Publications

2024

• Time-harmonic wave propagation in junctions of two periodic half-spaces
  
  • Amenoagbadji Pierre
  • Fliss Sonia
  • Joly Patrick
  , 2024. We are interested in the Helmholtz equation in a junction of two periodic half-spaces. When the overall medium is periodic in the direction of the interface, Fliss and Joly (2019) proposed a method which consists in applying a partial Floquet-Bloch transform along the interface, to obtain a family of waveguide problems parameterized by the Floquet variable. In this paper, we consider two model configurations where the medium is no longer periodic in the direction of the interface. Inspired by the works of Gérard-Varet and Masmoudi (2011, 2012), and Blanc, Le Bris, and Lions (2015), we use the fact that the overall medium has a so-called quasiperiodic structure, in the sense that it is the restriction of a higher dimensional periodic medium. Accordingly, the Helmholtz equation is lifted onto a higher dimensional problem with coefficients that are periodic along the interface. This periodicity property allows us to adapt the tools previously developed for periodic media. However, the augmented PDE is elliptically degenerate (in the sense of the principal part of its differential operator) and thus more delicate to analyse.
• 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.
• Notes de cours sur les équations de Maxwell et leur approximation
  
  • Ciarlet Patrick
  , 2024, pp.151.
• Coupled Boundary Element and Finite Volume Methods for Modeling Fluid-Induced Seismicity in Fault Networks within Low-Permeability Rocks
  
  • Romanet Pierre
  • Scuderi Marco Maria
  • Ampuero Jean-Paul
  • Chaillat Stéphanie
  • Cappa Frederic
  Geophysical Journal International, Oxford University Press (OUP), 2024, 243 (3). To better understand the mechanics of injection-induced seismicity, we developed a two-dimensional numerical code to simulate both seismic and aseismic slip on non-planar faults and fault networks driven by fluid diffusion along permeable faults. Our approach integrates a boundary element method to model fault slip governed by rate-and-state friction with a finite volume method for simulating fluid diffusion along fault networks. We demonstrate the method's capabilities with two illustrative examples: (1) fluid injection inducing slow slip on a primary rough, rate-strengthening fault, which subsequently triggers microseismicity on secondary, smaller faults, and (2) fluid injection on a single fault in a network of intersecting faults, leading to fluid diffusion and reactivation of slip throughout the network. In both cases, the simulated slow slip migrates more rapidly than the fluid pressure diffusion front. The observed migration patterns of microseismicity in the first example and slow slip in the second example resemble diffusion processes but involve diffusivity values that differ significantly from the fault hydraulic diffusivity. These results support the conclusion that the microseismicity front is not a direct proxy for the fluid diffusion front and cannot be used to directly infer hydraulic diffusivity, consistently with some decametric scale in-situ experiments of fault activation under controlled conditions. This work highlights the importance of distinguishing between mechanical and hydrological processes in the analysis of induced seismicity, providing a powerful tool for improving our understanding of fault behavior in response to fluid injection, in particular when a network of faults is involved. (10.1093/gji/ggaf377)
  DOI : 10.1093/gji/ggaf377
• A posteriori error estimates for the DD+$L^2$ jumps method on the Neutron Diffusion equations
  
  • Ciarlet Patrick
  • Do Minh-Hieu
  • Gervais Mario
  • Madiot François
  , 2024. We analyse a posteriori error estimates for the discretization of the neutron diffusion equations with a Domain Decomposition Method, the so-called DD+$L^2$ jumps method. We provide guaranteed and locally efficient estimators on a base block equation, the one-group neutron diffusion equation. Classically, one introduces a Lagrange multiplier to account for the jumps on the interface. This Lagrange multiplier is used for the reconstruction of the physical variables. Remarkably, no reconstruction of the Lagrange multiplier is needed to achieve the optimal a posteriori estimates.
• High-order numerical integration on self-affine sets
  
  • Joly Patrick
  • Kachanovska Maryna
  • Moitier Zoïs
  , 2024. 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.
• Propagation of ultrasounds in random multi-scale media and effecitve speed of sound estimation
  
  • Goepfert Quentin
  , 2024. Ultrasounds are widely used in medical imaging modalities. Originally, the ultrasound devices were built to image the internal structure of the tissues. In recent years, a change of paradigm operated and the goal is now also to assess physical parameters that can be used for medical diagnosis.The speed of acoustic waves inside soft tissues can be used for diagnosis of breast cancers or hepatic steatosis. Moreover, it determines the quality of the tomographic reconstruction of the tissues. Indeed, the images are usually computed by backpropagating the measured echoes at the speed of sound in water. However, the discrepancy between the speed of sound in water and the actual speed of sound inside the tissues results in nonphysical artifacts on the image.In order to establish a quantitative estimator of the propagation speed of sound inside the soft tissues, it is necessary to deeply understand the scattering of the medium. It is commonly admitted that the backscattered echoes are produced by numerous unresolved scatterers inside the medium (cell nuclei, mitochondria...). The scattering is then often modeled by the Born approximation. However, this model does not capture the variation of the effective speed of sound inside the tissue due to the unresolved scatterers. The goal of this thesis is thus to establish a propagation model that takes into account the variations of the effective speed of sound inside the tissues. Then, we will theoretically study the estimators previously introduced by Alexandre Aubry in his work.The tissue is here modeled as a bounded homogeneous mediumin which lie unresolved scatterers. As their distribution is unknown and inaccessible, their number and position is modeled as a random process. To obtain a simple form of the backscattered field, the techniques and tools developed for the quantitative stochastic homogenization theory will be used and a high-order asymptotic expansion will be proven.An asymptotic analysis of the imaging functional is carried out by using the high-order asymptotic expansion. Furthermore, the theoretical study of the estimators introduced by Alexandre Aubry and his team confirms and justifies some of the experimental results. In particular, it is possible to recover the effective speed of sound by a local spatial average of the imaging function.Numerical simulation supports each and every major result proven in this thesis.
• Guided modes in a hexagonal periodic graph like domain
  
  • Delourme Bérangère
  • Fliss Sonia
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2024, 22 (3), pp.1196-1245. This paper deals with the existence of guided waves and edge states in particular two-dimensional media obtained by perturbing a reference periodic medium with honeycomb symmetry. This reference medium is a thin periodic domain (the thickness is denoted δ > 0) with an hexagonal structure, which is close to an honeycomb quantum graph. In a first step, we show the existence of Dirac points (conical crossings) at arbitrarily large frequencies if δ is chosen small enough. We then perturbe the domain by cutting the perfectly periodic medium along the so-called zigzag direction, and we consider either Dirichlet or Neumann boundary conditions on the cut edge. In the two cases, we prove the existence of edges modes as well as their robustness with respect to some perturbations, namely the location of the cut and the thickness of the perturbed edge. In particular, we show that different locations of the cut lead to almost-non dispersive edge states, the number of locations increasing with the frequency. All the results are obtained via asymptotic analysis and semi-explicit computations done on the limit quantum graph. Numerical simulations illustrate the theoretical results. (10.1137/23M1600177)
  DOI : 10.1137/23M1600177
• The Sphericity Paradox and the Role of Hoop Stresses in Free Subduction on a Sphere
  
  • Chaillat Stéphanie
  • Gerardi Gianluca
  • Li Yida
  • Chamolly Alexander
  • Li Zhong‐hai
  • Ribe Neil M.
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2024, 129 (9), pp.e2024JB029500. Oceanic plates are doubly curved spherical shells, which influences how they respond to loading during subduction. Here we study a viscous fluid model for gravity‐driven subduction of a shell comprising a spherical plate and an attached slab. The shell is 100–1,000 times more viscous than the upper mantle. We use the boundary‐element method to solve for the flow. Solutions of an axisymmetric model show that the effect of sphericity on the flexure of shells is greater for smaller shells that are more nearly flat (the “sphericity paradox”). Both axisymmetric and three‐dimensional models predict that the deviatoric membrane stress in the slab should be dominated by the longitudinal normal stress (hoop stress), which is typically about twice as large as the downdip stress and of opposite sign. Our models also predict that concave‐landward slabs can exhibit both compressive and tensile hoop stress depending on the depth, whereas the hoop stress in convex slabs is always compressive. We test these two predictions against slab shape and earthquake focal mechanism data from the Mariana subduction zone, assuming that the deviatoric stress in our flow models corresponds to that implied by centroid moment tensors. The magnitude of the hoop stress exceeds that of the downdip stress for about half the earthquakes surveyed, partially verifying our first prediction. Our second prediction is supported by the near‐absence of earthquakes under tensile hoop stress in the portion of the slab having convex geometry. (10.1029/2024JB029500)
  DOI : 10.1029/2024JB029500
• Notes de cours sur les méthodes variationnelles pour l'analyse et la résolution de problèmes non coercifs
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Ciarlet Patrick
  , 2024.
• The T-coercivity approach for mixed problems
  
  • Barré Mathieu
  • Ciarlet Patrick
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2024. Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this note, we propose an alternative framework to study such problems by using the T-coercivity approach to derive a global inf-sup condition. Generally speaking, this is a constructive approach that, in addition, drives the design of suitable approximations. As a matter of fact, the derivation of the uniform discrete inf-sup condition for the approximate problems follows easily from the study of the original problem. To support our view, we solve a series of classical mixed problems with the T-coercivity approach. Among others, the celebrated Fortin Lemma appears naturally in the numerical analysis of the approximate problems.
• Accelerated iterative DG finite element solvers for large-scale time-harmonic acoustic problems
  
  • Modave Axel
  , 2024. Finite element methods are widely used to solve time-harmonic wave propagation problems, but solving large cases can be extremely difficult even with the computational power of parallel computers. In this work, the linear system resulting from the finite element discretization is solved with iterative solution methods, which are efficient in parallel but can require a large number of iterations. In standard discontinuous Galerkin (DG) methods, the numerical solution is discontinuous at the interfaces between the elements. In hybridizable DG methods, additional unknowns are introduced at the interfaces between the finite elements, and the physical unknowns are eliminated from the global system, resulting in a hybridized system. We have recently proposed a new strategy, called CHDG, where the additional unknowns correspond to transmission variables, whereas in the standard approach they are numerical fluxes. This strategy improves the properties of the hybridized system for faster iterative solution procedures. In this talk, we present and study a 3D CHDG implementation with nodal finite element basis functions. The resulting scheme has properties amenable to efficient parallel computing. Numerical results are presented to validate the method, and preliminary 3D computational results are proposed. (10.3397/IN_2024_2877)
  DOI : 10.3397/IN_2024_2877
• Far-field sound field estimation using robotized measurements and the boundary elements method
  
  • Pascal Caroline
  • Marchand Pierre
  • Chapoutot Alexandre
  • Doaré Olivier
  , 2024, 270 (11), pp.816-827. Sound Field Estimation (SFE) is a numerical technique widely used to identify and reconstruct the acoustic fields radiated by unknown structures. In particular, SFE proves to be useful when data is only available close to the source, but information in the whole space is required. However, the practical implementation of this method is still hindered by two major drawbacks: the lack of efficient implementation of existing numerical methodologies, and the time-consuming and tedious roll-out of acoustic measurements. This paper aims to provide a solution to both issues. First, the measurements step is fully automated by using a robotic arm, able to accurately gather geometric and acoustic data without any human assistance. In this matter, a particular attention has been paid to the impact of the robot on the acoustic pressure measurements. The sound field prediction is then tackled using the Boundary Element Method (BEM), and implemented using the FreeFEM++ BEM library. Numerically simulated measurements have allowed us to assess the method accuracy, and the overall solution has been successfully tested using actual robotized measurements of an unknown loudspeaker (10.3397/IN_2024_2661)
  DOI : 10.3397/IN_2024_2661
• Computation of Green's functions for the acoustic scattering by an elastic structure excited by a turbulent flow in water
  
  • Pacaut Louise
  • Serre Gilles
  • Mercier Jean-François
  • Chaillat Stéphanie
  • Cotté Benjamin
  , 2024, 270 (5), pp.5995-6006. To model the hydrodynamic noise produced by an elastic ship hull or propeller excited by a turbulent boundary layer, we need an efficient method to compute the acoustic scattering by an elastic body surrounded by a fluid. In 3D, Boundary Element Methods (BEM) are used to reduce the computational costs, for both the fluid and the elastic body. A natural way to compute the boundary integral representation (BIR) of the sound pressure is to use formulations based on the free space acoustic and elastic Green's functions. However, since the turbulent flow along the elastic body is known only statistically, the use of these Green's functions would be too expensive. A remedy is to compute a Green's function adapted to the physical problem, thus satisfying the transmission conditions of the fluid-structure problem. This so-called "tailored Green's function" is determined by solving a coupled acoustic-elastic problem with the BEM, and leads to a simplified BIR of the sound pressure compatible with a stochastic source term. We first validate the computation of the tailored Green's function over a classic spherical geometry. Then we compare the scattering of multiple quadrupoles by elastic or rigid NACA0012 profiles. (10.3397/IN_2024_3671)
  DOI : 10.3397/IN_2024_3671
• Multiscale modeling for a class of high-contrast heterogeneous sign-changing problems
  
  • Ye Changqing
  • Jin Xingguang
  • Ciarlet Patrick
  • Chung Eric T.
  , 2024. The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positive and negative values in different subdomains. These problems find their physical background in negative-index metamaterials, either as inclusions embedded into common materials as the matrix or vice versa. In this paper, we propose a numerical method based on the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) specifically designed for sign-changing problems. The construction of auxiliary spaces in the original CEM-GMsFEM is tailored to accommodate the sign-changing setting. The numerical results demonstrate the effectiveness of the proposed method in handling sophisticated coefficient profiles and the robustness of coefficient contrast ratios. Under several technical assumptions and by applying the T-coercivity theory, we establish the inf-sup stability and provide an a priori error estimate for the proposed method.
• 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.
• 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
• 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
• 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.
• 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 $k>1$.
• 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.
• 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