Vincent Martin
Statut : Maître de Conférences
Bureau : GI 115
I am interested in numerical analysis, finite elements (mixed FE and Lagrange FE), inverse problems, scientific computing, a posteriori estimates... mainly for the modelling of flow in fractured porous media (Darcy with interface), of blood flow in arteries (Stokes with interface, BC, coupling with MHD...), of contact between membranes, of diphasic flow with change of phases in porous media.
I am currently working on :
- the formal proof of the finite element method (both theory and code), in collaboration with Sylvie Boldo, François Clément, Micaela Mayero. After the formal proof of the Lax-Milgram theorem, we are now focusing on the Lebesgue integration theory.
Former students :
- Jad Dabaghi. PhD Title : A posteriori error estimates for variational inequalities : application to a two-phase flow in porous media, in French. Co-advisor with Martin Vohralík (Inria Paris). PhD of Sorbonne Université. He defended his PhD thesis at Inria Paris on June 4th, 2019. We worked on a posteriori error estimates for variational inequalities (PDE with linear constrains, models for membranes or diphasic flow), parabolic inequalities, and adaptive inexact semismooth Newton methods using criteria derived from the estimators.
He is currently working at CEA. - Fatma Cheikh. PhD Title : Identification of fractures in a porous medium, in French. Co-advisor with Hend Ben Ameur (Enit, Tunis) and Jean E. Roberts (Inria Paris). She defended her PhD thesis at Enit (Tunis) on Oct. 10th, 2016.
We worked on the inverse problem consisting in finding the position and parameters of fractures in porous media.
She was ATER at UTC, LMAC, in 2018-19. - Markus Koeppel. PhD Title : Flow in Heterogeneous Porous Media : Fractures and Uncertainty Quantification, under the supervision of Christian Rohde. Defense 31 july 2018, at the Universitat Stuttgart. He collaborated with us during his master’s thesis and his PhD.
We worked on the analysis of a Lagrange-multiplier finite element method (both stabilized and unstabilized) for flow in a fractured porous medium, with Jean E. Roberts.
He is currently working at Benz (Mercedes).
During two years (sept. 2009/sept. 2011), I worked in the REO team at Inria Paris-Rocquencourt with Jean-Frédéric Gerbeau and Miguel Fernández (j’étais en "délégation").
Travaux récents
Articles in reviewed journals
- A Coq Formalization of Lebesgue Integration of Nonnegative Functions.
S. Boldo, F. Clément, F. Faissole, V. Martin, M. Mayero. Journal of Automated Reasoning. Oct. 2021. DOI = 10.1007/s10817-021-09612-0. Available here.
(Preprint available here). - Adaptive inexact semismooth Newton methods for the contact problem between two membranes.
J. Dabaghi, V. Martin, M. Vohralík. Journal of Scientific Computing, J Sci Comput 84, 28 (2020), available here.
(Preprint available here.) - A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities.
J. Dabaghi, V. Martin, M. Vohralík. Computer Methods in Applied Mechanics and Engineering, vol. 367, 1 aug. 2020, available here.
(Preprint available here.) - A posteriori error estimates and adaptive stopping criteria for a compositional two-phase flow with nonlinear complementarity constraints.
I. Ben Gharbia, J. Dabaghi, V. Martin, M. Vohralík. Computational Geosciences, jan. 2020, available here.
(Preprint available here.) - A stabilized Lagrange-multiplier finite-element method for flow in porous media with fractures.
M. Koeppel, V. Martin, J. E. Roberts. International Journal on Geomathematics, 10, No 1, 2019, available here.
(Preprint available here.) - A Lagrange multiplier method for a discrete fracture model for flow in porous media.
M. Koeppel, V. Martin, J. Jaffré, J. E. Roberts. Computational Geosciences, sept. 2018, available here.
(Preprint available here.) - First-Order Indicators for the Estimation of Discrete Fractures in Porous Media,
H. Ben Ameur, G. Chavent, F. Cheikh, F. Clément, V. Martin, J. Roberts. Inverse Problems in Science & Engineering, 26, No 1, pp. 1-32, 2018, available here.
(Preprint available here.) - Modeling fractures as interfaces with non-matching grids,
N. Frih, V. Martin, J. Roberts, A. Saada. Computational Geosciences, 16, No 4, pp. 1043—1060, 2012, available here.
(Preprint available here.) - MagnetoHemoDynamics in Aorta and Electrocardiograms,
V. Martin, A. Drochon, O. Fokapu and J-F. Gerbeau. Physics in Medicine and Biology 57 (2012) 3177-3195.
(Preprint available here.) - Analysis of a stabilized finite element method for fluid flows through a porous interface,
A. Caiazzo, M. Fernández, V. Martin. Applied Math. Letters, 24, No 12, pp. 2124—2127, 2011.
(Preprint available here.) - Projection schemes for fluid flows through a porous interface,
A. Caiazzo, M. Fernández, J-F. Gerbeau, V. Martin. SIAM J. on Scientific Computing, 33, No 2, pp. 541—564, 2011.
(Preprint available here.) - Numerical simulation of blood flows through a porous interface,
M. Fernández, J-F. Gerbeau, V. Martin. ESAIM : M2AN, 42, No 6, pp. 961—990, 2008. Highlight paper.
(Preprint available here.) - Domain decomposition and skeleton programming with OCamlP3l,
F. Clément, V. Martin, A. Vodicka, R. Di Cosmo and P. Weis. Parallel Computing, 32, No 7-8, Algorithmic Skeletons, pp. 539—550, sept. 2006.
(Preprint available here.) - Modeling fractures and barriers as interfaces for flow in porous media,
V. Martin, J. Jaffré and J. Roberts. SIAM J. on Scientific Computing, 26, No 5, pp. 1667—1691, 2005.
(Preprint available here.)
Selected reviewed conference papers
- A Coq Formalization of Lebesgue Induction Principle and Tonelli’s Theorem
S. Boldo, F. Clément, V. Martin, M. Mayero, H. Mouhcine. FM 2023 - 25th International Symposium on Formal Methods, march 2023.
Preprint available here.
Research report available here.
- A Coq Formal Proof of the Lax—Milgram theorem,
S. Boldo, F. Clément, F. Faissole, V. Martin, M. Mayero.
6th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP 2017),
(computer science conference, available here.)
- MagnetoHemoDynamics effects on ElectroCardioGrams,
V. Martin, A. Drochon, O. Fokapu and J-F. Gerbeau. 6th
Internat. Conf. on Functional Imaging & Modelling of the Heart (FIMH 2011), New York University, 25-27 mai 2011.
- Blood flow through stents in abdominal aortic aneurysms,
A. Caiazzo, M. Fernández, J-F. Gerbeau, V. Martin, I.E. Vignon-Clementel. Proc. 1st Internat. Conf. on Computational & Mathematical Biomedical Engineering (CMBE09), Eds. P. Nithiarasu, R. Lohner, R. van Loon, Swansea, 2009, pp. 250-253.
- Domain Decomposition and Skeleton Programming with OCamlP3l,
F. Clément, V. Martin, A. Vodicka, R. Di Cosmo and P. Weis. Proc. of the Internat. Conf. on Parallel Computing : Current & Future Issues of High-End Computing, 2006, pp. 811-818.
- Parameter identification for a one-dimensional blood flow model,
V. Martin, F. Clément, A. Decoene, and J-F. Gerbeau. ESAIM : Proc., September 2005, Vol. 14, pp. 174—200.
(Preprint available here.)
- Décomposition de domaine pour un milieu poreux fracturé : un modèle en 3D avec fractures qui s’intersectent,
L. Amir, M. Kern, V. Martin, and J. Roberts (in French).
Proceedings of JANO 8, 8th conference on Numerical Analysis and Optimization, December 2005, Rabat, Morocco.
- Domain decomposition and functional programming with OcamlP3l,
F. Clément, V. Martin, A. Vodicka, R. Di Cosmo and P. Weis, Proceedings of the ECCOMAS Conference on Coupled Problems, May 2005, Santorini Island, Greece.
- Domain decomposition for flow simulation around a waste disposal site : direct simulation versus code coupling using OcamlP3l,
F. Clément, V. Martin, A. Vodicka, R. Di Cosmo and P. Weis. Proceedings of the Intern. Conf. on Supercomputing in Nuclear Appl. (SNA’2003, Paris, France).
- Generalized cell-centered finite volume method for flow in porous media with fault,
J. Jaffré, V. Martin and J. Roberts. Proceedings of Finite Volume for Complex Appl. 3 (FVCA3, Porquerolles, France), R. Herbin and D. Kroner Eds, 2002, pp. 357-364.
Other reports
- Lebesgue integration. Detailed proofs to be formalized in Coq,
F. Clément, V. Martin.
(Research Report RR-9386. Version 3, dec. 2022, major revision, available here.) - The Lax-Milgram Theorem. A detailed proof to be formalized in Coq,
F. Clément, V. Martin.
(INRIA Research Report RR-8934, 2016, available here.)
Conseils (amicaux) de lecture
Je vous suggère la lecture des romans de Manuel Benguigui :
Le collectionneur allemand a reçu des critiques dans Le Monde (janvier 2017) et dans Le Figaro (janvier 2017). Vous pouvez lire une critique ici (Nyctalopes, blog) ou là (Livre Hebdo).
Livres disponibles ici ou là, mais rien ne vaut un livre commandé chez votre libraire...