Alexei Lozinski

Maître de Conférences habilité (Assistant Professor)

Institut de Mathématiques de Toulouse Université Paul Sabatier
31062 Toulouse, France

Batiment 1R3, Bureau 110
Tel: 05 61 55 83 13
Fax: 05 61 55 83 85
e-mail : alexei.lozinski AT math.univ-toulouse.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, prise en compte des forces de lubrification
• 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
  Université Paul Sabatier
  Texte de l'habilitation : Méthodes numériques et modélisation pour certains problèmes multi-échelles
• Thèse soutenue en november 2003
  Ecole Polytechnique Fédérale de Lausanne, Section de Génie Mécanique.
  Texte de la thèse : Spectral methods for kinetic theory models of viscoelastic fluids
  Sous derection de Prof. Robert G. Owens et Prof. Alfio Quarteroni
  
• Diplôme d'ingénieur-mathématicien (MSc) soutenu en mai 1998
  Moscow Institute of Physics and Technology, Department of Management and Applied Mathematics.
  Travail du diplôme “Investigation of iterative methods with non-complete splitting of boundary conditions for solving a Stokes-type system in non-concentric rings”
  Sous derection de Prof. Boris V. Pal'tsev.

PUBLICATIONS

• 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).

• 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, submitted (preprint on arxiv).

• 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.
• A. 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, M. Picasso, 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).
• P. Degond, F. Deluzet, A. Lozinski, J. Narski and C. Negulescu, Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations, accepted to Comm. Math. Sci. (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, submitted (preprint on arxiv).

• 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.

ENSEIGNEMENT

• Les mathématiques licence 1ère année (parcours SDI - Sciences de l'ingénieur). Les feuilles de TD et les annales.
• Les mathématiques licence 3ème année (parcours Mécanique). Corrigés de quelques exercices.