Professeur à l’Université de Franche-Comté

Laboratoire de Mathématiques
UMR CNRS 6623
Université de Franche-Comté
16 route de Gray
25030 Besançon Cedex

Equipe de recherche  : Analyse Numérique et Calcul Scientifique

Bâtiment métrologie, bureau 312
Tél : +33 (0)3 81 66 63 16
Fax : +33 (0)3 81 66 66 23
alexei.lozinski univ-fcomte.fr

AXES DE RECHERCHE

• Méthodes numériques pour des problèmes multi-échelles – l’approche des patchs d’éléments finis ou « zoom numérique », MsFEM
• Ecoulements fluide-particules – simulations du mouvement des particules rigides ou bulles de gaz dans un fluide, approximation du type domaine fictif
• Estimation d’erreur a posteriori
• Solutions de polymères – simulation en utilisant les méthodes spectrales, modélisation
• Problèmes anisotropes – les schémas AP (préservant l’asymptotique), éléments finis anisotropes adaptatifs

DIPLOMES

• Habilitation à diriger des recherches soutenue le 8 décembre 2010 à l’Université Paul Sabatier.
  
  Méthodes numériques et modélisation pour certains problèmes multi-échelles
• Thèse soutenue en november 2003 à l’Ecole Polytechnique Fédérale de Lausanne,
  Section de Génie Mécanique.
  Spectral methods for kinetic theory models of viscoelastic fluids
  Encadré par Prof. Robert G. Owens et Prof. Alfio Quarteroni
  
• Diplôme d’ingénieur-mathématicien (MSc) soutenu en mai 1998
  à
  Moscow Institute of Physics and Technology,
  Department of Control and Applied Mathematics.
  Investigation of iterative methods with non-complete splitting of boundary conditions for solving a Stokes-type system in non-concentric rings”
  Encadré par Prof. Boris V. Pal’tsev.

PUBLICATIONS

Méthodes numériques pour des problèmes multi-échelles

• R. Glowinski, J. He, A. Lozinski, J. Rappaz and J. Wagner, Finite element approximation of multi-scale elliptic problems using patches of elements, Numer. Math. (2005) 101(4), 663 – 687.
• J. He, A. Lozinski and J. Rappaz, Accelerating the method of finite element patches using approximately harmonic functions, Comptes rendus Mathematique (2007) 345(2) 107 – 112 (extended version).
• A. Lozinski, J. Rappaz and J. Wagner, Finite Element Method with Patches for Poisson problems in polygonal domains, ESAIM Proceedings (2007) 21, 45-64 (preprint).
• V. Rezzonico, A. Lozinski, M. Picasso, J. Rappaz, and J. Wagner, Multiscale algorithm with patches of finite elements, Math. Comput. Simulation (2007), 76, 181-187.
• R. Glowinski, J. He, A. Lozinski, M. Picasso, J. Rappaz, V. Rezzonico, and J. Wagner, Finite element methods with patches and applications, Proceedings of the 16th International Conference on Domain Decomposition Methods (the pdf file), Lecture Notes in Computational Science and Engineering, Springer (2007), vol. 55, 77 - 89.
• F. Hecht, A. Lozinski, A. Perronnet, O. Pironneau, Numerical zoom for multiscale problems with an application to flows through porous media, Discrete Contin. Dyn. Syst. (2009) 23(1-2), 265 - 280.
• F. Hecht, A. Lozinski and O. Pironneau, Numerical Zoom and the Schwarz Algorithm, Proceedings of the 18th International Conference on Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering, Springer (2009), vol. 70, 63 - 74.
• A. Lozinski and O. Pironneau, Numerical Zoom for localized multiscales, Numerical Methods for Partial Differential Equations (2011), 27, 197 - 207. (preprint)
• C. Le Bris, F. Legoll, and A. Lozinski, MsFEM à la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems, Chinese Annals of Mathematics, Series B (2013), 34(1), 113 - 138. (preprint)
• A. Lozinski, Z. Mghazli, and K.O.A.O. Blal, Méthode des éléments finis multi-échelles pour le problème de Stokes. Comptes Rendus Mathematique (2013), 351(7), 271 - 275.
• P. Degond, A. Lozinski, B.P. Muljadi, and J. Narski, Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media, Communications in Computational Physics (2015), 17(4), 887-907. (preprint on hal)
• C. Le Bris, F. Legoll, and A. Lozinski, An MsFEM type approach for perforated domains, SIAM Multiscale Modeling & Simulation (2014), 12(3), 1046-1077. (preprint on arxiv)
• B.P. Muljadi, J. Narski, A. Lozinski, P. Degond, Nonconforming Multiscale Finite Element Method for Stokes Flows in Heterogeneous Media. Part I : Methodologies and Numerical Experiments. SIAM Multiscale Modeling & Simulation, (2015) 13(4), 1146-1172 (preprint on arxiv)
• M. Duval, A. Lozinski, J.C. Passieux, and M. Salaün, Residual error based adaptive mesh refinement with the non-intrusive patch algorithm, Computer Methods in Applied Mechanics and Engineering (2017).
• G. Jankowiak, and A. Lozinski, Nonconforming Multiscale Finite Element Method for Stokes Flows in Heterogeneous Media. Part II : error estimates for periodic microstructure. submitted (2018) (preprint on arxiv)

Ecoulements fluide-particules et les méthodes domaine fictif

• M. Romerio, A. Lozinski, and J. Rappaz, A new modelling for simulating bubble motions in a smelter, Light Metals 2005, 134th TMS Annual Meeting, San Francisco, CA. (2005), 547-552.
• A. Lozinski and M.V. Romerio, Motion of gas bubbles, considered as massless bodies, affording deformations within a prescribed family of shapes, in an incompressible fluid under the action of gravitation and surface tension, Mathematical Models and Methods in Applied Sciences (2007) 17(9), 1445 – 1478.
• M. Hillairet, A. Lozinski and M. Szopos, On discretization in time in simulations of particulate flows, Discrete and Continuous Dynamical Systems, Series B (2011) 11, 935 - 956. (preprint on arxiv)
• S. Court, M. Fournié and A. Lozinski, A fictitious domain approach for the Stokes problem based on the extended finite element method, International Journal for Numerical Methods in Fluids (2014), 74(2), 73-99. (preprint on arxiv)
• S. Court, M. Fournié and A. Lozinski, A fictitious domain approach for Fluid-Structure Interactions based on the eXtended Finite Element Method, ESAIM : Proceedings and Surveys (2014), 45, 308-317. (esaim-proc)
• A. Lozinski, A new fictitious domain method : optimal convergence without cut elements, Comptes rendus Mathematique 354.7 (2016) : 741-746. (preprint and accompanying FreeFem++ code)
• M. Fournié and A. Lozinski, Stability and optimal convergence of unfitted extended finite element methods with Lagrange multipliers for the Stokes equations, in Geometrically Unfitted Finite Element Methods and Applications - Proceedings of the UCL Workshop 2016, to be published by Springer (2017). Preprint on arxiv.

Estimation d’erreur a posteriori

• A. Lozinski, M. Picasso, and V. Prachittham, An anisotropic error estimator for the Crank-Nicolson method : application to a parabolic problem, SIAM Journal on Scientific Computing (2009) 31(4), 2757 - 2783 (preprint).
• O. Gorynina, A. Lozinski, and M. Picasso, Time and space adaptivity of the wave equation discretized in time by a second order scheme, submitted (2017),
  (preprint on arxiv).
• O. Gorynina, A. Lozinski, and M. Picasso, An easily computable error estimator in space and time for the wave equation , submitted (2017),
  (preprint on arxiv).

Problèmes anisotropes

• P. Degond, F. Deluzet, A. Lozinski, J. Narski and C. Negulescu, Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations, Comm. Math. Sci. (2012) 10(1), 1-31 (preprint on arxiv).
• P. Degond, A. Lozinski, J. Narski and C. Negulescu, An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition, J. of Computational Physics (2011) 231(7), 2724 - 2740 (preprint on arxiv).
• A. Lozinski, J. Narski and C. Negulescu, Highly anisotropic temperature balance equation and its asymptotic-preserving resolution, M2AN (2014) 48(6), 1701–1724. (preprint on arxiv).
• A. Lozinski, J. Narski and C. Negulescu, Numerical analysis of an asymptotic-preserving scheme for anisotropic elliptic equations, submitted (2016) (preprint on arxiv).

Solutions de polymères – simulation et modélisation

• A. Lozinski, R.G. Owens and A. Quarteroni, On the simulation of unsteady flow of an Oldroyd-B fluid by spectral methods, J. Sci. Comput. (2002), 17, 375 – 383.
• A. Lozinski, C. Chauvière, J. Fang and R.G. Owens, A Fokker-Planck simulation of fast flows of melts and concentrated polymer solutions in complex geometries, J. Rheol (2003), 47, 535 – 561.
• C. Chauvière, J. Fang, A. Lozinski, and R.G. Owens, On the numerical simulation of flows of polymer solutions using high-order methods based on the Fokker-Planck equation, Int. J. Mod. Phys. B (2003), 17, 9-14.
• C. Chauvière and A. Lozinski, An efficient technique for simulations of viscoelastic flows, derived from the Brownian configuration field method, SIAM J. Sci. Comput. (2003), 24(5), 1823 – 1837.
• A. Lozinski and R.G. Owens, An energy estimate for the Oldroyd B model : Theory and applications, J. Non-Newtonian Fluid Mech. (2003), 112, 161 – 176.
• C. Chauvière and A. Lozinski, Simulation of dilute polymer solutions using a Fokker-Planck equation, Computers and Fluids (2004), 33 687 – 696.
• A. Lozinski and C. Chauvière, A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations : 2D FENE model, J. Comp. Phys. (2003), 189, 607 – 625.
• C. Chauvière and A. Lozinski, Simulation of complex viscoelastic flows using Fokker-Planck equation : 3D FENE model, J. Non-Newtonian Fluid Mechanics (2004), 122(1-3), 201 – 214.
• J. Fang, A. Lozinski and R.G. Owens, Towards more realistic kinetic models for concentrated solutions and melts, J. Non-Newtonian Fluid Mechanics (2004), 122(1-3), 79 – 90.
• A. Lozinski, R.G. Owens and J. Fang, A Fokker-Planck-based numerical method for modelling non-homogeneous flows of dilute polymeric solutions, J. Non-Newtonian Fluid Mechanics (2004), 122(1-3), 273 – 286.
• P. Delaunay, A. Lozinski and R.G. Owens, Sparse tensor-product Fokker-Planck-based methods for nonlinear bead-spring chain models of dilute polymer solutions, Equations aux derivees partielles de grande dimension en sciences et genie, CRM Proceedings and Lecture Notes (2007) 41, 73 – 89.
• Bonito, A. Lozinski, T. Mountford, Modeling Viscoelastic Flows using Reflected Stochastic Differential Equations, Comm. Math. Sci. (2010) 8(3), 655 - 670 (preprint).
• P. Degond, A. Lozinski and R.G. Owens, Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited, J. Non-Newtonian Fluid Mech. (2010) 165(9-10), 509-518 (preprint on arxiv).
• A. Lozinski, R.G. Owens and T.N. Phillips, The Langevin and Fokker-Planck Equations in Polymer Rheology, in Handbook of Numerical Analysis, vol. 16 (2010), (Table of contents).
• A. Lozinski and R.G. Owens, Some remarks on the equivalence of Kirkwood’s diffusion equation and the coupled fluctuating polymer and solvent kinetic equations of Oono and Freed, J. Non-Newtonian Fluid Mech. (2011) 166(21), 1297 - 1303.

Autres travaux récents

• A. Lozinski, A primal discontinuous Galerkin method with static condensation on very general meshes. Submitted (2018) (preprint on arxiv)
• L. Blank A. Caiazzo, F. Chouly, A. Lozinski, J. Mura, Analysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes and Darcy problems. Submitted (2018) (preprint on HAL)

Et aussi

• A.A. Mayer and A.S. Losinskii, Self-switching of fundamental solitons in tunnelling-coupled optical waveguides, Doklady Akademii Nauk (1997), 356(3), 325 – 328.
• A.A. Mayer and A.S. Losinskii, Self-switching and amplification of unidirectional distributed-coupled solitons of orthogonal polarization, Doklady Akademii Nauk (1998), 358(4), 470 – 475.
• A.A. Mayer and A.S. Losinskii, Self-switching of solitons in quadratical-nonlinear tunnelling-coupled optical waveguides, Doklady Akademii Nauk (1998), 360(5), 616 – 621.
• A.S. Lozinskii, On the acceleration of finite-element implementations of iterative processes with splitting of boundary conditions for a Stokes-type system, Comp. Math. Math. Phys. (2000), 40(9), 1284 – 1037.
• A.S. Lozinskii, Finite-element implementation of iterative processes with splitting of boundary conditions for a Stokes-type system in non-concentric Annuli, Comp. Math. Math. Phys. (2001), 41(8), 1145 – 1157.