Il est affilié à l'Institut National des Sciences Appliquées (INSA) et l'Université Paul Sabatier (UPS) de Toulouse, ainsi que l'Université Joseph Fourier (UJF) de Grenoble. Il est qualifié d'Instrument de Recherche et p ermet à tout chercheur ? venant du monde entier ? de réaliser des expériences sous champ intense. Implanté sur deux sites, il offre des champs magnétiques statiques allant jusqu'à 36 Tesla sur son site de Grenoble, et des champs magnétiques pulsés allant jusqu'à 81 Tesla de manière CHAPITRE 10, MODÉLISATION D'AIMANTS RÉSISTIFS À HAUT CHAMP 3.4 Performances Hélice complète Considérons maintenant une hélice complète. L'espace d'approximation élément fini est composé de 5 ? 10 5 degrés de liberté, répartis sur 15 processeurs de type Intel(R) Xeon(R) X5650 à 2.67 GHz. Le nombre maximal d'itérations de Picard est fixé à 20 ,
des bases EIM prend 2h30. La construction d'un élément de la base réduite nécessite 10 minutes En terme de temps de calcul, nous estimons que l'utilisation de la méthode des bases réduites devient intéressante ? en comparaison avec la méthode des éléments finis ? à partir de 6 évaluations. Cependant, puisque la partie hors-ligne nécessite autant de résolutions FE qu'il y a d'éléments dans la base réduite, l'utilisation de la méthode RB devient intéressante seulement après 10 évaluations. Cela est dû au temps ? non négligeable ? requis par le processus d'assemblage. Il est important de noter que, contrairement au modèle FE pour lequel les matrices sont assemblées à chaque simulation (aucun pré-calcul n'est possible), l'utilisation de la décomposition affine en paramètres par le framework- RBM permet d'assembler les matrices une seule fois au moment de l'étape hors-ligne quel que soit le nombre d'éléments dans la base réduite. Afin d'illustrer nos propos, on se propose de faire le même calcul ,
add(t 1) ;c t x r b . add(t 2) ;c t x r b . add(t 3) ,
The heterogeneous multiscale method, Acta Numerica, vol.21, issue.2, pp.1-8 ,
DOI : 10.1017/S0962492912000025
URL : https://hal.archives-ouvertes.fr/hal-01111169
The 42+ T Hybrid Magnet Project at??CNRS-LNCMI-Grenoble, Journal of Low Temperature Physics, vol.16, issue.1-2 ,
DOI : 10.1007/s10909-009-0136-0
A brief introduction to homogenization and miscellaneous applications, ESAIM : Proceedings, pp.1-49, 2012. ,
DOI : 10.1051/proc/201237001
URL : https://doaj.org/article/cd6b49ef3da94a7da7fa9e7a6f7bbb93
Automatic choice of global shape functions in structural analysis, AIAA Journal, vol.16, issue.5 ,
DOI : 10.2514/3.7539
The Elements of UML (TM) 2.0 Style, 2005. ,
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, pp.1-5 ,
DOI : 10.1137/S0895479899358194
URL : https://hal.archives-ouvertes.fr/hal-00808293
Hybrid scheduling for the parallel solution of linear systems, Parallel Computing, vol.32, issue.2, pp.136-156, 2006. ,
DOI : 10.1016/j.parco.2005.07.004
URL : https://hal.archives-ouvertes.fr/inria-00070599
A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.139, issue.3, pp.153-176, 2006. ,
DOI : 10.1016/j.jnnfm.2006.07.007
URL : https://hal.archives-ouvertes.fr/hal-01004909
A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.2-3, pp.98-121, 2007. ,
DOI : 10.1016/j.jnnfm.2007.03.009
Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.), Computer Methods in Applied Mechanics and Engineering, vol.105, issue.1, pp.125-141, 1993. ,
DOI : 10.1016/0045-7825(93)90119-I
Homogenisation averaging processes in periodic media.S p r i n g e r ,
DOI : 10.1007/978-94-009-2247-1
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries, pp.9-9 ,
DOI : 10.1007/978-1-4612-1986-6_8
PARAMETRIC FAMILIES OF REDUCED FINITE ELEMENT MODELS. THEORY AND APPLICATIONS, Mechanical Systems and Signal Processing, vol.10, issue.4 ,
DOI : 10.1006/mssp.1996.0027
An ???empirical interpolation??? method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol.339, issue.9, pp.6-6 ,
DOI : 10.1016/j.crma.2004.08.006
URL : https://hal.archives-ouvertes.fr/hal-00021702
On the Reduced Basis Method, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, p.5 ,
DOI : 10.1002/zamm.19950750709
Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language, Journal of Symbolic Computation, vol.33, issue.1, pp.1-1 ,
DOI : 10.1006/jsco.2001.0494
Convergence Rates for Greedy Algorithms in Reduced Basis Methods, SIAM Journal on Mathematical Analysis, vol.43, issue.3 ,
DOI : 10.1137/100795772
URL : https://hal.archives-ouvertes.fr/hal-00767082
Multi-level adaptive solutions to boundary-value problems, Mathematics of Computation, vol.31, issue.138 ,
DOI : 10.1090/S0025-5718-1977-0431719-X
Augmented spaces, two-level methods, and stabilizing subgrids. International journal for numerical methods in fluids, pp.3-4, 2002. ,
DOI : 10.1002/fld.265
CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.04, issue.04 ,
DOI : 10.1142/S0218202594000327
Mixed and hybrid finite element methods, 1991. ,
Am u l t i g r i dt u t o r i a l .S i a m ,
A priori convergence of the greedy algorithm for the parametrized reduced basis method, ESAIM : Mathematical Modelling and Numerical Analysis ,
URL : https://hal.archives-ouvertes.fr/hal-00659314
Spectral methods.S p r i n g e r, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-01296839
A Posteriori Error Analysis of the Reduced Basis Method for Nonaffine Parametrized Nonlinear PDEs, SIAM Journal on Numerical Analysis, vol.47, issue.3 ,
DOI : 10.1137/080724812
Accurate a posteriori error evaluation in the reduced basis method, Comptes Rendus Mathematique, vol.350, issue.9-10 ,
DOI : 10.1016/j.crma.2012.05.012
URL : https://hal.archives-ouvertes.fr/hal-00761221
Accurate and efficient evaluation of the a posteriori error estimator in the reduced basis method, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00761735
Vers la simulation des écoulements sanguins, 2013. ,
Une méthode combinée d'éléments finis à deux grilles/bases réduites pour l'approximation des solutions d'une edp paramétrique, Comptes Rendus Mathematique, vol.3, issue.7, pp.4-7 ,
DOI : 10.1016/j.crma.2009.02.019
Domain decomposition algorithms, Acta Numerica, vol.37, issue.1, pp.6-7 ,
DOI : 10.1016/0041-5553(78)90012-5
Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2d maxwell s problem, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00976057
An overview of the proper generalized decomposition with applications in computational rheology, Journal of Non-Newtonian Fluid Mechanics, vol.166, issue.11 ,
DOI : 10.1016/j.jnnfm.2010.12.012
URL : https://hal.archives-ouvertes.fr/hal-01005239
The finite element method for elliptic problems, pp.2-4, 2002. ,
An introduction to homogenization, volume 17 of oxford lecture series in mathematics and its applications ,
Certified real-time solution of parametrized partial differential equations, Handbook of Materials Modeling, pp.1529-1564, 2005. ,
Applications of reduced order modeling to high magnetic field resistive magnets developments, Conference Record of the 23th International Conference on Magnet Technology ,
Reduced order modeling of high magnetic field magnets, Conference Record of the 9th International Symposium of Electric and Magnetic Fields ,
URL : https://hal.archives-ouvertes.fr/hal-00955232
A Reduced Basis Framework: Application to large scale non-linear multi-physics problems, ESAIM: Proceedings, vol.43, pp.225-254, 2013. ,
DOI : 10.1051/proc/201343015
URL : https://hal.archives-ouvertes.fr/hal-00786557
Reduced basis method for multi-parameter-dependent steady Navier???Stokes equations: Applications to natural convection in a cavity, Journal of Computational Physics, vol.228, issue.12 ,
DOI : 10.1016/j.jcp.2009.03.008
Diffuse Optical Tomography for Tumour Detection, 2016. ,
OpenTURNS, an Open Source initiative to Treat Uncertainties, Risks'N Statistics in a structured industrial approach, 41èmes Journées de Statistique, SFdS ,
URL : https://hal.archives-ouvertes.fr/inria-00386719
Convergence of a Nonconforming Multiscale Finite Element Method, SIAM Journal on Numerical Analysis, vol.37, issue.3, pp.8-8, 2000. ,
DOI : 10.1137/S0036142997330329
Ap o s t e r i o r ierror bounds for the empirical interpolation method, Comptes Rendus Mathematique, vol.3, issue.9, pp.4-8, 2010. ,
An hp Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations, Mathematical and Computer Modelling of Dynamical Systems, vol.7, issue.1 4 ,
DOI : 10.1007/978-3-642-15337-2_15
URL : http://augustine.mit.edu/methodology/papers/atp_SIAM_JSC_preprint_accepted_Jul2010.pdf
A Two-Step Certified Reduced Basis Method, Journal of Scientific Computing, vol.26, issue.3 ,
DOI : 10.1007/s10915-011-9494-2
URL : http://hdl.handle.net/1721.1/79382
DC High Field Magnets at the LNCMI, IEEE Transactions on Applied Superconductivity, vol.22, issue.3 ,
DOI : 10.1109/TASC.2012.2183109
On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, pp.21-28, 1983. ,
DOI : 10.1002/zamm.19830630105
Deriving upwinding, mass lumping and selective reduced integration by residual-free bubbles, Applied Mathematics Letters, vol.9, issue.5, pp.83-88, 1996. ,
DOI : 10.1016/0893-9659(96)00078-X
URL : http://doi.org/10.1016/0893-9659(96)00078-x
Certified rapid solution of partial differential equations for real-time parameter estimation and optimization of PDE-constrained optimization : Real-time PDE-constrained optimization. SIAM computational science and engineering book series, Proceedings of the 2nd Sandia workshop ,
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations, ESAIM : Mathematical Modelling and Numerical Analysis ,
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.41, issue.3 ,
DOI : 10.1051/m2an:2007031
URL : https://hal.archives-ouvertes.fr/hal-00112154
Eigen v3, 2010. ,
Convergence Rates of the POD???Greedy Method, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.3 ,
DOI : 10.1051/m2an/2012045
Reduced basis method for finite volume approximations of parametrized linear evolution equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.42, issue.2 ,
DOI : 10.1051/m2an:2008001
Multi-grid methods and applications,v o l u m e4 . S p r i n g e r -V e r l a g Berlin, 1985. ,
DOI : 10.1007/978-3-662-02427-0
Le probleme de Cauchy et les équations aux dérivées partiel les linéaires hyperboliques,v o l u m e1 9 3 . P a r i s, pp.9-12 ,
The chaco user's guide version 2.0, 1995. ,
DOI : 10.2172/10106339
A survey of software for sparse eigenvalue problems, 2009. ,
SLEPc, ACM Transactions on Mathematical Software, vol.31, issue.3, pp.31351-362, 2005. ,
DOI : 10.1145/1089014.1089019
Berko oz. Turbulence, coherent structures, dynamical systems and symmetry, 1998. ,
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients Mathematics of Computation of the ,
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, Journal of Computational Physics, vol.134, issue.1, pp.169-189, 1997. ,
DOI : 10.1006/jcph.1997.5682
Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Computer Methods in Applied Mechanics and Engineering, vol.127, issue.1-4, pp.387-401, 1995. ,
DOI : 10.1016/0045-7825(95)00844-9
The variational multiscale method?a paradigm for computational mechanics Computer methods in applied mechanics and engineering, pp.6-6 ,
Multiscale and stabilized methods, 2004. ,
DOI : 10.1002/9781119176817.ecm051
URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA439478
A successive constraint linear optimization method for lower bounds of parametric coercivity and inf???sup stability constants, Comptes Rendus Mathematique, vol.345, issue.8 ,
DOI : 10.1016/j.crma.2007.09.019
Spectral/hp element methods for CFD, 1999. ,
A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices ,
Certified reduced basis methods for parametrized parabolic partial differential equations with non-affine source terms, Computer Methods in Applied Mechanics and Engineering, vol.209, issue.212 ,
DOI : 10.1016/j.cma.2011.10.010
Reduced basis approximation and a posteriori error estimates for am u l t i s c a l el i q u i dc r y s t a lm o d e l, Mathematical and Computer Modelling of Dynamical Systems, vol.7, issue.1 4, pp.4-4 ,
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics, SIAM Journal on Numerical Analysis, vol.40, issue.2, pp.492-515, 2002. ,
DOI : 10.1137/S0036142900382612
The structure of inhomogeneous turbulent flows Atmospheric turbulence and radio wave propagation ,
Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, pp.153-158, 2000. ,
DOI : 10.1016/S0764-4442(00)00270-6
A general multipurpose interpolation procedure: the magic points, Communications on Pure and Applied Analysis, vol.8, issue.1, 2007. ,
DOI : 10.3934/cpaa.2009.8.383
URL : https://hal.archives-ouvertes.fr/hal-00174797
Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations, Comptes Rendus Mathematique, vol.335, issue.3 ,
DOI : 10.1016/S1631-073X(02)02466-4
URL : https://hal.archives-ouvertes.fr/hal-00798389
A priori convergence theory for reducedbasis approximations of single-parameter elliptic partial differential equations, Journal of Scientific Computing, vol.7, issue.1 1 ,
URL : https://hal.archives-ouvertes.fr/hal-00798389
An Open Source Approach to Developing Software in a Small Organization, Software, IEEE, pp.4-6 ,
DOI : 10.1109/MS.2007.5
Mastering CMake 4th Edition, 2008. ,
A space-time Petrov-Galerkin certified reduced basis method : Application to the boussinesq equations, SIAM Journal on Scientific Computing, 2012. ,
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real-Time Bayesian Parameter Estimation, Computational Methods for Large Scale Inverse Problems and Uncertainty Quantification ,
DOI : 10.1002/9780470685853.ch8
Recent advances in reduction methods for nonlinear problems, Computers & Structures, vol.3, issue.1 1, pp.3-4 ,
On making large nonlinear problems small Computer methods in applied mechanics and engineering ,
DOI : 10.1016/0045-7825(82)90096-2
Reduced basis technique for nonlinear analysis of structures, 20th Structures, Structural Dynamics, and Materials Conference ,
DOI : 10.2514/6.1979-747
Asymptotic analysis for periodic structures, 1978. ,
Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations. MIT Pappalardo Graduate Monographs in Mechanical Engineering, 2006. ,
Spectral element approximation of the incompressible Navier-Stokes equations evolving in a moving domain and applications, 2009. ,
The Reduced Basis Method for Incompressible Viscous Flow Calculations, SIAM Journal on Scientific and Statistical Computing, vol.10, issue.4, 0777. ,
DOI : 10.1137/0910047
Estimation of the error in the reduced basis method solution of nonlinear equations, Mathematics of Computation, vol.45, issue.172 ,
DOI : 10.1090/S0025-5718-1985-0804937-0
Contributions to Real-Time Reliable Simulations and Certain Aspects of Scientific Computing.H a b i l i t a t i o nàd i r i g e rd e sr e c h e r c h e s ,U n i v e r s i t é Pierre et Marie Curie, 2005. ,
URL : https://hal.archives-ouvertes.fr/tel-00389031
A domain specific embedded language in C++ for automatic differentiation, projection, integration and variational formulations, Scientific Programming ,
URL : https://hal.archives-ouvertes.fr/hal-00319980
A reduced basis multiscale method. Talk given at International Conference on Spectral and High Order Methods, ICOSAHOM'09. invited conference, 2009. ,
Feel++ : A Computational Framework for Galerkin Methods and Advanced Numerical Methods, ESAIM : Proc ,
URL : https://hal.archives-ouvertes.fr/hal-00662868
Advances in feel++ : A domain specific embedded language in C++ for partial differential equations, European Congress on Computational Methods in Applied Sciences and Engineering, p.2012, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00762442
Feel++ : Finite Element Embedded Language in C++. Free Software available at http ://www.feelpp.org. Contributions from A ,
Reduced-basis output bounds for approximately parameterized elliptic coercive partial differential equations, Computing and Visualization in Science, vol.6, issue.2 ,
Reliable real-time solution of parametrized partial differential equations : Reduced-basis output bound methods, Journal of Fluids Engineering, vol.124, issue.1, pp.70-80, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00798326
Life : Overview of a unified c++ implementation of the finite and spectral element methods in 1d, 2d and 3d, Applied Parallel Computing. State of the Art in Scientific Computing,v o l u m e4 6 9 9o fLecture Notes in Computer Science, pp.712-721, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00319983
Certified reduced basis approximation for parametrized partial differential equations and applications, Journal of Mathematics in Industry, vol.1, issue.1, pp.1-4 ,
DOI : 10.1137/090780122
URL : http://doi.org/10.1186/2190-5983-1-3
Domain decomposition methods for partial differential equations. Number CMCS-BOOK-2009-019, 1999. ,
On the theory and error estimation of the reduced basis method for multi-parameter problems, 1992. ,
Reduced-basis output bound methods for parabolic problems, IMA Journal of Numerical Analysis, vol.26, issue.3 ,
DOI : 10.1093/imanum/dri044
URL : https://hal.archives-ouvertes.fr/hal-00112600
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Archives of Computational Methods in Engineering, vol.5, issue.1 3, pp.1-4 ,
DOI : 10.1007/bf03024948
Unified Modeling Language Reference Manual, The. Pearson Higher Education, 2004. ,
Non-homogeneous media and vibration theory, Nonhomogeneous media and vibration theory ,
Capturing Small Scales in Elliptic Problems Using a Residual-Free Bubbles Finite Element Method, Multiscale Modeling & Simulation, vol.1, issue.3 ,
DOI : 10.1137/S1540345902411402
High Performance Computing for the Reduced Basis Method. Application to Natural Convection, ESAIM : Proceedings, pp.255-273, 2013. ,
DOI : 10.1051/proc/201343016
URL : https://hal.archives-ouvertes.fr/hal-00786560
Reduced basis approximation and a posteriori error estimation for noncoercive el liptic problems : application to acoustics, 2007. ,
Reduced-basis approximation and a posteriori error estimation for manyparameter heat conduction problems, Numerical Heat Transfer, Part B : Fundamentals ,5, vol.4, issue.5 ,
Petsc introductory tutorial, 2006. ,
Domain Decomposition, 1996. ,
DOI : 10.1007/978-3-540-70529-1_411
Domain decomposition methods : algorithms and theory, 2005. ,
DOI : 10.1007/b137868
Reduced order modeling of high magnetic field magnets, 17th U.S. National Congress on Theoretical and Applied Mechanics ,
URL : https://hal.archives-ouvertes.fr/hal-00955232
A new error bound for reduced basis approximation of parabolic partial differential equations, Comptes Rendus Mathematique, vol.350, issue.3-4, pp.203-207, 2012. ,
DOI : 10.1016/j.crma.2012.01.026
A successive constraint method with minimal offline constraints for lower bounds of parametric coercivity constant, 2011. ,
The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model, SIAM Journal on Scientific Computing, vol.36, issue.3, 2012. ,
DOI : 10.1137/120887709
Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basisa posteriori error bounds, International Journal for Numerical Methods in Fluids, vol.42, issue.8-9, 0773. ,
DOI : 10.1002/fld.867
Reduced-basis approximation of the viscous Burgers equation : Rigorous ap o s t e r i o r ierror bounds, C. R. Acad. Sci. Paris, Série I, vol.3, issue.9, pp.3-7 ,
Ap osteriorierror bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic 224 BIBLIOGRAPHIE BIBLIOGRAPHIE partial differential equations (AIAA Paper 2003-3847), Proceedings of the 16th AIAA Computational Fluid Dynamics Conference ,
A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations : " convex inverse " bound conditioners. ESAIM : Control, Optimisation and Calculus of Variations ,
Prud'homme, and C. Trophime. A computational framework for certified reduced basis methods : application to a multiphysic problem, Conference Record of the 6th European Congress on Computational Methods in Applied Sciences and Engineering ,
Reduced order modeling of high magnetic field magnets, Conference Record of the 11th International Workshop on Finite Elements for Microwave Engineering ,
URL : https://hal.archives-ouvertes.fr/hal-00955232
Multiscale modeling and computation. Notices of the AMS, p.0 ,
The Heterogeneous Multi-Scale Method for Homogenization Problems, Multiscale methods in science and engineering, 2005. ,
DOI : 10.1007/3-540-26444-2_4
Heterogeneous multiscale method : a general methodology for multiscale modeling, Physical Review B, vol.7, issue.6 9 ,
Introduction to multigrid methods, 1995. ,