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Internal Seminar

Internal Seminar Calendar

2023 – 2024

25 April 2024 – 11h00 to 12h00 Martin Werner Licht:
4 April 2024 – 11h00 to 12h00 Roland Maier: A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods. (abstract)
2 April 2024 – 14h00 to 15h00 Andreas Rupp: Homogeneous multigrid for hybrid discretizations: application to HHO methods. (abstract)
18 January 2024 – 14h00 to 15h00 Zoubida Mghazli: Modeling some biological phenomena via the porous media approach. (abstract)
23 November 2023 – 11h00 to 12h00 Olivier Hénot: Computer-assisted proofs of radial solutions of elliptic systems on R^d. (abstract)
16 November 2023 – 17h00 to 18h00 Maxime Theillard: A Volume-Preserving Reference Map Method for the Level Set Representation. (abstract)
13 November 2023 – 11h00 to 12h00 Charles Parker: Implementing $H^2$-conforming finite elements without enforcing $C^1$-continuity. (abstract)
09 November 2023 – 11h00 to 12h00 Maxime Breden: Computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem. (abstract)

2022 – 2023

25 May 2023 – 11h00 to 12h00 Martin Vohralík: A posteriori error estimates robust with respect to nonlinearities and final time. (abstract)
11 May 2023 – 11h00 to 12h00 Konstantin Brenner: On the preconditioned Newton’s method for Richards’ equation. (abstract)
4 May 2023 – 11h00 to 12h00 Ludmil Zikatanov: High order exponential fitting discretizations for convection diffusion problems. (abstract)
23 March 2023 – 11h00 to 12h00 Marien Hanot: Polytopal discretization of advanced differential complexes.(abstract)
9 February 2023 – 11h00 to 12h00 Roland Maier: Semi-explicit time discretization schemes for elliptic-parabolic problems. (abstract)
2 February 2023 – 11h00 to 12h00 Simon Legrand: Parameter studies automation with Prune_rs. (abstract)
28 November 2022 – 11h00 to 12h00 Xuefeng Liu: Guaranteed eigenvalue/eigenfunction computation and its application to shape optimization problems. (abstract)
17 November 2022 – 11h00 to 12h00 Fabio Vicini: Flow simulations on porous fractured media: a small numerical overview from my perspective. (abstract)
20 October 2022 – 10h00 to 11h00 Iuliu Sorin Pop: Non-equilibrium models for flow in porous media. (abstract)
06 October 2022 – 15h00 to 16h00 Rekha Khot: Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes. (abstract)

2021 – 2022

21 September 2022 – 15h00 to 16h00 Alexandre IMPERIALE: Numerical methods for time domain wave propagation problems applied to ultrasonic testing modelling. (abstract)
16 June 2022 – 11h30 to 12h30 Cherif Amrouche: Elliptic Problems in Lipschitz and in $C^{1,1}$ Domains. (abstract)
13 June 2022 – 11h00 to 12h00 Jean-Luc Guermond: Invariant-domain preserving IMEX time stepping methods. (abstract)
5 May 2022 – 11h00 to 12h00 Daniel Zegarra Vasquez: Simulation d’écoulements monophasiques en milieux poreux fracturés par la méthode des éléments finis mixtes hybrides. (abstract)
19 April 2022 – 14h00 to 15h00 Christos Xenophontos: Finite Element approximation of singularly perturbed eigenvalue problems. (abstract)
14 April 2022 – 11h00 to 12h00: Idrissa Niakh: Stable model reduction for linear variational inequalities with parameter-dependent constraints. (abstract)
7 April 2022 – 17h00 to 18h00: Christoph Lehrenfeld: Embedded Trefftz Discontinuous Galerkin methods. (abstract)
24 March 2022 – 11h00 to 12h00: Miloslav Vlasak: A posteriori error estimates for discontinuous Galerkin method. (abstract)
10 March 2022 – 11h00 to 12h00: Ruma Maity: Parameter dependent finite element analysis for ferronematics solutions. (abstract)
3 February 2022 – 11h00 to 12h00: Pierre Matalon: An h-multigrid method for Hybrid High-Order discretizations of elliptic equations. (abstract)
27 January 2022 – 11h00 to 12h00: Frédéric Lebon: On the modeling of nonlinear imperfect solid/solid interfaces by asymptotic techniques. (abstract)
20 January 2022 – 11h00 to 12h00: Isabelle Ramière: Automatic multigrid adaptive mesh refinement with controlled accuracy for quasi-static nonlinear solid mechanics. (abstract)
13 January 2022 – 11h00 to 12h00: Koondanibha Mitra: A posteriori estimates for nonlinear degenerate parabolic and elliptic equations. (abstract)
10 December 2021 – 11h00 to 12h00: Gregor Gantner: Applications of a space-time first-order system least-squares formulation for parabolic PDEs. (abstract)
25 November 2021 – 11h00 to 12h00: Pierre Gosselet: Asynchronous Global/Local coupling. (abstract)
24 November 2021 – 10h30 to 11h30: Grégory Etangsale: A primal hybridizable discontinuous Galerkin method for modelling flows in fractured porous media. (abstract)

2020 – 2021

06 September 2021 – 15h00 to 16h00: Rolf Stenberg: Nitsche’s Method for Elastic Contact Problems. (abstract)
17 June 2021 – 11h00 to 12h00: Elyes Ahmed: Adaptive fully-implicit solvers and a posteriori error control for multiphase flow with wells. (abstract)
3 June 2021 – 11h00 to 12h00: Oliver Sutton: High order, mesh-based multigroup discrete ordinates schemes for the linear Boltzmann transport problem. (abstract )
29 April 2021 – 11h00 to 12h00: Lorenzo Mascotto: Enriched nonconforming virtual element methods (abstract )
1 April 2021 – 11h00 to 12h00: André Harnist : Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems (abstract )
11 March 2021 – 15h00 to 16h00: Omar Duran : Explicit and implicit hybrid high-order methods for the wave equation in time regime (abstract )
25 February 2021 – 14h00 to 15h00: Buyang Li : A bounded numerical solution with a small mesh size implies existence of a smooth solution to the time-dependent Navier–Stokes equations (abstract)
18 February 2021 – 11h00 to 12h00: Roland Maier : Multiscale scattering in nonlinear Kerr-type media (abstract)
10 December 2020 – 16h00 to 17h00: Ani Miraçi : A-posteriori-steered and adaptive p-robust multigrid solvers (abstract)
9 December 2020 – 16h00 to 17h00: Riccardo Milani : Compatible Discrete Operator schemes for the unsteady incompressible Navier–Stokes equations (abstract)
26 November 2020 – 16h00 to 17h00: Koondanibha Mitra : A posteriori error bounds for the Richards equation (abstract)
19 November 2020 – 11h00 to 12h00: Joëlle Ferzly : Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: adaptivity and inexact resolution (abstract)
5 November 2020 – 11h00 to 12h00: Zhaonan Dong : On a posteriori error estimates for non-conforming Galerkin methods (abstract)
22 October 2020 – 11h00 to 12h00: Théophile Chaumont-Frelet : A posteriori error estimates for Maxwell’s equations based on flux quasi-equilibration (abstract)
15 October 2020 – 11h00 to 12h00: Florent Hédin : A hybrid high-order (HHO) method with non-matching meshes in discrete fracture networks (abstract)

2019 – 2020

16 March 2020 – 15h00 to 16h00: Bochra Mejri : Topological sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity (abstract)
25 February 2020 – 15h00 to 16h00: Jakub Both : Robust iterative solvers for thermo-poro-visco-elasticity via gradient flows (abstract)
16 October 2019 – 14h00 to 15h00: Nicolas Pignet : Hybrid High-Order method for nonlinear solid mechanics (abstract)
27 September 2019 – 15h00 to 16h00: Ivan Yotov : A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media (abstract)
5 September 2019 – 15h00 to 16h00: Koondi Mitra : A fast and stable linear iterative scheme for nonlinear parabolic problems (abstract)

2018 – 2019

11 July 2019 – 11h00 to 12h00: Jose Fonseca : Towards scalable parallel adaptive simulations with ParFlow (abstract)
6 June 2019 – 11h00 to 12h00: Quanling Deng : High-order generalized-alpha methods and splitting schemes (abstract)
12 April 2019 – 14h30 to 15h30: Menel Rahrah : Mathematical modelling of fast, high volume infiltration in poroelastic media using finite elements (abstract)
18 March 2019 – 14h to 15h: Patrik Daniel : Adaptive hp-finite elements with guaranteed error contraction and inexact multilevel solvers (abstract)
14 February 2019 – 15h to 16h: Thibault Faney, Soleiman Yousef : Accélération d’un simulateur d’équilibres thermodynamiques par apprentissage automatique (abstract)
7 February 2019 – 11h to 12h: Gregor Gantner : Optimal adaptivity for isogeometric finite and boundary element methods (abstract)
31 January 2019 – 14h30 to 15h30: Camilla Fiorini : Sensitivity analysis for hyperbolic PDEs systems with discontinuous solution: the case of the Euler Equations. (abstract)
9 January 2019 – 11h to 12h: Zhaonan Dong : hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes (abstract)
13 December 2018 – 11h to 12h: Maxime Breden : An introduction to a posteriori validation techniques, illustrated on the Navier-Stokes equations (abstract)
5 December 2018 – 11h00 to 12h00: Amina Benaceur : Model reduction for nonlinear thermics and mechanics (abstract)

2017 – 2018

16 April 2018 – 15h to 16h: Simon Lemaire : An optimization-based method for the numerical approximation of sign-changing PDEs (abstract)
20 Febraury 2018 – 15h to 16h: Thirupathi Gudi : An energy space based approach for the finite element approximation of the Dirichlet boundary control problem (abstract)
15 Febraury 2018 – 14h to 15h: Franz Chouly : About some a posteriori error estimates for small strain elasticity (abstract)
30 November 2017 – 14h to 15h: Sébastien Furic : Construction & Simulation of System-Level Physical Models (abstract)
2 November 2017 – 11h to 12h: Hend Benameur: Identification of parameters, fractures ans wells in porous media (abstract)
10 October 2017 – 11h to 12h: Peter Minev: Recent splitting schemes for the incompressible Navier-Stokes equations (abstract)
18 September 2017 – 13h to 14h: Théophile Chaumont: High order finite element methods for the Helmholtz equation in highly heterogeneous media (abstract)

2016 – 2017

29 June 2017 – 15h to 16h: Gouranga Mallik: A priori and a posteriori error control for the von Karman equations (abstract)
22 June 2017 – 15h to 16h: Valentine Rey: Goal-oriented error control within non-overlapping domain decomposition methods to solve elliptic problems (abstract)
15 June 2017 – 15h to 16h:
- Jad Dabaghi: Adaptive inexact semi-smooth Newton methods for a contact between two membranes (abstract)
- Patrik Daniel: An adaptive hp-refinement strategy with computable guaranteed error reduction factors (abstract)
6 June 2017 – 11h to 12h: Ivan Yotov: Coupled multipoint flux and multipoint stress mixed finite element methods for poroelasticity (abstract)
1 June 2017 – 10h to 12h:
- Joscha Gedicke: An adaptive finite element method for two-dimensional Maxwell’s equations (abstract)
- Martin Eigel: Adaptive stochastic FE for explicit Bayesian inversion with hierarchical tensor representations (abstract)
- Quang Duc Bui: Coupled Parareal-Schwarz Waveform relaxation method for advection reaction diffusion equation in one dimension (abstract)
16 May 2017 – 15h to 16h: Quanling Deng: Dispersion Optimized Quadratures for Isogeometric Analysis (abstract)
11 May 2017 – 15h to 16h: Sarah Ali Hassan: A posteriori error estimates and stopping criteria for solvers using domain decomposition methods and with local time stepping (abstract)
13 Apr. 2017 – 15h to 16h: Janelle Hammond: A non intrusive reduced basis data assimilation method and its application to outdoor air quality models (abstract)
30 Mar. 2017 – 10h to 11h: Mohammad Zakerzadeh: Analysis of space-time discontinuous Galerkin scheme for hyperbolic and viscous conservation laws (abstract)
23 Mar. 2017 – 15h to 16h: Karol Cascavita: Discontinuous Skeletal methods for yield fluids (abstract)
16 Mar. 2017 – 15h to 16h: Thomas Boiveau: Approximation of parabolic equations by space-time tensor methods (abstract)
9 Mar. 2017 – 15h to 16h: Ludovic Chamoin: Multiscale computations with MsFEM: a posteriori error estimation, adaptive strategy, and coupling with model reduction (abstract)
2 Mar. 2017 – 15h to 16h: Matteo Cicuttin: Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. (abstract)
23 Feb. 2017
– 10h to 10h45 : Lars Diening: Linearization of the p-Poisson equation (abstract)
– 10h45 to 11h30 : Christian Kreuzer: Quasi-optimality of discontinuous Galerkin methods for parabolic problems (abstract)
26 Jan. 2017 – 15h to 16h: Amina Benaceur: An improved reduced basis method for non-linear heat transfer (abstract)
19 Jan. 2017 – 15h to 16h: Laurent Monasse: A 3D conservative coupling between a compressible flow and a fragmenting structure (abstract)
5 Jan. 2017 – 15h to 16h: Agnieszka Miedlar: Moving eigenvalues and eigenvectors by simple perturbations (abstract)
8 Dec. 2016 – 15h to 16h: Luca Formaggia: Hybrid dimensional Darcy flow in fractured porous media, some recent results on mimetic discretization (abstract)
22 Sept. 2016 – 15h to 16h: Paola Antonietti: Fast solution techniques for high order Discontinuous Galerkin methods (abstract)

2015 – 2016

29 Oct. 2015 – 15h to 16h: Sarah Ali Hassan: A posteriori error estimates for domain decomposition methods (abstract)
05 Nov. 2015 – 16h to 17h: Iain Smears: Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method (abstract)
12 Nov. 2015 -16h to 17h: Elyes Ahmed: Space-time domain decomposition method for two-phase flow equations (abstract)
19 Nov. 2015 – 16h to 17h: Géraldine Pichot: Generation algorithms of stationary Gaussian random fields (abstract)
26 Nov. 2015-16h to 17h: Jérôme Jaffré: Discrete reduced models for flow in porous media with fractures and barriers (abstract)
03 Dec. 2015 – 16h to 17h: François Clément: Safe and Correct Programming for Scientific Computing (abstract)
10 Dec. 2015 – 16h to 17h: Nabil Birgle: Composite Method on Polygonal Meshes (abstract)11 Feb. 2016: Michel
Kern: Reactive transport in porous media: Formulations and numerical methods
25 Feb. 2016: Martin Vohralík
3 March 2016: François Clément: Safe and Correct Programming for Scientific Computing pt II

14th April – ‪Idrissa Niakh: Stable model reduction for linear variational inequalities with parameter-dependent constraints

‪Idrissa Niakh Thursday 14th April at 11:00 ABSTRACT: We consider model reduction for linear variational inequalities with parameter-dependent constraints. We study the stability of the reduced problem in the context of a dualized formulation of the constraints using Lagrange multipliers. Our main result is an algorithm that guarantees inf-sup stability of the reduced problem. The algorithm is computationally effective since it can be performed in the offline phase even for parameter-dependent constraints. Moreover, we also propose a modification of the Cone Projected Greedy algorithm so as to avoid ill-conditioning issues when manipulating the reduced dual basis. Our results are illustrated numerically on the frictionless Hertz contact problem between two half-spheres with parameter-dependent radius and on the membrane obstacle problem with parameter-dependent obstacle geometry.

10th March – ‪Ruma Maity: Parameter dependent finite element analysis for ferronematics solutions

Ruma Maity‬‬ Thursday 10th March at 11:00 ABSTRACT: In this talk, we focus on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well, referred to as ferronematics. We discuss the asymptotic analysis of global energy minimizers in the limit of vanishing elastic constant, where the re-scaled elastic constant l is inversely proportional to the domain area. The conforming finite element method is used to approximate the regular solutions of the corresponding non-linear system of partial differential equations with cubic nonlinearity and non-homogeneous Dirichlet boundary conditions. We establish the existence and local uniqueness of the discrete solutions, error estimates in the energy and L2 norms with l- discretization parameter dependency. The theoretical results are complemented by the numerical experiments on the discrete solution profiles, and the numerical convergence rates that corroborate the theoretical estimates. This talk is based on joint works with Apala Majumdar (Department of Mathematics and Statistics, University of Strathclyde, UK) and Neela Nataraj (Department of Mathematics, Indian Institute of Technology Bombay, India).

27th January – ‪Frédéric Lebon‬‬ : On the modeling of nonlinear imperfect solid/solid interfaces by asymptotic techniques

Frédéric Lebon‬‬ Thursday 27th January at 11:00 ABSTRACT: In this talk, we will focus on the theoretical and numerical modelling of interfaces between solids (adhesion, bonding, friction, etc.). We will present a general methodology based on matched asymptotic theory to obtain families of models including the relative rigidity of the interphase (soft or hard), geometrical or material non-linearities (plasticity, curvature, finite strain, …), damage and multiphysics couplings (thermics, piezoelectricity, …). Numerical results will be presented.

3rd Feburary – ‪Pierre Matalon‬‬ : An h-multigrid method for Hybrid High-Order discretizations of elliptic equations

Pierre Matalon Thursday 3rd Feburary at 11:00 ABSTRACT: We consider a second order elliptic PDE discretized by the Hybrid High-Order method, for which globally coupled unknowns are located at faces. To efficiently solve the resulting linear system, we propose a geometric multigrid algorithm that keeps the degrees of freedom on the faces at every grid level. The core of the algorithm lies in the design of the prolongation operator that passes information from coarse to fine faces through the reconstruction of an intermediary polynomial of higher degree on the cells. High orders are natively handled by the use of the same polynomial degree at every grid level. The proposed algorithm requires a hierarchy of polyhedral meshes such that the faces (and not only the elements) are successively coarsened. Numerical tests on homogeneous and heterogeneous diffusion problems show fast convergence, asymptotic optimality with respect to the mesh size, robustness to the polynomial order, and robustness with respect to heterogeneity of the diffusion coefficient.

20 January – ‪Isabelle Ramiere‬ : Automatic multigrid adaptive mesh refinement with controlled accuracy for quasi-static nonlinear solid mechanics

Isabelle Ramiere‬ Thursday 20th January at 11:00 ABSTRACT: Many real industrial problems involve localized effects (nonlinearity, contact, heterogenity,…). Adaptive Mesh Refinement (AMR) approaches are well-suited numerical techniques to take into account mesoscale phenomena in simulation processes. For implicit solvers (such as for quasi-static mechanics problems), classical h and/or p-adaptive refinement strategies consisting in generating a unique global mesh locally refined (in mesh step and/or in degree of basis function) are limited by the resulting size of problems to be solved (cf. number of DoFs). Hence, we were interested in local multigrid methods, consisting in adding local refined nested meshes in zones of interest without modifying the initial computation mesh. An iterative process (similar to standard multigrid solvers) enables to correct to various levels solutions. We have extended the multigrid Local Defect Correction (LDC) method (Hackbusch, 1984), initially introduced in Computational Fluid Dynamics, to elastostaticity (Barbié et al., 2014) with a multilevel generalization of the algorithm. In order to automatically detect the zone of interest and hence to avoid the pollution error, the LDC method has been coupled with an a posteriori error estimate of Zienckiewicz-Zhu type (Barbié et al., 2014; Barbié et al., 2015; Liu et al., 2017). We also proposed an original stopping criterion in case of local singularity (Ramière et al., 2019). We have compared in (Koliesnikova et al.,2021) within a unified AMR framework the efficiency of the LDC method with respect to conforming and nonconforming h-adaptive strategies. We have also extended the LDC method to structural mechanics nonlinearities. In (Liu et al., 2017), an efficient algorithm has been developed in order to deal with frictional contact via the LDC method. For nonlinear material behaviours, a one time step algorithm has been first introduced in (Barbié et al., 2015) while a fully automatic algorithm in time with…

13 January – Koondanibha Mitra : A posteriori estimates for nonlinear degenerate parabolic and elliptic equations

Koondanibha Mitra Thursday 13th January at 11:00 ABSTRACT: Nonlinear advection-diffusion-reaction equations are used to model various complex flow processes in porous media, and in biological systems. They also exhibit parabolic-hyperbolic and parabolic-elliptic kinds of degeneracies resulting in the loss of regularity of the solutions. The nonlinear degenerate nature of the equations makes it challenging to provide sharp error bounds to any numerical solutions of the problem. When discretized in time, such equations result in a sequence of nonlinear degenerate elliptic problems which requires linear iterative schemes to solve. The linear iterates can be used to provide upper/lower bounds to the error, and to separate the error contributions due to linearization and discretization. However, the nonlinearity, as before, impedes the derivation of sharp error bounds in the standard error norm. In the first part of this study, we provide reliable, fully computable, and locally space-time efficient a posteriori error bounds for numerical approximations of such nonlinear degenerate parabolic problems. For showing global reliability, a nonlocal-in-time error estimate is derived individually for the time-integrated $H^1(H^{-1})$, $L^2(L^2)$, and the $L^2(H^1)$ errors. A maximum principle and a degeneracy estimator are employed for the last one. Global and local space-time efficiency error bounds are then obtained in a standard $H^1(H^{-1})\cap L^2(H^1)$ norm. The reliability and efficiency norms employed coincide when there is no nonlinearity. Moreover, error contributors such as flux nonconformity, time discretization, quadrature, and data oscillation are identified and separated. Numerical tests are conducted for nondegenerate and degenerate cases having exact solutions, as well as for realistic cases. It is shown that the estimators correctly identify the errors up to a factor of the order of unity. In the second part, using linear iterative schemes, we derive reliable, fully computable, and efficient error bounds for the finite element solution of the elliptic problem which…

10 December – Gregor Gantner: Applications of a space-time first-order system least-squares formulation for parabolic PDEs.

Gregor Gantner Friday 10th December at 11:00 ABSTRACT: Currently, there is a growing interest in simultaneous space-time methods for solving parabolic evolution equations. The main reasons are that, compared to classical time-marching methods, space-time methods are much better suited for massively parallel implementation, are guaranteed to give quasi-optimal approximations from the employed trial space, have the potential to drive optimally converging simultaneously space-time adaptive refinement routines, and they provide enhanced possibilities for reduced order modelling of parameter-dependent problems. On the other hand, space-time methods require more storage. This disadvantage however vanishes for problems of optimal control, for which the solution is needed simultaneously over the whole time interval anyway. While the common space-time variational formulation of a parabolic equation results in a bilinear form that is non-coercive, [1] recently proved the well-posedness of a space-time first-order system least-squares formulation of the heat equation. Least-squares formulations always correspond to a symmetric and coercive bilinear form. In particular, the Galerkin approximation from any conforming trial space exists and is a quasi-best approximation. Additionally, the least-squares functional automatically provides a reliable and efficient error estimator. In [2], we have generalized the least-squares method of [1] to general second-order parabolic PDEs with possibly inhomogeneous Dirichlet or Neumann boundary conditions. For homogeneous Dirichlet conditions, we present in this talk convergence of a standard adaptive finite element method driven by the least-squares estimator, which has also been demonstrated in [2]. The convergence analysis is applicable to a wide range of least-squares formulations for other PDEs, answering a long-standing open question in the literature. Moreover, we employ the space-time least-squares method for parameter-dependent problems as well as optimal control problems. In both cases, the coercivity of the corresponding bilinear form plays a crucial role. [1] T. Führer and M. Karkulik. Space–time least-squares finite elements for parabolic equations.…

25 November – Pierre Gosselet: Asynchronous Global/Local coupling

Pierre Gosselet: Thursday 25th November at 11:00 ABSTRACT: Non-intrusive global/local coupling can be seen as an exact iterative version of the submodeling (structural zoom) technique widely used by industry in their simulations. A global model, coarse but capable of identifying general trends in the structure, is locally patched by fine models with refined geometries, materials and meshes. The coupling is achieved by alternating Dirichlet resolutions on the patches and global resolutions with a well-chosen immersed Neumann condition. After the preliminary work of (Whitcomb, 1991), the method has been rediscovered by many authors. Our work starts with (Gendre et al., 2009). From a theoretical point of view, the method is related to the optimized Schwarz domain decomposition methods (Gosselet et al., 2018). It has been applied in many contexts (localized or generalized (visco)plasticity, stochastic calculations, cracking, damage, fatigue…). In the ANR project ADOM, we are working on the implementation of an asynchronous version of the method. The expected benefits of asynchronism (Magoulès et al., 2018; Glusa et al., 2020) are to reach the solution faster, to adapt to many computational hardware by being more resilient in case of poor load balancing, network latencies or even outages. During the presentation, I will show how to adapt the global/local coupling to asynchronism and will illustrate its performance on thermal and linear elasticity calculations. This work is realized with the support of National Research Agency, project [ANR-18-CE46-0008]. [1] Gendre, Lionel et al. (2009). “Non-intrusive and exact global/local techniques for structural problems with local plasticity”. In: Computational Mechanics 44.2, pp. 233–245. [2] Glusa, Christian et al. (2020). “Scalable Asynchronous Domain Decomposition Solvers”. In: SIAM Journal on Scientific Computing 42.6, pp. C384–C409. doi: 10.1137/19M1291303. [3] Gosselet, Pierre et al. (2018). “Non-invasive global-local coupling as a Schwarz domain decomposition method: acceleration and generalization”. In: Advanced Modeling and…

24 November – Grégory Etangsale: A primal hybridizable discontinuous Galerkin method for modelling flows in fractured porous media

Grégory Etangsale: Wednesday 24th November at 10:30 ABSTRACT: Modeling fluid flow in fractured porous media has received tremendous attention from engineering, geophysical, and other research fields over the past decades. We focus here on large fractures described individually in the porous medium, which act as preferential paths or barriers to the flow. Two different approaches are available from a computational aspect: The first one, and definitively the oldest, consists of meshing inside the fracture. In this case, the flow is governed by a single Darcy equation characterized by a large scale of variation of the permeability coefficient within the matrix region and the fracture, respectively. However, this description becomes quite challenging since it requires a considerable amount of memory storage, severely increasing the CPU time. A more recent approach differs by considering the fracture as an encapsulated object of lower dimension, i.e., (d − 1)-dimension. As a result, the flow process is now governed by distinctive equations in the matrix region and fractures, respectively. Thus, coupling conditions are added to close the problem. This mathematical description of the fractured porous media has been initially introduced by Martin et al. in [4] and is referred to as the Discrete Fracture-Matrix (DFM) model. The DFM description is particularly attractive since it significantly simplifies the meshing of fractures and allows the coupling of distinctive discretizations such as Discontinuous and Continuous Galerkin methods inside the bulk region and the fracture network, respectively. For instance, we refer the reader to the recent works of Antonietti et al. [1] (and references therein), where the authors coupled the Interior Penalty DG method with the (standard) H1-Conforming finite element method to solve the DFM problem (see e.g., [3]). However, it is well-known that DG methods are generally more expensive than most other numerical methods due to their high…

06 September – Rolf Stenberg: Nitsche’s Method for Elastic Contact Problems

Rolf Stenberg: Monday 06th June at 15:00 ABSTRACT: In this talk, we present a priori and a posteriori error estimates for the frictionless contact problem between two elastic bodies. The analysis is built upon interpreting Nitsche’s method as a stabilised finite element method for which the error estimates can be derived with minimal regularity assumptions and without a saturation assumption. The stabilising term corresponds to a master-slave mortaring technique on the contact boundary. The numerical experiments show the robustness of Nitsche’s method and corroborate the efficiency of the a posteriori error estimators. [1] T. Gustafsson, R. Stenberg, J. Videman. On Nitsche’s method for elastic contact problems. SIAM Journal of Scientific Computing. 42 (2020) B425–B446 [2] T. Gustafsson, R. Stenberg, J. Videman. The masters-slave Nitsche method for elastic contact problems. Numerical Mathematics and Advanced Applications – ENUMATH 2019. J.F. Vermolen, C. Vuik, M. Moller (Eds.). Springer Lecture Notes in Computational Science and Engineering. 2021

Internal Seminar