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140 results on '"Kern, Michel"'

3. A space-time multiscale mortar mixed finite element method for parabolic equations

Author

Jayadharan, Manu, Kern, Michel, Vohralík, Martin, and Yotov, Ivan

Subjects
Mathematics - Numerical Analysis
Abstract

We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a space-time variational formulation that couples mixed finite elements in space with discontinuous Galerkin in time. Continuity of flux (mass conservation) across space-time interfaces is imposed via a coarse-scale space-time mortar variable that approximates the primary variable. Uniqueness, existence, and stability, as well as a priori error estimates for the spatial and temporal errors are established. A space-time non-overlapping domain decomposition method is developed that reduces the global problem to a space-time coarse-scale mortar interface problem. Each interface iteration involves solving in parallel space-time subdomain problems. The spectral properties of the interface operator and the convergence of the interface iteration are analyzed. Numerical experiments are provided that illustrate the theoretical results and the flexibility of the method for modeling problems with features that are localized in space and time.

Published
2021

4. Preconditioning a coupled model for reactive transport in porous media

Author

Amir, Laila and Kern, Michel

Subjects
Mathematics - Numerical Analysis
Abstract

We study numerical methods for solving reactive transport problems in porous media that allow a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. After recalling how each individual subsystem can be solved, we give a formulation that eliminates the local chemical concentrations, and keeps the total concentrations as unknowns. The block structure of the model is exploited both at the nonlinear level, by eliminating some unknowns, and at the linear level by using block Gauss-Seidel or block Jacobi preconditioning. The methods are applied to the easy 1D case of the MoMaS benchmark.

Published
2017

5. Space-time domain decomposition for advection-diffusion problems in mixed formulations

Author

Hoang, Thi-Thao-Phuong, Japhet, Caroline, Kern, Michel, and Roberts, Jean E.

Subjects
Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs
Abstract

This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time steps can be used in different parts of the domain. Global-in-time, non-overlapping domain-decomposition methods are coupled with operator splitting making possible the different treatment of the advection and diffusion terms. Two domain-decomposition methods are considered: one uses the time-dependent Steklov--Poincar{\'e} operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Robin transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interface is derived, and different time grids are employed to adapt to different time scales in the subdomains. A generalized Neumann-Neumann preconditioner is proposed for the first method. To illustrate the two methods numerical results for two-dimensional problems with strong heterogeneities are presented. These include both academic problems and more realistic prototypes for simulations for the underground storage of nuclear waste.

Published
2016

6. Space-time Domain Decomposition and Mixed Formulation for solving reduced fracture models

Author

Hoang, Thi-Thao-Phuong, Japhet, Caroline, Kern, Michel, and Roberts, Jean E.

Subjects
Mathematics - Numerical Analysis
Abstract

In this paper we are interested in the "fast path" fracture and we aim to use global-in-time, nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture. We consider a reduced model in which the fracture is treated as an interface between the two subdomains. Two domain decomposition methods are considered: one uses the time-dependent SteklovPoincar{\'e} operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Ventcell transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interface is derived, and different time grids are employed to adapt to different time scales in the subdomains and in the fracture. Demonstrations of the well-posedness of the Ventcell subdomain problems is given for the mixed formulation. An analysis for the convergence factor of the OSWR algorithm is given in the case with fractures to compute the optimized parameters. Numerical results for two-dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods.

Published
2015

7. Global–in–Time Domain Decomposition for a Nonlinear Diffusion Problem

Author

Ahmed, Elyes, Japhet, Caroline, Kern, Michel, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Haynes, Ronald, editor, MacLachlan, Scott, editor, Cai, Xiao-Chuan, editor, Halpern, Laurence, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, and Widlund, Olof, editor

Published
2020
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9. Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations

Author

Hoang, Thi Thao Phuong, Jaffré, Jérôme, Japhet, Caroline, Kern, Michel, and Roberts, Jean

Subjects
Mathematics - Numerical Analysis
Abstract

This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov-Poincar\'e operator and the other uses Optimized Schwarz Waveform Relaxation (OSWR) based on Robin transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interfaces between subdomains is derived, and different time grids are employed to adapt to different time scales in the subdomains. Demonstrations of the well-posedness of the subdomain problems involved in each method and a convergence proof of the OSWR algorithm are given for the mixed formulation. Numerical results for 2D problems with strong heterogeneities are presented to illustrate the performance of the two methods.

Published
2013

10. A global method for coupling transport with chemistry in heterogeneous porous media

Author

Laila, Amir and Kern, Michel

Subjects
Mathematics - Numerical Analysis
Abstract

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark., Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=14

Published
2009
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11. Initialization of the Circulant Embedding method to speed up the generation of Gaussian random fields

Author

Pichot, Géraldine, Legrand, Simon, Kern, Michel, Tepakbong-Tematio, Nathanael, Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Service Expérimentation et Développement [Paris] (SED), and Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO)

Subjects
Statistics and Probability, circulant embedding method, Computational Mathematics, Numerical Analysis, Modeling and Simulation, Matérn covariances, stationary Gaussian random fields, fast Fourier transform, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). The main idea is to embed the covariance matrix in a larger nested block circulant matrix, whose factorization can be rapidly computed thanks to the fast Fourier transform (FFT) algorithm. The CEM requires the extended matrix to be at least positive semidefinite which is proven to be the case if the enclosing domain is sufficiently large, as proven by Theorem 2.3 in [Graham et al, SIAM Journal on Numerical Analysis, 2018] for cubic domains. In this paper, we generalize this theorem to the case of rectangular parallelepipeds. Then we propose a new initialization stage of the CEM algorithm that makes it possible to quickly jump to a domain size close to the one needed for the CEM algorithm to work. These domain size estimates are based on fitting functions. Examples of fitting functions are given for the Mat\'ern family of covariances. These functions are inspired by our numerical simulations and by the theoretical work from [Graham et al, SIAM Journal on Numerical Analysis, 2018]. The parameters estimation of the fitting functions is done numerically. Several numerical tests are performed to show the efficiency of the proposed algorithms, for both isotropic and anisotropic Matérn covariances.

Published
2022
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12. Ventcell Conditions with Mixed Formulations for Flow in Porous Media

Author

Hoang, Thi Thao Phuong, Japhet, Caroline, Kern, Michel, Roberts, Jean, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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15. Space–Time Domain Decomposition for Mixed Formulations of Diffusion Equations

Author

Hoang, Thi-Thao-Phuong, Jaffré, Jérôme, Japhet, Caroline, Kern, Michel, Roberts, Jean, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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16. Numerical simulation of two-phase multicomponent flow with reactive transport in porous media: application to geological sequestration of CO2

Author

Ahusborde Etienne, Kern Michel, and Vostrikov Viatcheslav

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

In this work, we consider two-phase multicomponent flow in heterogeneous porous media with chemical reactions. Equations governing the system are the mass conservation law for each species, together with Darcy’s law and complementary equations such as the capillary pressure law. Coupling with chemistry occurs through reactions rates. These rates can either be given non-linear functions of concentrations in the case of kinetic chemical reactions or are unknown in the case of equilibrium chemical reactions (such as reactions in aqueous phase). In this latter case, each reaction gives rise to a mass action law, an algebraic relation that relates the activities of the implied species. The resulting system will couple partial differential equations with algebraic equations. The aim of this paper is to develop a numerical method for the simulation of this system. We consider a sequential approach that consists in splitting the initial problem into two sub-systems. The first subsystem is a two-phase two-component flow, while the second subsystem is devoted to a reactive transport problem. For the two-phase two-component flow part, we have used an already existing module of the open-source parallel multiphase flow simulator DuMuX. To solve the reactive transport problem, we have implemented a new module in the DuMuX framework that solves a single phase multicomponent transport problem, and we have coupled it with a locally developed code for chemical equilibrium, called ChemEqLib, through a sequential iterative approach. Then, both modules have been coupled to propose a simple, but mathematically consistent, iterative method that handles two-phase flow with reactive transport. The approach is validated on a 2D example from the literature representative of a model for the long-term fate of sequestered CO2.

Published
2015
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27. Reactive Multiphase Flow in Porous Media at the Darcy Scale: a Benchmark proposal

Author

de Hoop, Stephan, Voskov, Denis, Ahusborde, Etienne, Amaziane, Brahim, Kern, Michel, Delft University of Technology (TU Delft), Stanford University, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), and École des Ponts ParisTech (ENPC)

Subjects
[SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Published
2022

28. Intersecting fractures in porous media: mathematical and numerical analysis.

Author

Amir, Laila, Kern, Michel, Mghazli, Zoubida, and Roberts, Jean E.

Subjects
*POROUS materials, *NUMERICAL analysis, *MATHEMATICAL analysis, *DOMAIN decomposition methods
Abstract

This paper studies a model for flow in a fractured porous medium with intersecting fractures. The fractures are treated as lower-dimensional manifolds and then physical transmission conditions express the pressure jump and the continuity of the flux across the fractures. Specific attention is borne to the conditions when several fractures intersect. The resulting system is discretized with mixed finite element, and the well-posedness of both the continuous and the discrete problems are proved. Then a domain decomposition method is formulated, so that the problem is reduced to the set of fractures, and a simple preconditioner is proposed. Numerical results exemplify the performance of the method. [ABSTRACT FROM AUTHOR]

Published
2023
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29. Analyse de performances du code ComPASS

Author

Ould Rouis, Yacine, Kern, Michel, Lopez, Simon, Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École des Ponts ParisTech (ENPC), Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Maison de la Simulation, BRGM (Bureau de recherches géologiques et minières), ANR-16-CE06-0009,CHARMS,Modèles de Réservoirs Quantitatifs pour les Systèmes Hydrothermaux Complexes(2016), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)

Subjects
[SDU.STU]Sciences of the Universe [physics]/Earth Sciences, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Published
2021

32. Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

Author

Amir, Laila, Kern, Michel, Laboratoire d’Ingénierie Informatique et Systèmes (L2Is), Faculté des Sciences et Techniques Marrakech, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Faculté des Sciences et Techniques Marrakech (FSTG), Université Cadi Ayyad [Marrakech] (UCA)-Université Cadi Ayyad [Marrakech] (UCA), and ANR-16-CE06-0009,CHARMS,Modèles de Réservoirs Quantitatifs pour les Systèmes Hydrothermaux Complexes(2016)

Subjects
lcsh:TD201-500, lcsh:Hydraulic engineering, lcsh:Water supply for domestic and industrial purposes, finite volume methods, lcsh:TC1-978, Newton-Krylov methods, Newton–Krylov methods, reactive transport, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], porous media flow and transport
Abstract

International audience; Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro-thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or differential equations, describing the chemical reactions. Solution methods for the resulting large nonlinear system can be either fully coupled or can iterate between transport and chemistry. This paper extends previous work by the authors where an approach based on the Newton-Krylov method applied to a reduced system has been developed. The main feature of the approach is to solve the nonlinear system in a fully coupled manner while keeping transport and chemistry modules separate. Here we extend the method in two directions. First, we take into account mineral precipitation and dissolution reactions by using an interior point Newton method, so as to avoid the usual combinatorial approach. Second, we study two-dimensional heterogeneous geometries. We show how the method can make use of an existing transport solver, used as a black box. We detail the methods and algorithms for the individual modules, and for the coupling step. We show the performance of the method on synthetic examples.

Published
2021
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34. Global-in-Time Domain Decomposition for a Nonlinear Diffusion Problem

Author

Ahmed, Elyes, Japhet, Caroline, Kern, Michel, Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Bergen (UiB), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), R. Haynes, S. MacLachlan, X.-C. Cai, L. Halpern, H. H. Kim, A. Klawonn, O. Widlund, ANR-14-CE23-0005,DEDALES,Décomposition de domaines algébriques et géométriques pour les écoulements souterrains(2014), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS)

Subjects
ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We study a simplified model for two–phase flow in porous media, where the medium is made of two (or more) different rock types. Each rock type is a subdomain with a distinct capillary pressure function so that the saturation becomes discontinuous across the interface between the different regions. This leads to the phenomenon of capillary trapping (see [12] or [4]).

Published
2018
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35. Geothermal Modeling in Complex Geological Systems with the ComPASS Code

Author

Lopez, Simon, Masson, Roland, Beaude, Laurence, Birgle, Nabil, Brenner, Konstantin, Kern, Michel, Smaï, Farid, Xing, Feng, Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Stanford University, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)

Subjects
Unstructured meshes, Reservoir modeling, Fracture network, Multiphase flow, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Hydrothermal simulations, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

International audience; Deep geothermal systems often lie in complex geological settings, with multi-scale geological structures that exert a dominant control on convective processes and the transfer of geothermal heat. Methods based on the implicit description of geometrical objects offer an efficient framework to quickly build structural models of such contexts with the occurrence of discontinuities like faults and fractures. Yet, when it comes to discretizing such models the implicit nature of surfaces make volume meshing a non-trivial task and the results are unstructured polyhedral meshes. Over the last few years, much progress has been made towards the consistent and robust discretization of diffusion processes in porous media. These research efforts resulted in several numerical schemes designed with a sound mathematical basis and able to deal with subsurface spatial heterogeneities (permeability variations, anisotropies…) and general polyhedral meshes. We introduce hereafter the ComPASS platform, an open source initiative that aims at building a geotermal simulation platform relying on one such scheme and recent numerical techniques. The current code is able to handle compositional multiphase Darcy flows, relying on a Coats type formulation, coupled to the conductive and convective transfers of energy. Simulations can be run on unstructured meshes including complex networks of fractures with intersecting, immersed and non immersed fractures. Flow inside the fractures is modelled with a so called hybrid-dimensional model, using a 2D model in the fractures that can have variable apertures and permeability and is coupled with 3D transfers in the matrix. The physics is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the PETSc library and can be run on large computing clusters. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. A high level interface to describe the simulation contexts is provided by the Python language, whereas the core routine are written in Fortran and C++. The paper will review the theoretical foundations and the current architecture of the code. Then it will present applications examples and present the current development roadmap.

Published
2018

37. Space-time domain decomposition methods and a posteriori error estimates for the heat equation

Author

Ali Hassan, Sarah, Japhet, Caroline, Kern, Michel, Vohralík, Martin, Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), This work was supported by ANDRA, the French agency for nuclear waste management, and by the ANR project DEDALES under grant ANR-14-CE23-0005. It has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 647134 GATIPOR)., ANR-14-CE23-0005,DEDALES,Décomposition de domaines algébriques et géométriques pour les écoulements souterrains(2014), European Project: 647134,H2020 ERC,ERC-2014-CoG,GATIPOR(2015), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Japhet, Caroline, Appel à projets générique - Décomposition de domaines algébriques et géométriques pour les écoulements souterrains - - DEDALES2014 - ANR-14-CE23-0005 - Appel à projets générique - VALID, and Guaranteed fully adaptive algorithms with tailored inexact solvers for complex porous media flows - GATIPOR - - H2020 ERC2015-09-01 - 2020-09-01 - 647134 - VALID

Subjects
discontinuous Galerkin in time, optimized Robin transmission conditions, stopping criteria, space-time domain decomposition, Heterogeneous diffusion, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], a posteriori error estimate, mixed finite element method, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience This paper develops a posteriori estimates for global-in-time, nonoverlapping domain decomposition (DD) methods for heterogeneous diffusion problems. The method uses optimized Schwarz waveform relaxation (OSWR) with Robin transmission conditions on the space-time interface between subdomains, and a lowest-order Raviart–Thomas–Nédélec discretization in the subdomains. Our estimates yield a guaranteed and fully computable upper bound on the error measured in the space-time energy norm of [19, 20], at each iteration of the space-time DD algorithm, where the spatial discretization, the time discretization, and the domain decomposition error components are estimated separately. Thus, an adaptive space-time DD algorithm is proposed, wherein the iterations are stopped when the domain decomposition error does not affect significantly the global error, allowing important savings in terms of the number of domain decomposition iterations while guaranteeing a user-given precision. Numerical results for a two-dimensional heat equation are presented to illustrate the efficiency of our a posteriori estimates and the performance of the adaptive stopping criteria for the space-time DD algorithm.

Published
2017

39. Space-time Domain Decomposition and Mixed Formulation for solving reduced fracture models

Author

Hoang, Thi-Thao-Phuong, Japhet, Caroline, Kern, Michel, Roberts, Jean E., Simulation for the Environment : Reliable and Efficient Numerical Algorithms (SERENA), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ho Chi Minh City University of Pedagogy, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)

Subjects
domain decomposition, mixed formulations, optimized Schwarz waveform relaxation, Ventcell transmission conditions, convergence factor, FOS: Mathematics, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, AMS 65M55, 65M50, 65M60, 76S05, 35K20, nonconforming time grids, time-dependent SteklovPoincaré op-erator, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], reduced fracture model
Abstract

International audience; In this paper we are interested in the "fast path" fracture and we aim to use global-in-time, nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture. We consider a reduced model in which the fracture is treated as an interface between the two subdomains. Two domain decomposition methods are considered: one uses the time-dependent SteklovPoincaré operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Ventcell transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interface is derived, and different time grids are employed to adapt to different time scales in the subdomains and in the fracture. Demonstrations of the well-posedness of the Ventcell subdomain problems is given for the mixed formulation. An analysis for the convergence factor of the OSWR algorithm is given in the case with fractures to compute the optimized parameters. Numerical results for two-dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods.

Published
2016
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41. Numerical simulation of two-phase multi-component flow with reactive transport in porous media

Author

Ahusborde, Etienne, Kern, Michel, Vostrikov, Viatcheslav, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Maison de la Simulation (MDLS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), and Ahusborde, Etienne

Subjects
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience

Published
2015

43. Space-Time Domain Decomposition for Mixed Formulations of Diffusion Equations

Author

Hoang, Thi Thao Phuong, Jaffré, Jérôme, Japhet, Caroline, Kern, Michel, Roberts, Jean, Environmental Modeling, Optimization and Programming Models (POMDAPI), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Maison de la Simulation (MDLS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Contrat avec Andra, Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Kern, Michel

Subjects
optimized Schwarz waveform relaxation, mixed finite elements, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], time-dependent Steklov-Poincaré operator, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; The far field simulation of underground nuclear waste disposal site requires a high computational cost due to the widely varying properties of different materials, the different length and time scales, and the high accuracy requirements. Nonoverlapping domain decomposition methods allow local adaptation in both space and time and result in parallel algorithms. We have extended the optimized Schwarz waveform relaxation (OSWR) method, successfully used for finite elements and finite volumes, to the case of mixed finite elements with their local mass-conservation property. Another choice is the substructuring method, which has been shown to be efficient for steady state problems with strong heterogeneities. We study a time-dependent Schur complement method, which is the algebraic counterpart of the discrete Steklov Poincaré operator, and introduce the Neumann preconditioner as well as weight matrices designed to make the convergence speed independent of the heterogeneities. Both methods enable the use of local time steps when the subdomains have highly different physical properties. Their performance is illustrated on test cases suggested by nuclear waste disposal problems.

Published
2012

45. Simulation numérique d'écoulements diphasiques multiconstituants avec transport réactif en milieu poreux : application au stockage géologique du CO2

Author

Ahusborde, Etienne, Kern, Michel, Vostrikov, Viatcheslav, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Environmental Modeling, Optimization and Programming Models (POMDAPI), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Maison de la Simulation (MDLS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

COM; International audience; no abstract

Published
2014

46. PRECONDITIONING A COUPLED MODEL FOR REACTIVE TRANSPORT IN POROUS MEDIA.

Author

AMIR, LAILA and KERN, MICHEL

Subjects
*COUPLED mode theory (Wave-motion), *POROUS materials, *PROBLEM solving, *NUMERICAL solutions to partial differential equations, *ROBUST control
Abstract

Reactive transport problems involve the coupling between the chemical interactions of different species and their transport by advection and diffusion. It leads to the solution of a non-linear systems of partial differential equations coupled to local algebraic or differential equations. Developping software for these two components involves fairly different techniques, so that methods based on loosely coupled modules are desirable. On the other hand, numerical issues such as robustness and convergence require closer couplings, such as simultaneous solution of the overall system. The method described in this paper allows a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. We give a formulation that eliminates the local chemical concentrations and keeps the total concentrations as unknowns, then recall how each individual subsystem can be solved. The coupled system is solved by a Newton{Krylov method. The block structure of the model is exploited both at the nonlinear level, by eliminating some unknowns, and at the linear level by using block Gauss-Seidel or block Jacobi preconditioning. The methods are applied to a 1D case of the MoMaS benchmark. [ABSTRACT FROM AUTHOR]

Published
2019

47. Couplage par composants logiciels de codes d'hydrogéologie

Author

Erhel, Jocelyne, Ackerer, Philippe, De Dreuzy, Jean-Raynald, Kern, Michel, Leroy, Hugues, Pérez, Christian, Algorithms Adapted to Intensive Numerical Computing (ALADIN), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mécanique des Fluides et des Solides (IMFS), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Centre National de la Recherche Scientifique (CNRS), Géosciences Rennes (GR), Université de Rennes (UR)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre Armoricain de Recherches en Environnement-Centre National de la Recherche Scientifique (CNRS), Parameter estimation and modeling in heterogeneous media (ESTIME), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Biological systems and models, bioinformatics and sequences (SYMBIOSE), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Programming distributed parallel systems for large scale numerical simulation (PARIS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Cachan (ENS Cachan)-Inria Rennes – Bretagne Atlantique, ACI HydroGrid, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre Armoricain de Recherches en Environnement-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Cachan (ENS Cachan)-Inria Rennes – Bretagne Atlantique, and Kern, Michel

Subjects
hydrogéologie, Couplage de code, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], composants logiciels, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

National audience; Notre objectif est d'étudier la modélisation de phénomènes couplés et leur mise en oeuvre sur une grille de calcul, en développant quatre applications. Les deux premiers couplages sont de type physico-chimique et physico-physique (couplage algébrique d'équations). Ils sont appliqués respectivement à la contamination d'aquifères et à l'intrusion d'eau salée. Les deux autres couplages sont géométriques de type multidomaines ou multi-échelles et sont appliqués au stockage profond de déchets radioactifs, d'une part dans un milieu peu fracturé, d'autre part dans un réseau de fractures.Nous choisissons une approche par composants logiciels, qui permet d'encapsuler chaque code modélisant un phénomène physique. Les interfaces des composants permettent d'eectuer les échanges de données nécessaires au couplage numérique.L'exécutif PadicoTM garantit un calcul à haute performances sur une grille de calcul avec différents types de réseaux, grâce notamment à un modèle de composants parallèles, qui permet de passer à l'échelle.

Published
2002

48. Block Preconditioning for a Coupled Model of Transport with Sorption in Porous Media

Author

Kern, Michel, Taakili, Abdelaziz, Parameter estimation and modeling in heterogeneous media (ESTIME), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Faculté des Sciences et Techniques - Errachidia (FSTE Errachidia), Université Moulay Ismail (UMI), and INRIA

Subjects
[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
Abstract

Session 5; International audience

Published
2011

49. Simulation of Transport in 2D heterogeneous Porous media via a Random-Walk Particle Tracking Method

Author

Pichot , Géraldine, Beaudoin , Anthony, Charrier , Julia, Soualem , Nadir, Erhel , Jocelyne, De Dreuzy , Jean-Raynald, Kern , Michel, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS), Hydrodynamique et Ecoulements Environnementaux (HydEE), Département Fluides, Thermique et Combustion (FTC), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique de Rennes (IRMAR), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Géosciences Rennes (GR), Université de Rennes (UR)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR), Université de Rennes (UR)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Centre National de la Recherche Scientifique (CNRS), Parameter estimation and modeling in heterogeneous media (ESTIME), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers, ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-Institut Pprime (PPRIME), ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers, AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR)-Centre National de la Recherche Scientifique (CNRS), Pichot, Géraldine, Simulations and Algorithms on Grids for Environment ( SAGE ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -SYSTÈMES LARGE ÉCHELLE ( IRISA-D1 ), Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), CentraleSupélec-Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Télécom Bretagne-Institut National des Sciences Appliquées ( INSA ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -École normale supérieure - Rennes ( ENS Rennes ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Bretagne Sud ( UBS ) -CentraleSupélec-Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Télécom Bretagne-Institut National des Sciences Appliquées ( INSA ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -École normale supérieure - Rennes ( ENS Rennes ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Bretagne Sud ( UBS ) -Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Télécom Bretagne-Institut National des Sciences Appliquées ( INSA ) -École normale supérieure - Rennes ( ENS Rennes ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Bretagne Sud ( UBS ), Institut Pprime ( PPRIME ), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Géosciences Rennes ( GR ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut national des sciences de l'Univers ( INSU - CNRS ) -Observatoire des Sciences de l'Univers de Rennes ( OSUR ) -Centre National de la Recherche Scientifique ( CNRS ), Parameter estimation and modeling in heterogeneous media ( ESTIME ), and Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria )

Subjects
[ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience

Published
2011

50. Problèmes inverses

Author

Kern, Michel, Environmental Modeling, Optimization and Programming Models (POMDAPI), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Claude Brezinski

Subjects
[SPI]Engineering Sciences [physics], état adjoint, identification de paramètres, Régularisation, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

National audience

Published
2010

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