to the sign-changing coefficients in the equations, it is not straightforward to obtain uniform energy estimates to apply the usual homogenization techniques. The goal of this work is to explain how to proceed in this context. The analysis of Maxwell's equations is based on a precise study of two associated scalar problems: one involving the sign-changing permittivity with Dirichlet boundary conditions, another involving the sign-changing permeability with Neumann boundary conditions. For both problems, we obtain a criterion on the physical parameters ensuring uniform invertibility of the corresponding operators as the size of the inclusions tends to zero. In the process, we explain the link existing with the so-called Neumann-Poincaré operator, complementing the existing literature on this topic. Then we use the results obtained for the scalar problems to derive uniform energy estimates for Maxwell's system. At this stage, an additional difficulty comes from the fact that Maxwell's equations are also sign-indefinite due to the term involving the frequency. To cope with it, we establish some sort of uniform compactness result 5.

6.7.1 Bayesian inference of thermodynamic models from vapor flow experiments

Giulio Gori, Olivier P. Le Maître, Pietro M. Congedo

The present work concerns the inference of the coefficients of fluid-dependent thermodynamic models, applicable to complex molecular compounds with non-ideal effects. The main objective is to numerically assess the potential of using experimental measurements of some expansion flows to infer the model parameters. The Bayesian formulation incorporates uncertainties in the flow conditions and measurement errors and compares the measurements with the predictions of Computational Fluid Dynamics (CFD) simulations which depend on the parameter values. The resulting parameters posterior distribution is sampled using a Markov-Chain Monte-Carlo method. Polynomial-Chaos (PC) surrogates substitute the CFD predictions in the definition of the Bayesian posterior, in order to alleviate the computational burden of solving multiple CFD problems. We rely on synthetic data i.e., generated numerically, to assess the potential of expansion flow experiments. Using synthetic data prevents experimental bias, enables the control of model errors (thermodynamic and flow models) and permits the measurement of quantities in conditions that would be hardly achievable in practice. We test three expansion flows with increasing non-ideal effects. Our analyses reveal that the considered experiments have limited potential for the inference of the thermodynamic coefficients. Measuring the temperature, in addition to pressure, improves the posterior knowledge of the specific heat ratio, but other parameters remain highly uncertain. Also, the selection of an expansion condition yielding higher non-ideal effects somehow improves the inference, but the trend is limited, and experimenting with these conditions may be challenging. Our work also supports the use of Bayesian analysis with synthetic data to investigate, analyze, and design new experiments in the future.

6.7.2 A surrogate-based optimal likelihood function for the Bayesian calibration of catalytic recombination in atmospheric entry protection materials

A. Del Val, O.P. Le Maitre, P.M. Congedo, T. Magin, O. Chazot

This work deals with the inference of catalytic recombination parameters from plasma wind tunnel experiments for reusable thermal protection materials. One of the critical factors affecting the performance of such materials is the contribution to the heat flux of the exothermic recombination reactions at the vehicle surface. The main objective of this work is to develop a dedicated Bayesian framework that allows us to compare uncertain measurements with model predictions which depend on the catalytic parameter values. Our framework accounts for all the uncertainties involved in the model definition and incorporates all measured variables with their respective uncertainties. The physical model used for the estimation consists of a 1D boundary layer solver along the stagnation line. The chemical production term included in the surface mass balance depends on the catalytic recombination efficiency. As not all the different quantities needed to simulate a reacting boundary layer can be measured or known (such as the flow enthalpy at the inlet boundary), we propose an optimization procedure built on the construction of the likelihood function to determine their most likely values based on the available experimental data. This procedure avoids the need to introduce any a priori estimates on the nuisance quantities, namely, the boundary layer edge enthalpy, static and dynamic pressures, and wall temperatures, which would entail the use of very wide priors. Furthermore, we substitute the optimal likelihood of the experimental measurements with a surrogate model to make the inference procedure both faster and more robust. We show that the resulting Bayesian formulation yields meaningful and accurate posterior probability distributions of the catalytic parameters with a reduction of more than twenty pourcent of the standard deviation with respect to previous works. We also study the implications of an extension of the experimental procedure on the improvement of the quality of the inference.

6.8.1 A confidence-based Aerospace Design Approach Robust to structural Turbulence Closure Uncertainty

G. Gori, P.M. Congedo, O. Le Maitre

We propose a confidence-based design approach robust to turbulence closures model-form uncertainty in Reynolds-Averaged Navier-Stokes computational models. The Eigenspace Perturbation Method is employed to compute turbulence closure uncertainty estimates of the performance targeted by the optimizer. The magnitude of the uncertainty estimates is exploited to establish an indicator parameter associated to the credibility of numerical prediction. The proposed approach restricts the optimum search only to design space regions for which the credibility indicator suggests trustworthy RANS model predictions. In this way, we improve the efficiency of the design process, potentially avoiding designs for which the computational model is unreliable. The reference test case consists in a two-dimensional single element airfoil resembling a morphing wing section in a high-lift configuration. Results show that the prediction credibility constraint has a non negligible impact on the definition of the optimal design.

6.9.1 Surrogate based shape optimization and uncertainty assessment of a ERCOFTAC pump

A. Fracassi, P.M. Congedo, A. Ghidoni

Centrifugal pumps, being used nowadays for many applications, must be suited for a wide range of pressure ratios and flow rates. To overcome difficulties arising from the design and performance prediction of this class of turbomachinery, many researchers proposed the coupling of CFD codes and optimization algorithms for the fast and robust design. However, uncertainties are present in most engineering applications such as turbomachines, and their in uence on turbomachinery performance should be considered. In this work we apply some advanced optimization techniques to the blade optimization of an ERCOFTAC-like pump, and we assess the robustness of the optimal profiles through an uncertainty propagation study. The main source of uncertainty is constituted by the uncertainty of the operating conditions, primarily the rotational speed of the pump shaft that affects also the flow rate.

6.9.2 Assessment of robust optimization for design of rotorcraft airfoils in forward flight

F. Fusi, P.M. Congedo, A. Guardone, G. Quaranta

This work compares the deterministic and robust approaches to improve the aerodynamic design of helicopter airfoils. The two formulations are different due to the characteristics of each approach. In the deterministic case, the objective of optimization is the minimization of drag while maintaining a level of lift that guarantees satisfaction of trimming condition. In the case of robust design, a range of angles of attack and not a single trim condition is considered. Thus, the robust optimization takes the lift-to-drag ratio as a measure of the performance of the airfoil, imposing at the same time inequality constraint on the lift coefficient to guarantee a sufficient level of lift, and then checking after optimization that the trimming condition can be satisfied. The two approaches are compared showing pros and cons of the robust framework. In general, the robust approach shows the capability to reach the same mean performance of the deterministic one, but with a lower degradation of performances in off-design situations considered through the uncertainty. On the other side, the difficulties in imposing the lift trim condition for the robust formulation may lead to results of limited use.

8.1.1 Inria International Labs

P.M. Congedo is the Inria Coordinator of the CWI-Inria Inria International Lab. IIL CWI-Inria

9.1.1 Scientific events: organisation

9.1.2 Journal

9.1.3 Invited talks

• M. Bonazzoli: NonlocalDD ANR project workshop, Florence, Italy, September 2020 (cancelled due to COVID-19 crisis).
• M. Bonazzoli: Workshop Numerical Waves, Nice, France, June 2020 (postponed to October 2021).

• P.M. Congedo, Uncertainties, models and prediction in numerical simulation: an overview, NITROS Workshop (Politecnico di Milano), 28-29/01/2020.
• P.M. Congedo, Présentation de quelques résultats récents dans le domaine de la rentrée atmosphérique, CEA CESTA, 09/11/2020.
• H. Haddar, Applied Mathematics Webinar, Spetember 2020
• H. Haddar, Duality between Invisibilty and resonances, Journée CMAP, October 2020,
• H. Haddar, Transmission eigenvalues and scattering poles and related spectra, KIPA, December 2020

9.1.4 Leadership within the scientific community

• J.-R. Li is Member of the SIAM Committee on Programs and Conferences.

9.1.5 Scientific expertise

• M. Bonazzoli evaluated (on behalf of Inria) two MATHAmSud projects.

• P.M. is Deputy Coordinator of "Maths/Engineering" Program of the Labex Mathématiques Hadamard

9.1.6 Research administration

• M. Bonazzoli is the International partnerships Scientific Correspondent for Inria Saclay.
• M. Bonazzoli is a volunteer member of Opération Postes (newsletter and website, which gathers detailed information about the French competitive selections for permanent positions in Mathematics and Informatics, supported by the French academic societies SMAI, SMF, SFdS, and SIF).
• J.-R. Li is the International Correspondant for Centre de Mathematiques Appliquees, Ecole Polytechnique.

9.2.1 Teaching

• Master: Marcella Bonazzoli, Fonctions de variable complexe, for students in the first year of Ensta Paris curriculum, 6 TDs of 2h each.
• Master: Marcella Bonazzoli, La méthode des éléments finis, for students in the second year of Ensta Paris curriculum, 6 TDs of 2h each + one project.
• Master: Lucas Chesnel, Elementary tools of analysis for partial differential equations, for students in the first year of Ensta ParisTech curriculum, 25 equivalent TD hours.
• Master: Lucas Chesnel, Fonctions de variable complexe, for students in the first year of Ensta Paris curriculum, 6 TDs of 2h each.
• Master: P.M. Congedo, Numerical methods in Fluid Mechanics, ENSTA ParisTech, 12 h.
• Master: P.M. Congedo, Numerical methods for Hyperbolic Problems, von Karman Institute for Fluid Dynamics, 12 h.
• Master: Jing Rebecca Li, Lecturer of course Mathematical and numerical foundations of modeling and simulation using partial differential equations French-Vietnam Master in Applied Mathematics, University of Science, Ho Chi Minh City, 12/2020. 2 weeks.

• Master: Grégoire Allaire, Approximation Numérique et Optimisation, for students in the second year of Ecole Polytechnique curriculum: 8 lessons of 1h30.
• Master: Grégoire Allaire, Transport and diffusion, for students in the third year of Ecole Polytechnique curriculum. 9 lessons of 2h jointly with F. Golse.
• Master: Houssem Haddar, Waves and imaging: Concepts, Theory and Applications, Master M2 ”mathematical modeling”: 9 lessons of 3h.
• Master: Houssem Haddar, Inverse scattering problems, Master M2, ENIT, 10 lessons of 3h.
• Master: Grégoire Allaire, Optimal design of structures, for students in the third year of Ecole Polytechnique curriculum. 9 lessons of 1h30.
• Master: Grégoire Allaire, Theoretical and numerical analysis of hyperbolic systems of conservation laws, Master M2 ”mathematical modeling”, 8 lessons of 3h.
• Doctorat: Houssem Haddar, Inverse problems, Executive Education, Ecole Polytechnique, 9h

9.2.2 Supervision

• PhD defended in May 2020: M. Rivier, optimization under uncertainty through a Bounding-Box concept, P.M. Congedo.
• PhD defended in December 2020: H. Girardon, Non destructive testing of PWR tubes using eddy current rotating coils, H. Haddar and L. Audibert.
• PhD in progress: Tuan Anh Vu, One-shot inversion methods and domain decomposition, (to be defended in 2023), M. Bonazzoli and H. Haddar.
• PhD in progress: M. Rihani, Maxwell's equations in presence of metamaterials (to be defended in 2021), A.-S. Bonnet-BenDhia and L. Chesnel.
• PhD in progress: Dorian Lerévérend, 3D audio for connecting children with classrooms, (to be defended in 2023), M. Aussal and H. Haddar.
• PhD in progress: Joao Reis, Advanced methods for stochastic elliptic PDEs (to be defended in June 2021), P.M. Congedo, O. Le Maitre.
• PhD in progress: Anabel Del Val, Advanced bayesian methods for aerospace applications (to be defended in June 2021), P.M. Congedo, O. Le Maitre, O. Chazot, T. Magin.
• PhD in progress: P. Novello, Deep learning for reentry atmosperic flows (to be defended in November 2021), P.M. Congedo, D. Lugato, G. Poette.
• PhD in progress: E. Solai, Virtual Prototyping of the EVE expander (to be defended in March 2022), P.M. Congedo, H. Beaugendre.
• PhD in progress: N. Leoni, Bayesian inference of model error in imprecise models (to be defended in February 2022), P.M. Congedo, O. Le Maitre, M.G. Rodio.
• Master internship: Tuan Anh Vu, Coupled iterations of domain decomposition and gradient descent methods for inverse problems solution, Marcella Bonazzoli and Houssem Haddar.
• Master internship: Qingqing Hu, Numerical study for the dielectric/metamaterial transmission problems via the singular complement method, Lucas Chesnel and Patrick Ciarlet.
• Master internship: Lorenzo Scaglione, Abnormal acoustic transmission near complex resonances. Application to invisbility., Lucas Chesnel.
• PhD in progress: Chengran Fang, Enabling cortical cell-specific sensitivity on clinical multi-shell diffusion MRI microstructure measurements. (to be defended in 2022). Jing Rebecca Li and Demian Wassermann.
• PhD in progress: Zheyi Yang, Reduced models of diffusion MRI in the brain white matter using parametrized deformation fields. (to be defended in 2024). Jing Rebecca Li.
• Software engineer: Syver Doving Agdestein, Improving the diffusion MRI simulation toolbox SpinDoctor. Jing Rebecca Li.
• Master internship: Doan Khanh Thanh Tin, Study of the notion of the diffusion time using Laplace eigenfunctions for diffusion MRI. Jing-Rebecca Li.
• Master internship: Kidist Kebede, the morphology of neuronal dendrites using diffusion MRI. Jing-Rebecca Li.
• PhD in progress:J. Desai sur l'optimisation topologique de structures au comportement non-linéaire avec des méthodes de déformation de maillage (IRT SystemX, to be defended in 2021). G. Allaire and F. Jouve.
• PhD in progress: Nouha Jenhani, Differential sampling methods for defect imaging in periodic layers. (to be defended in 2022) Houssem Haddar and Mourad Bellasoued.
• PhD in progress: Amal Labidi, Inverse problems for wave equation with magnetic potential. (to be defended in 2022) Houssem Haddar and Mourad Bellasoued.
• PhD in progress: Marwa Mansouri, Inside outside duality for artificial backgrounds. (to be defended in 2022) Houssem Haddar, Lucas Chesnel and Moez Khenissi.
• PhD in progress: M. Bihr sur la fabrication additive et l'optimisation topologique de structures (to be defended in 2022) G. Allaire and B. Bogosel.
• PhD in progress: R. Delvaux sur les algorithmes de couplage à convergence super-linéaire entre neutronique, thermohydraulique et thermique (to be defended in 2022) G. Allaire and C. Patricot.
• PhD in progress: A. Touiti sur l'optimisation de l'anisotropie pour des structures issues de la fabrication additive (to be defended in 2022) G. Allaire and F. Jouve.

9.3.1 Internal or external Inria responsibilities

P.M. Congedo is the coordinator of the Sustainable development committe of Inria Saclay Île-de-France

J.R. Li is a member of Inria's Commission d'Evaluation.

International journals

• 1 article LorenzoL. Audibert, LucasL. Chesnel, HoussemH. Haddar and KevishK. Napal. Qualitative indicator functions for imaging crack networks using acoustic waves SIAM Journal on Scientific Computing 2020
  HAL back to text
• 2 articleMatthieuM. Aussal, YosraY. Boukari and HoussemH. Haddar. Data Completion Method For the Helmholtz Equation Via Surface Potentials for Partial Cauchy DataInverse Problems365April 2020, 055012
  HALDOIback to text
• 3 article AntoineA. Bera, Anne-SophieA.-S. Bonnet-Ben Dhia and LucasL. Chesnel. A continuation method for building invisible obstacles in waveguides Quarterly Journal of Mechanics and Applied Mathematics February 2021
  HAL back to text
• 4 article LaurentL. Bourgeois and LucasL. Chesnel. On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates ESAIM: Mathematical Modelling and Numerical Analysis March 2020
  HAL DOI back to text
• 5 article RenataR. Bunoiu, LucasL. Chesnel, KarimK. Ramdani and MahranM. Rihani. Homogenization of Maxwell's equations and related scalar problems with sign-changing coefficients Annales de la Faculté des Sciences de Toulouse. Mathématiques. 2020
  HAL back to text
• 6 articleFioralbaF. Cakoni, DavidD. Colton and HoussemH. Haddar. A duality between scattering poles and transmission eigenvalues in scattering theoryProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences4762244December 2020, 20200612
  HALDOIback to text
• 7 article LucasL. Chesnel and Sergei AS. Nazarov. Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides Zeitschrift für Angewandte Mathematik und Physik May 2020
  HAL back to text
• 8 article LucasL. Chesnel, SergeiS. Nazarov and JariJ. Taskinen. Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography Asymptotic Analysis 2020
  HAL back to text
• 9 articleAndrea FA. Cortesi, Paul GP. Constantine, ThierryT. Magin and Pietro MarcoP. Congedo. Forward and backward uncertainty quantification with active subspaces: application to hypersonic flows around a cylinderJournal of Computational Physics407April 2020, 109079
  HALDOI
• 10 articleChengranC. Fang, Van-DangV.-D. Nguyen, DemianD. Wassermann and Jing-RebeccaJ.-R. Li. Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron ModuleNeuroImage222November 2020, 117198
  HALDOIback to text
• 11 articleFrancescaF. Fusi, Pietro MarcoP. Congedo, AlbertoA. Guardone and GiuseppeG. Quaranta. Assessment of robust optimization for design of rotorcraft airfoils in forward flightAerospace Science and Technology107June 2020, 106355
  HALDOI
• 12 articleGiulioG. Gori, MartaM. Zocca, GiorgiaG. Cammi, AndreaA. Spinelli, Pietro MarcoP. Congedo and AlbertoA. Guardone. Accuracy assessment of the Non-Ideal Computational Fluid Dynamics model for siloxane MDM from the open-source SU2 suiteEuropean Journal of Mechanics - B/Fluids79January 2020, 109-120
  HALDOI
• 13 articleGiulioG. Gori, MartaM. Zocca, AlbertoA. Guardone, OlivierO. Le Maitre and Pietro MarcoP. Congedo. Bayesian inference of thermodynamic models from vapor flow experimentsComputers and Fluids205June 2020, 104550
  HALDOI
• 14 articleHoussemH. Haddar and AlexanderA. Konschin. Factorization Method for Imaging a Local Perturbation in Inhomogeneous Periodic Layers from Far Field MeasurementsInverse Problems and Imaging141February 2020, 133-152
  HALDOIback to text
• 15 articleHoussemH. Haddar and XiaoliX. Liu. A time domain factorization method for obstacles with impedance boundary conditionsInverse Problems3610October 2020, 105011
  HALDOIback to text
• 16 article Jing-RebeccaJ.-R. Li, Try NguyenT. Tran and Van‐DangV. Nguyen. Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions NMR in Biomedicine 33 10 October 2020
  HAL DOI back to text
• 17 articleImenI. Mekkaoui, JeromeJ. Pousin, JanJ. Hesthaven and Jing-RebeccaJ.-R. Li. Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domainsJournal of Magnetic Resonance318September 2020, 106809
  HALDOIback to text
• 18 article VinodV. Menon, GuillermoG. Gallardo, MarkM. Pinsk, Van-DangV.-D. Nguyen, Jing-RebeccaJ.-R. Li, WeidongW. Cai and DemianD. Wassermann. Microstructural organization of human insula is linked to its macrofunctional circuitry and predicts cognitive control eLife 9 June 2020
  HAL DOI back to text
• 19 articleFatemehF. Pourahmadian and HoussemH. Haddar. Differential tomography of micromechanical evolution in elastic materials of unknown micro/macrostructureSIAM Journal on Imaging Sciences1332020, 1302–1330
  HALDOIback to text
• 20 articleNassimN. Razaaly and Pietro MarcoP. Congedo. Extension of AK-MCS for the efficient computation of very small failure probabilitiesReliability Engineering and System Safety203November 2020, 107084
  HALDOI
• 21 articleNassimN. Razaaly, DaanD. Crommelin and Pietro MarcoP. Congedo. Efficient Estimation of Extreme Quantiles using Adaptive Kriging and Importance SamplingInternational Journal for Numerical Methods in Engineering1219May 2020, 2086-2105
  HALDOI
• 22 articleNassimN. Razaaly, GiacomoG. Persico, GiulioG. Gori and Pietro MarcoP. Congedo. Quantile-based robust optimization of a supersonic nozzle for organic rankine cycle turbinesApplied Mathematical Modelling82June 2020, 802-824
  HALDOI

Conferences without proceedings

• 23 inproceedings Van-DangV.-D. Nguyen, ChengranC. Fang, DemianD. Wassermann and Jing-RebeccaJ.-R. Li. Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module ISMRM 2020 - 28th Annual Meeting & Exhibition Sydney, Australia April 2020
  HAL

Reports & preprints

• 24 misc LorenzoL. Audibert, HugoH. Girardon, HoussemH. Haddar and PierreP. Jolivet. Inversion of Eddy-Current Signals Using a Level-Set Method and Block Krylov Solvers December 2020
  HAL back to text
• 25 report LorenzoL. Audibert, HugoH. Girardon and HoussemH. Haddar. Shape Reconstruction of Deposits Inside a Steam Generator Using Eddy Current Measurements INRIA Saclay - Equipe DeFI; EDF Lab Chatou, 6 quai Watier, 78400 Chatou; CMAP Ecole Polytechnique April 2020
  HAL back to text
• 26 misc MarcellaM. Bonazzoli, XavierX. Claeys, FrédéricF. Nataf and Pierre-HenriP.-H. Tournier. Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems November 2020
  HAL back to text
• 27 misc Anne-SophieA.-S. Bonnet-Ben Dhia, LucasL. Chesnel and MahranM. Rihani. Maxwell's equations with hypersingularities at a conical plasmonic tip October 2020
  HAL back to text
• 28 misc LucasL. Chesnel, JérémyJ. Heleine and Sergei AS. Nazarov. Design of a mode converter using thin resonant ligaments February 2021
  HAL
• 29 misc LucasL. Chesnel and SergeiS. Nazarov. Abnormal acoustic transmission in a waveguide with perforated screens July 2020
  HAL back to text
• 30 misc LucasL. Chesnel and Sergei AS. Nazarov. Design of an acoustic energy distributor using thin resonant slits November 2020
  HAL back to text
• 31 misc VinodV. Menon, GuillermoG. Gallardo, MarkM. Pinsk, Van-DangV.-D. Nguyen, Jing-RebeccaJ.-R. Li, WeidongW. Cai and DemianD. Wassermann. Quantitative modeling links in vivo microstructural and macrofunctional organization of human and macaque insular cortex, and predicts cognitive control abilities January 2020
  HAL DOI
• 32 report NassimN. Razaaly, GiulioG. Gori, GiacomoG. Persico and Pietro MarcoP. Congedo. Quantile-based robust optimization of a supersonic nozzle for Organic Rankine Cycle turbines Inria Saclay January 2020
  HAL