dufaud_comm.bib

@conference{dufa12b,
  author = {Dufaud, T.},
  title = {An algebraic multilevel preconditioning framework based on information
        of a Richardson process},
  booktitle = {21st International Conference on Domain Decomposition Methods (DD21)},
  year = {2012},
  address = {Rennes, France},
  month = {June},
  note = {organizer of a minisymposium},
  abstract = {A fully algebraic framework for constructing coarse spaces for multilevel
        preconditioning techniques is proposed. Multilevel techniques are
        known to be robust for scalar elliptic Partial Differential Equations
        with standard discretization and to enhance the scalability of domain
        decomposition method such as RAS preconditioning techniques. An issue
        is their application to linear system encountered in industrial applications
        which can be derived from non-elliptic PDEs. Moreover, the building
        of coarse levels algebraically becomes an issue since the only known
        information is contained in the operator to inverse. Considering
        that a coarse space can be seen as a space to represent an approximated
        solution of a smaller dimension than the leading dimension of the
        system, it is possible to build a coarse level based on a coarse
        representation of the solution. Drawing our inspiration from the
        Aitken-SVD methodology, dedicated to Schwarz methods, we proposed
        to construct an approximation space by computing the Singular Value
        Decomposition of a set of iterated solutions of the Richardson process
        associated to a given preconditioner. This technique does not involve
        the knowledge of the underlying equations and can be applied to build
        coarse levels for several preconditioners. Numerical results are
        provided on both academic and industrial problems, using two-level
        additive preconditioners built with this methodology.},
  x-international-audience = {yes},
  x-invited-conference = {yes},
  x-proceedings = {no}
}

@conference{dufa12c,
  author = {Dufaud, T.},
  title = {On a numerical method to compute flow in complex 3D geological fractured
	porous media},
  booktitle = {3 \`eme Conf\'erence Internationale de la Soci\'et\'e Marocaine de Math\'ematiques
	Appliqu\'ees (SM2A)},
  year = {2012},
  address = {Marrakech, Maroc},
  month = {September},
  note = {invited in a minisymposium},
  abstract = {This communication focuses on numerical techniques to compute flow
	in complex 3D geological fractured porous media, where water can
	flow both in the rock matrix and in the fractures. This study is
	an extension of the model of 2D fractured porous media proposed in
	[C. Alboin, et al. Modeling fractures as interfaces for flow and
	transport in porous media. (2002) and N. Frih, et al. Modeling fractures
	as interfaces: a model for Forchheimer fractures. (2008)]. It also
	uses techniques to compute flow in 3D fractures network [J. Erhel,
	et al. flow simulations in three-dimensional discrete fracture networks.
	(2009) and G. Pichot, et al. A mixed hybrid mortar method for solving
	flow in discrete fracture networks. (2010)] or 3D rock matrix. The
	numerical model deals with steady-state flow for single phaseand
	incompressible fluid. In the rock matrix, the flow is governed by
	Darcy’s law, while the flow in the fractures is governed by Poiseuille’s
	law. For both, the law of mass conservation is verified. In a first
	part we present the model, and assume that the numerical method for
	flow in 2D fractured porous media can be derive for 3D as in [L.
	Amir, et al. Décomposition de domaine pour un milieu poreux fracturé
	: un modèle en 3d avec fractures qui s’intersectent. (2006)]. Then
	we propose the kind of case we propose to study and its discretization
	considering Mixed Hybrid Finite Element Method.},
  x-international-audience = {yes},
  x-invited-conference = {yes},
  x-proceedings = {no}
}

@conference{CFM11,
  author = {Berenguer, L. and Dufaud, T. and Tromeur-Dervout, D.},
  title = {Une m\'ethode de d\'ecomposition de domaine pour r\'esoudre l'\'equation de Darcy 3D dans les milieux poreux fortement h\'et\'erog\`enes},
  booktitle = {20\`eme congr\`es fran\c{c}ais de m\'ecanique},
  year = {2011},
  address = {Besan\c{c}on, France},
  url = {http://documents.irevues.inist.fr/handle/2042/46592},
  publisher = {AFM, Maison de la M\'ecanique, 39/41 rue Louis Blanc, 92400 Courbevoie, France(FR)},
  abstract = {Nous pr\'esentons une m\'ethode parall\`ele pour r\'esoudre l'\equation de Darcy 3D o\`u le champ de perm\'eabilit\'e varie al\eatoirement suivant une distribution log normale et avec de fortes amplitudes dans des domaines discr\'etis\'es de 10^8 à 10^9 inconnues. Cette technique de d\'ecomposition de domaine de type Aitken-Schwarz conduit \`a un parall\'elisme \`a deux niveaux o\`u les probl\`emes locaux sont r\'esolus par multigrille alg\'ebrique parall\`ele (AGMG de Y. Notay). L'influence sur la construction de l'acc\'el\'eration d'Aitken de l'espace d'approximation pour repr\'esenter la solution sur les interfaces sera discut\'e.},
  x-international-audience = {no},
  x-invited-conference = {yes},
  x-proceedings = {no}
}