Book

    Christine Bernardi, Yvon Maday, Francesca Rapetti
    Discretisations variationnelles de problemes aux limites elliptiques
    Mathematiques & Applications, Vol. 45, n. ISBN-3-540-21369-4, Springer-Verlag, May 2004.

    Papers in journals

    • Parameter reconstruction for plasma applications

      D. Auroux, P. Ghendrih, L. Lamerand, F. Rapetti, E. Serre
      Asymptotic behavior, non-local dynamics, and data assimilation tailoring of the reduced k-epsilon model to address turbulent transport of fusion plasmas
      Physics of Plasmas 29, 102508, 2022, on line.

      L. Lamerand, D. Auroux, P. Ghendrih, F. Rapetti, E. Serre
      Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma
      subm. on Dec. 2022.

    Editor of Special Issues

    A. Alonso Rodriguez, D. N. Arnold, D. Pauly, F. Rapetti
    Hilbert Complexes: Analysis, Applications, and Discretizations.
    Oberwolfach Rep. 19, no. 2, pp. 1603-1659, 2022, EMS Press DOI 10.4171/OWR/2022/29.

    Proceedings

    F. Rapetti (joint with A. Alonso Rodriguez)
    Basics on high order polynomial interpolation of physical fields on simplices
    Oberwolfach Rep. 43, Sept. 2023, pp. 36-39, DOI 10.4171/OWR/2023/43.

    L. Bruni Bruno, A. Alonso Rodriguez, F. Rapetti
    Computing weights for high order Whitney edge elements
    SA 2022 procs., spec. issue of Dolomite Research Notes on Approximation, Vol. 15, pp. 1-12.

    A. Alonso Rodriguez, L. Bruni Bruno, F. Rapetti
    Flexible weights for high order face based finite element reconstructions
    to appear in ICOSAHOM 2021+1 procs, LNCSE, Springer-Verlag.

    A. Alonso Rodriguez, L. Bruni Bruno, F. Rapetti
    Minimal sets of unisolvent weights for high order Whitney forms on simplices
    EnuMath 2019 procs., LNCSE Vol. 139, Springer-Verlag, 2020.

    F. Rapetti, A. Alonso Rodriguez
    High order Whitney forms on simplices and the question of potentials
    EnuMath 2019 procs, LNCSE Vol. 139, Springer-Verlag, 2020.

    A. Alonso Rodriguez, F. Rapetti
    Small trees for high order Whitney elements
    ICOSAHOM 2018 procs., LNCSE Vol. 134, Springer-Verlag, pp. 587-597.

    A. Alonso Rodriguez, F. Rapetti
    The discrete relations between fields and potentials with high order Whitney forms
    in ``Numerical Mathematics and Advanced Applications'', F.A. Radu et al. eds.
    Enumath 2017 procs., LNCSE Vol. 126, Springer-Verlag, 2018.

    M. Bonazzoli, F. Rapetti, P.-H. Tournier, C. Venturini
    High Order Edge Elements for Electromagnetic Waves: Remarks on Numerical Dispersion
    in ``Spectral and High Order Methods for PDEs'', M. Bittencourt, N. Dumont, J.S. Hesthaven eds.,
    ICOSAHOM 2016 procs., LNCSE Vol. 119, pp. 215-227, Springer-Verlag, 2017.

    H. Heumann, F. Rapetti, M. D. Truong
    FEMs on composite meshes for plasma equilibrium simulations in tokamaks
    19th European Conference on Mathematics for Industry (ECMI 2016), Santiago-de-Compostela Spain, Mathematics in Industry, hal-01397386.

    M. Bonazzoli, V. Dolean, R. Pasquetti, F. Rapetti
    Schwarz preconditioning for high order edge element discretizations of the time-harmonic Maxwell's equations
    in Lee CO. et al. eds., Domain Decomposition Methods in Science and Engineering XXIII, LNCSE Vol. 116, p. 117-124, Springer, 2017, hal-01250761.

    I. El Kanfoud, V. Dolean, C. Migliaccio, J. Lanteri, I. Aliferis, C. Pichot, P.-H. Tournier, F. Nataf, F. Hecht, S. Semenov, M. Bonazzoli, F. Rapetti, R. Pasquetti, M. de Buhan, M. Kray, M. Darbas
    Whole-Microwave System Modeling for Brain Imaging
    2015 IEEE Conference on Antenna Measurements and Applications (CAMA), pp. 1-4.

    M. Bonazzoli, E. Gaburro, V. Dolean, F. Rapetti
    High order edge finite element approximations for the time-harmonic Maxwell's equations
    2014 IEEE Conference on Antenna Measurements and Applications (CAMA), pp. 1-4.

    A. Christophe, F. Rapetti, L. Santandrea, G. Krebs, Y. Le Bihan
    Mortar FEs on overlapping subdomains for eddy current non destructive testing
    Enumath 2013 procs., LNCSE Vol. 103, pp. 785-793, Springer-Verlag, 2014.

    A. Bossavit, F. Rapetti
    Whitney elements, from Manifolds to Fields
    in ``Spectral and high order methods for PDEs'', M. Azaiez, H. El Fekihand, J.S. Hestaven eds.,
    ICOSAHOM 12 procs., LNCSE Vol. 95, pp. 179-189, Springer-Verlag, 2014.

    P. E. Antonietti, I. Mazzieri, A. Quarteroni, F. Rapetti
    High order space-time discretization for elastic wave propagation problems
    in ``Spectral and high order methods for PDEs'', M. Azaiez, H. El Fekihand, J.S. Hestaven eds.,
    ICOSAHOM 12 procs., LNCSE Vol. 95, pp. 87-97, Springer-Verlag, 2014.

    R. Pasquetti, F. Rapetti
    Spectral element methods on simplicial meshes
    in ``Spectral and high order methods for PDEs'', M. Azaiez, H. El Fekihand, J.S. Hestaven eds.,
    ICOSAHOM 12 procs., LNCSE Vol. 95, pp. 37-55, Springer-Verlag, 2014.

    I. Mazzieri, C. Smerzini, P. E. Antonietti, F. Rapetti, M. Stupazzini, R. Paolucci, A. Quarteroni
    Non-conforming spectral approximations for the elastic wave equation in heterogeneous media
    Compdyn 2011 procs., Eccomas thematic conf. on Comput. Meth. in Structural and Earthquake Engng.,
    M. Papadrakakis, N.D. Lagaros, M. Fragiadakis eds., Corfu, Greece, 26-28 May, 2011.

    V. Dolean, R. Pasquetti, F. Rapetti
    p-Multigrid for Fekete spectral element method
    in ''Domain Decomposition Methods in Science and Engineering'',
    LNCSE Vol. 60, pp. 485-492, Springer-Verlag, 2007.

    R. Pasquetti, L. F. Pavarino, F. Rapetti, E. Zampieri
    Overlapping Schwarz preconditioners for Fekete spectral elements
    in ''Domain Decomposition Methods in Science and Engineering'', O.B. Widlund and D. Keyes Editors,
    LNCSE Vol. 55, pp. 717-724, Springer-Verlag, 2006.

    Y. Maday, F. Rapetti, B. I. Wohlmuth
    The influence of quadrature formula in 2D and 3D mortar methods
    in ``Recent Developments in Domain Decomposition Methods'', L. F. Pavarino and A. Toselli Editors
    LNCSE Vol. 23, pp. 203-221, Springer-Verlag, 2004.

    Y. Maday, F. Rapetti, B. I. Wohlmuth
    Mortar element coupling between global scalar and local vector potentials to solve eddy current problems
    in ``Numerical mathematics and advanced applications'', Enumath 2001 proc.,
    Brezzi F., Buffa A., Corsaro S., Murli A. eds., Springer-Verlag Italy (Milan) pp. 847-865, 2003.
    See also Part I, Technical Report N. 02009, Lab. J.-L. Lions, Paris 6 University.

    A. Buffa, Y. Maday, F. Rapetti
    Applications of the mortar element method to 3D electromagnetic moving structures
    in ``Computational Electromagnetics'', C. Carstensen et al. Editors
    LNCSE Vol. 28, pp. 35-50, Springer-Verlag, 2003.

    A. Buffa, Y. Maday, F. Rapetti
    The mortar element method for 3D Maxwell's equations : analysis and application to magnetodynamics
    in ``Domain Decomposition Methods in Science and Engineering'',
    procs. 12th Int. Conf. on Domain Decomposition Methods, Chiba, Japan,
    eds. T. Chan, T. Kako, H. Kawarada, O. Pironneau, ddm.org publications, pp. 259-270, 2001.

    Rapports de recherche INRIA

    H. Fahs, S. Lanteri, F. Rapetti
    A hp-like discontinuous Galerkin method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes
    RR-6162, INRIA, 41 pages, 2007.

    H. Fahs, S. Lanteri, F. Rapetti
    Etude de stabilite d'une methode Galerkin discontinu pour la resolution numerique des equations de Maxwell 2D en domaine temporel sur des maillages triangulaires non-conformes
    RR-6023, INRIA, 46 pages, 2006.