Selected Publications of Frédéric Nataf

F. Nataf & E. Parolin, Coarse spaces for non-symmetric two-level preconditioners based on local generalized eigenproblems , preprint, 2024.
A. Lechevallier, F. Nataf, T. Faney, E. Flauraud, & S. Desroziers, (2023), Hybrid Newton method for the acceleration of well event handling in the simulation of CO2 storage using supervised learning. , In preparation, 2024.
N. Bootland, V. Dolean, F. Nataf and P.-H. Tournier, A robust and adaptive GenEO-type domain decomposition preconditioner for H(curl) problems in general non-convex three-dimensional geometries, In preparation, 2023.
M. Bonazzoli, X. Claeys, F. Nataf, P.-H. Tournier, How does the partition of unity influence SORAS preconditioner? , prepublication, 2023.
N. Bootland, V. Dolean, F. Nataf and P.-H. Tournier, Two-level DDM preconditioners for positive Maxwell equations, 2023.
F. Nataf, P.-H. Tournier, , A GenEO Domain Decomposition method for Saddle Point problems , Comptes Rendus. Mécanique, vol 351, 2023.
N. Bouziani, F. Nataf, P.-H. Tournier, , A Unified Framework for Double Sweep Methods for the Helmholtz Equation , Journal of Computational Physics, 2023.
F. Nataf, P.-H. Tournier, , Recent advances in domain decomposition methods for large-scale saddle point problems , J Comptes Rendus. Mécanique, 2022.
V. Dolean, F. Hecht, P. Jolivet, F. Nataf, P.-H. Tournier, , Advances in Adaptive Coarse Spaces and Availability in Open Source Libraries , MathematicS In Action, Tome 11, 2022.
F. Assous, F. Nataf Full-waveform redatuming via a TRAC approach: a first step towards target oriented inverse problem , Journal of Computational Physics, 2021.
M. Bonazzoli, X. Claeys, F. Nataf, P.-H. Tournier, Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems , J. Sci. Comput., 2021.
P. Marchand, X. Claeys, P. Jolivet, F. Nataf, P.-H. Tournier, Two-level preconditioning for h-version boundary element approximation of hypersingular operator with GenEO , Numerische Mathematik, vol. 146, n3 2020.
M. J. Grote , F. Nataf , J. Hoe Tang , P.-H. Tournier , Parallel Controllability Methods For the Helmholtz Equation , CMAME, vol 362, 2020.
F. Nataf, Mathematical Analysis of Robustness of Two-Level Domain Decomposition Methods with respect to Inexact Coarse Solves, DOI: 10.1007/s00211-020-01102-6, Numerische Mathematik, 144(4) , 2020.
R. Haferssas, P.-H. Tournier, F. Nataf, S. Cotin, Simulation of soft tissue deformation in real-time using domain decomposition, 2019.
P.H. Tournier, I. Aliferis, M. Bonazzoli, M. De Buhan, M. Darbas, V. Dolean, F. Hecht, P. Jolivet, I. El Kanfoud, C. Migliaccio, F. Nataf, C. Pichot, S. Semenov , Microwave Tomographic Imaging of Cerebrovascular Accidents by Using High-Performance Computing , Parallel Computing, 85, pp. 88-97, 2019.
Coulet, J., Faille, I., Girault, V., Guy, N., Nataf, F., A fully coupled scheme using Virtual Element Method and Finite Volume for poroelasticity, Computational Geosciences, Springer, 2019.
M. Graff-Kray, M. Grote, F. Nataf, F. Assous, How to solve inverse scattering problems without knowing the source term: a three-step strategy , Inverse Problems, vol 35, Number 10, 2019.
J Coulet, I Faille, V Girault, N Guy, F Nataf, A fully coupled scheme using Virtual Element Method and Finite Volume for poroelasticity , ECMOR XVI-16th European Conference on the Mathematics of Oil Recovery, 2018.
GR. Barrenechea, M. Bosy, V. Dolean, F. Nataf, P.H. Tournier, Hybrid discontinuous Galerkin discretisation and preconditioning of the Stokes problem with non standard boundary conditions , arXiv preprint arXiv:1610.09207, Computational Methods in Applied Mathematics, 2018.
R. Haferssas, P. Jolivet, F. Nataf, An additive Schwarz method type theory for Lions algorithm and Optimized Schwarz Methods , SIAM Journal on Scientific Computing 39 (4), 2017.
P.H. Tournier, I. Aliferis, M. Bonazzoli, M. De Buhan, M. Darbas, V. Dolean, F. Hecht, P. Jolivet, I. El Kanfoud, C. Migliaccio, F. Nataf, C. Pichot, S. Semenov, Numerical Modeling and High-Speed Parallel Computing: New Perspectives on Tomographic Microwave Imaging for Brain Stroke Detection and Monitoring , IEEE Antennas and Propagation Magazine 59 (5), 98-110, 2017.
PH Tournier, F Hecht, F Nataf, M Bonazzoli, F Rapetti, V Dolean, Microwave tomography for brain stroke imaging, Antennas and Propagation & USNC/URSI National Radio Science Meeting, 2017.
MJ Grote, M Kray, F Nataf, F Assous, Time-dependent wave splitting and source separation, Journal of Computational Physics 330, 981-996, 2017.
R. Haferssas, P. Jolivet, F. Nataf, A robust coarse space for Optimized Schwarz methods SORAS-GenEO-2 , C. R. Math. Acad. Sci. Paris, 353 (2015) 10, 959-963 .
V. Dolean, P. Jolivet, F. Nataf, An Introduction to Domain Decomposition Methods: algorithms, theory and parallel implementation SIAM bookstore , 2015. pdf , Erratum
N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein, R. Scheichl. Abstract Robust Coarse Spaces for Systems of PDEs via Gereralized Eigenproblems in the Overlap. Numer. Math. 126 (2014), no. 4, 741 770.
P. Jolivet, F. Nataf, HPDDM: high-performance unified framework for domain decomposition methods , MPI-C++ library, 2014.
C. Japhet, Y. Maday, F. Nataf, Robin Schwarz algorithm for the NICEM Method: the $P_q$ finite element case, , SINUM, 52 (2014), no. 4, 1497-1524.
L. Conen, V. Dolean, R. Krause, F. Nataf, A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator, Journal of Computational and Applied Mathematics, Volume 271, 1 December 2014, Pages 83-99.
P. Jolivet, F. Hecht, F. Nataf, C. Prud'homme, Scalable Domain Decomposition Preconditioners, SuperComputing SC13, 2013. Best paper finalist.
L. Qu, L. Grigori, F. Nataf, Parallel Design and Performance of Nested Filtering Factorization Preconditioner, SuperComputing SC13, 2013. Best student paper finalist.
F. Nataf, Absorbing boundary conditions and perfectly matched layers in wave propagation problems , book chapter in "Direct and Inverse problems in Wave Propagation and Applications", RICAM book series, de Gruyter 2013.
C. Japhet, Y. Maday and F. Nataf, A New Cement to Glue Nonconforming Grids with Robin Interface Conditions: The P1 Finite Element Case, M3AS, pp 1-40, 2013.
P. Havé, R. Masson, F. Nataf, M. Szydlarski, H. Xiang and T. Zhao, Algebraic Domain Decomposition Methods for Highly Heterogeneous Problems , SIAM SISC, Vol. 35, Issue 3, 2013.
P. Jolivet, V. Dolean, F. Hecht, F. Nataf, C. Prud'homme and N. Spillane, High performance domain decomposition methods on massively parallel architectures with FreeFem++, Journal of Numerical Mathematics, 20, 2012.
F. Assous, M. Kray, F. Nataf, Retournement Temporel avec Conditions Absorbantes (TRAC) et Super-résolution : Reconstruction du passé et applications aux problèmes inverses , Instrumentation, Mesure, Métrologie (2012), Vol. 12, no 1-2, pp 177-198.
V. Dolean, F. Nataf, R. Scheichl, N. Spillane, Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet--to--Neumann maps , CMAM, 2012 vol. 12.
Cluzeau Th., Dolean V., Nataf F. and Quadrat A., Symbolic methods for developing new domain decomposition algorithms, Inria Tech. Rep. RR-7953 (2012)
Assous F., Kray M. and Nataf F., Time Reversed Absorbing Condition in the Partial Aperture Case, Wave Motion, vol 49 (7) (2012)
Nataf F., Xiang H., V. Dolean and N. Spillane, A Coarse Space Construction Based on Local Dirichlet to Neumann Maps , SIAM J. Sci. Comput. 33, 1623 (2011)
L. Grigori, F. Nataf and Q. Niu, Two sides tangential filtering decomposition, Journal of Computational and Applied Mathematics, 2011, doi:10.1016/j.physletb.2003.10.071
Assous F., Kray M., Nataf F. and Turkel E., Time Reversed Absorbing Condition: Application to inverse problem, Inverse Problems 27 (2011) 065003.
Assous F., Kray M., Nataf F., Turkel E., Time Reversed Absorbing Conditions, C. R. Math. Acad. Sci. Paris 348 (2010), no. 19-20, 1063--1067., doi:10.1016/j.crma.2010.09.014
Nataf F., Xiang H. and V. Dolean , A Two Level Domain Decomposition Preconditionner Based on Local Dirichlet to Neumann Maps , C. R. Math. Acad. Sci. Paris 348 (2010), no. 21-22, 1163--1167.
Nicolas Lantos, F. Nataf, Perfectly Matched Layers for the heat and advection-diffusion equations, C. R. Math. Acad. Sci. Paris 348 (2010), no. 13-14, 781--785., http://dx.doi.org/10.1016/j.crma.2010.05.004.
Nicolas Lantos and F. Nataf, Perfectly Matched Layers for the heat and advection-diffusion equations , J. Comput. Phys. 229 (2010), no. 24, 9042--9052.
Q. Niu, L. Grigori, P. Kumar, F. Nataf, Modified Tangential Frequency Filtering Decomposition and its Fourier Analysis, Numerische Mathematik, vol 116, no. 1 (2010)
I. Faille, F. Nataf, F. Willien and S. Wolf, Local time steps for a finite volume scheme , ESAIM: Proceedings, Vol. 29 (2009) p. 58--72

V. Dolean, F. Nataf and G. Rapin, Deriving a new domain decomposition method for the Stokes equations using the Smith factorization. Math. Comp. 78 (2009), no. 266, 789--814.

S. Desroziers, F. Nataf and R. Sentis, SIMULATION OF LASER PROPAGATION IN A PLASMA WITH A FREQUENCY WAVE EQUATION , Journal of Computational Physics, 227 pp 2610-2625 (2008)

C. Chniti, F. Nataf and F. Nier, Improved Interface conditions for 2D domain decomposition with corners: a theoretical determination Calcolo, 45 (2008) and Numerical applications Journal of Scientific Computing, 38 (2009) no 2, p207-228 , short version Improved interface conditions for a non overlapping domain decomposition of a non-convex polygonal domain , notes CRAS, 342 (2006), no 11, 883--886

V. Dolean and F. Nataf, Domain decomposition algorithms for the compressible Euler equations. Analysis and simulation of fluid dynamics. , 69--88, Adv. Math. Fluid Mech., Birkhauser, Basel (2007)

F. Magoules and F. Nataf, Optimized Schwarz methods: a general presentation. Domain decomposition methods: theory and applications, 1--36, GAKUTO Internat. Ser. Math. Sci. Appl., 25, (2006)

V. Dolean and F. Nataf, A New Domain Decomposition Method for the Compressible Euler Equations. M2AN, 40 (2006), no. 4, 689--703

F. Nataf, A new construction of perfectly matched layers for the linearized Euler equations. J. Comput. Phys., 214 (2006) no 2, 757--772, short version notes aux CRAS 340 (2005) no 10, 775--778.

E. Flauraud and F. Nataf, Optimized Interface Conditions in Domain Decomposition Methods for Problems with Extreme Contrasts in the Coefficients. J. Comput. Appl. Math, 189 (2006) no 1-2, 539--554

L. Gerardo-Giorda and F. Nataf, Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients, J. Num. Math, 13 (2005) no 4, 265--294

M. Gander and F. Nataf, An incomplete LU preconditioner for problems in acoustics , J. Comput. Acoust. 13 (2005) no 3, 455--476

V. Dolean and F. Nataf, An optimized Schwarz algorithm for the compressible Euler equations. CMAP Internal report

V. Dolean, F. Nataf and G. Rapin, New constructions of domain decomposition methods for systems of PDEs. notes aux CRAS, 340, (2005), no 9, 693--696.

L. Saas, I. Faille, F. Nataf and F. Willien, Finite Volume Methods for Domain Decomposition on Nonmatching Grids with Arbitrary Interface Conditions, SIAM J. Num. Ana., 43 (2005) no 2, 860--890

V. Dolean, S. Lanteri, F. Nataf, Convergence Analysis of a Schwarz Type Domain Decomposition Method for the Solution of the Euler Equations, Applied Numerical Mathematics., 9 (2004), no. 2, 153--186

L. Saas, I. Faille, F. Nataf and F. Willien, Finite Volume Methods for Domain Decomposition on Nonmatching Grids with Arbitrary Interface Conditions and Highly Heterogeneous Media , Domain Decomposition Methods in Science and Engineering Series : Lecture Notes in Computational Science and Engineering , Vol. 40, Kornhuber, R.; Hoppe, R.; Periaux, J.; Pironneau, O.; Widlund, O.; Xu, J. (Eds.) 2004

M. Gander, C. Japhet, Y. Maday and F. Nataf, A New Cement to Glue Nonconforming Grids with Robin Interface Conditions: The Finite Element Case, Domain Decomposition Methods in Science and Engineering Series : Lecture Notes in Computational Science and Engineering , Vol. 40, Kornhuber, R.; Hoppe, R.; Periaux, J.; Pironneau, O.; Widlund, O.; Xu, J. (Eds.) 2004

L. Gerardo-Giorda, P. Le Tallec et F. Nataf, A Robin-Robin preconditioner for strongly heterogeneous advection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 193 (2004), no. 9-11, 745--764

Y. Achdou and F. Nataf, Dimension-wise Iterated Frequency Filtering Decomposition , Num. Lin. Alg. and Appl., 10, 511-539, 2003

M. Gander , L. Halpern and F. Nataf, Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation, SIAM J. Num. An., 41, no.~5, 1643--1681, 2003

V. Dolean, S. Lanteri, F. Nataf, Optimized Interface Conditions for Domain Decomposition Methods in Fluid Dynamics, Int. J. Numer. Meth. Fluids, 40, 1539-1550, 2002.

E. Flauraud, F. Nataf, S. Pegaz-Fiornet, F. Schneider et F. Willien, A new fault model in geological basin modelling. Application of a finite volume scheme and domain decomposition methods, Finite Volumes for Complex Applications III: Problems and Perspectives, edited by R. Herbin and D. Kromer, 2002, Hermes Penton Science, pp 543-550

L. Saas, I. Faille, F. Nataf et F. Willien, Domain decomposition with Robin interface conditionson non-matching grids using finite volume method, Finite Volumes for Complex ApplicationsIII: Problems and Perspectives, edited by R. Herbin and D. Kromer, 2002, Hermes Penton Science, pp 243-250

V. Dolean, S. Lanteri, F. Nataf, Construction of interface conditions for solving the compressible Euler equations by non-overlapping domain decomposition methods, Int. J. Numer. Meth. Fluids, 40, 1485-1492, 2002.

Y. Achdou, C. Japhet, F. Nataf and Y. Maday , A New Cement to Glue Non-Conforming Grids with Robin Interface Conditions: The Finite Volume Case, Ecole Polytechnique, TR n° 419, 1999, Numerische Mathematik, 92 (2002), no. 4, 593--620.

M. Gander , F. Magoulès and F. Nataf, Optimized Schwarz Methods without Overlap for the Helmholtz Equation , Ecole Polytechnique, TR n° 465, SIAM J. Sci. Comp., 24 (2002), no 1, 38--60

F. Nataf, Interface Connections in Domain Decomposition Methods, NATO Advanced Study Institute, Modern Methods in Scientific Computing and Applications, Université de Montréal, Juillet 2001, vol.75 in the NATO Science Ser.II.

C. Japhet and F. Nataf, The Best Interface Conditions for Domain Decomposition Methods: Absorbing Boundary Conditions, Absorbing Boundaries and Layers, Domain Decomposition Methods. Applications to Large Scale Computations, L. Tourrette and L. Halpern, eds., Nova Science Publishers, Inc., New York, 2001, pp 348-373, Nova Science, (2001)

M. Gander and F. Nataf, AILU for Helmholtz problems: A new Preconditioner Based on the Analytic Parabolic Factorization, J. of Comput. Acoustics., Vol. 9, No 4, 1499--1506 (2001)

M. Gander and F. Nataf, AILU: A Preconditioner Based on the Analytic Factorization of the Elliptic Operator, Numerical Linear Algebra with Applications, 7 (2000), no. 7-8, 505--526, n°436, 2000.

C. Japhet, F. Nataf and F. Rogier, The Optimized Order 2 method. Application to convection-diffusion problems, Future Generation Computer Systems, Vol 18, Elsevier Science, 2000. no. 1,

Y. Achdou, C. Japhet, P. Le Tallec, F. Nataf, F. Rogier and M. Vidrascu, Domain Decomposition Methods for Non-Symmetric Problems, Invited talk at DD11

Y. Achdou, P. Le Tallec, F. Nataf and M. Vidrascu, A domain decomposition preconditioner for an advection-diffusion problem, CMAME, 184 (2000) 145-170.

F. Nataf and F. Nier, Convergence of Domain Decomposition Methods via Semi-Classical Calculus, Commun. in Partial Differential Equations, 23 (5 & 6), p1007-1059, 1998.

C. Japhet, F. Nataf et F.X. Roux, Extension of a coarse grid preconditioner to non-symmetric problems. Domain decomposition methods, 10 (Boulder, CO, 1997), 279--286, Contemp. Math., 218, Amer. Math. Soc., Providence, RI, 1998.

F Willien, I Faille, F Nataf and F Schneider, Domain Decomposition Methods for Fluid Flow in Porous Medium, 6th European Conference on the Mathematics of Oil Recovery, 1998.

F. Nataf, A Schwarz additive method with high order interface conditions and nonoverlapping subdomains, M2AN, 32, n°1, p. 107-116, 1998.

F. Nataf and F. Nier, Convergence rate of some Domain Decomposition Methods for Overlapping and Nonoverlapping Subdomains, Numerische Mathematik, vol 75, n°3, p. 357-377, 1997.

Ph. Chevalier and F. Nataf, An OO2 (Optimized Order 2) method for the Helmholtz and Maxwell Equations, Contemporary Mathematics 218, AMS, "Tenth International Conference on Domain Decomposition Methods in Science and in Engineering", (Boulder, 1997), p. 400-407.

F. Nataf, Absorbing Boundary Conditions in Block Gauss-Seidel Methods for the Convection Problems, M3AS, 6, n°4, p. 481-502, 1996.

F. Nataf, F. Rogier and E. de Sturler, Domain Decomposition Methods for Fluid Dynamics, Navier-Stokes Equations and Related Nonlinear Analysis, Edited by A. Sequeira, Plenum Press Corporation, pp367-376, 1995.

Y. Achdou and F. Nataf, Preconditionners for the Mortar Method based on Local Approximations of the Steklov-Poincaré Operator, M3AS, 5, n°7, p967-997, 1995.

F. Nataf and F. Rogier, Factorization of the Convection-Diffusion Operator and a (Possibly) Non Overlapping Schwarz Method, M3AS, 5, n°1, p. 67-93, 1995.

F. Nataf, F. Rogier and E. de Sturler, Optimal interface conditions for domain decomposition methods, I.R. n°301, CMAP (Ecole Polytechnique).

Lohéac J.P., F. Nataf and M. Schatzman , Parabolic Approximations of the Convection-Diffusion Equation, Math. of Comp., 60 (202), p.515-530, 1993.

F. Nataf, Paraxial Approximations of the Steady Advection-Diffusion Equation. Padé Approximants for Operators, Asymptotic Analysis, 5, p. 533-552, 1992.

F. Nataf, Parabolized Algorithm for the Advection-Diffusion Equation, Int. Report CMAP Ecole Polytechnique, n° 214, April 1990.

F. Nataf, An Open Boundary Condition for the Computation of the Steady Incompressible Navier-Stokes Equations, Journal of Computational Physics, vol 85, n°1, Nov. 1989, pp. 104-129.

L.Anquez and F. Nataf, Délaminage d'un barreau composite soumis à une traction uniforme, Journal de Mécanique théorique et appliquée, vol 6, n°3, 1987, p.335-350.

Other publications

F. Nataf, Domain Decomposition Methods for Non-Symmetric Problems, Parallel and Distributed Processing for Computational Mechanics III, (B. H. V. Topping ed.), Saxe-Coburg Publications, to appear.

Last modified: Wed Nov 15 15:58:23 CET 2017