Alexander Zlotnik
- Research Professor: Faculty of Economic Sciences / Department of Mathematics
- Alexander Zlotnik has been at HSE University since 2010.
Education, Degrees and Academic Titles
Computation Centre of the Siberian Branch of the Russian Academy of Sciences
Lomonosov Moscow State University
Lomonosov Moscow State University
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Research interests
Numerical methods for solving parabolic, hyperbolic, elliptic differential equations, the Schrödinger equation, gas and hydrodynamics systems of equations: sharp and optimal error estimates, stability, the case of unbounded domains, effective implementation methods, optimal control, computer simulation.
Systems of quasilinear equations for viscous compressible gases and liquids flow: existence, uniqueness, regularity, stabilization of solutions, continuous dependence of solutions on data, homogenization, regularized systems and their properties.
Courses (2024/2025)
- Introduction to Finite-difference Methods (Optional course (university); 3 module)Rus
- Mathematics for Economists (Bachelor’s programme; Faculty of Economic Sciences field of study Economics; 1 year, 3, 4 module)Rus
- Numerical Methods for Solving Applied Partial Differential Equations (Mago-Lego; 4 module)Rus
- Past Courses
Courses (2023/2024)
- Calculus 1 (Bachelor’s programme; Faculty of Economic Sciences field of study Economics; 1 year, 1, 2 module)Rus
Courses (2022/2023)
- Calculus (Bachelor’s programme; Graduate School of Business field of study Business Informatics; 1 year, 1-4 module)Rus
Courses (2021/2022)
- Differential Equations (Bachelor’s programme; Graduate School of Business field of study Business Informatics; 2 year, 1, 2 module)Rus
Courses (2020/2021)
- Calculus (Bachelor’s programme; Graduate School of Business field of study Business Informatics; 1 year, 3, 4 module)Rus
Conferences
- 2024
Вычислительная математика и приложения. Presentation: Компактные схемы 4-го порядка точности для акустического волнового уравнения с переменной скоростью звука
IX Всероссийская научная конференция «Теплофизика и физическая гидродинамика» (Сочи). Presentation: Квазигомогенная форма системы четырех уравнений динамики гетерогенных смесей газов и жидкостей, ее регуляризация и реализация
IX Всероссийская научная конференция «Теплофизика и физическая гидродинамика» (Сочи). Presentation: О регуляризованных уравнениях динамики гетерогенных бинарных смесей "сжатых" газов Ноубла-Абеля и их применении
Вычислительная классическая и многофазная гидродинамика и термомеханика сплошной среды (пгт Сириус). Presentation: Квазигомогенная форма системы четырех уравнений динамики гетерогенных смесей газов и жидкостей, ее регуляризация и применение
- 2022
Всероссийская научная конференция «Теоретические основы конструирования численных алгоритмов и решение задач математической физики», посвященная памяти К.И. Бабенко -2022 (Пущино). Presentation: О параболическом и гиперболическом 2-го порядка возмущениях симметричной гиперболической системы 1-го порядка
- 2019
International Conference on Differential and Difference Equations and Applications 2019 (Lisbon). Presentation: L^2-dissipativity of explicit regularized and linearized finite-difference schemes on a non-uniform spatial mesh for the 1d gas dynamics equations
International Conference on Differential Equations 2019 (Leiden). Presentation: On the strong continuity on data in weaker norms of global weak solutions to 1D viscous compressible Navier-Stokes equations and an error of their two-scale homogenization
17th International Conference of Numerical Analysis and Applied Mathematics (Rodos). Presentation: On Aggregated Regularized Equations for Homogeneous Binary Gas Mixture Flows with Viscous Compressible Components
- 2018
23rd International Conference Mathematical Modelling and Analysis (Сигулда). Presentation: On numerical simulation of spiral-vortical structures in rotating gaseous disks
- 2017
22nd International Conference Mathematical Modelling and Analysis (Druskininkai). Presentation: Fast FFT-based solvers for higher order FEM on rectangular parallelepipeds for PDE
22nd International Conference Mathematical Modelling and Analysis (Druskininkai). Presentation: Weak conservativeness criterions for QGD-schemes for 1D gas dynamics equations
International Conference on Differential & Difference Equations and Applications 2017 (Lisbon). Presentation: On a barotropic quasi-hydrodynamic system of equations for the two-component mixture with a diffuse interface
Sixth China-Russia Conference on Numerical Algebra and Applications (Москва). Presentation: On fast Fourier solvers for the tensor product high-order finite element method for a generalized Poisson equation
International Conference on Computer Simulation in Physics and beyond (Москва). Presentation: Numerical methods with discrete transparent boundary conditions for solving the time-dependent Schrödinger equation in unbounded domains
- 2016
Mathematical Modelling and Analysis 2016 (Тарту). Presentation: Properties of the Numerov-Crank-Nicolson Scheme on a Non-Uniform Mesh for the 1D Time-Dependent Schrödinger Equation
Computational Methods in Applied Mathematics - 7 (Jyvaskyla). Presentation: On conservative spatial discretizations for quasi-gasdynamic systems of equations
XXI Всероссийская конференция "Теоретические основы и конструирование численных алгоритмов для решения задач математической физики", посвященная памяти К.И. Бабенко (Дюрсо). Presentation: Новая пространственная дискретизация многомерной квазигазодинамической системы уравнений со свойством неубывания полной энтропии
- 2015
Numerical Methods for Optimal Control and Inverse Problems 2015 (Munich). Presentation: Error estimates for methods of solving the time-dependent Schrödinger equations in unbounded domains
SCICADE2015 (Потсдам). Presentation: On error estimates for some numerical methods with discrete TBC for the time-dependent Schrödinger equation
- 2014
Numerical Methods for Optimal Control and Inverse Problems (Munich). Presentation: Sharp error estimates for splitting finite element methods of solving second order hyperbolic equations
Sixth Conference on Finite Difference Methods: Theory and Applications (Lozenetz). Presentation: New Results on Numerical Methods with Discrete TBC for Solving the TD Schrödinger Equation in Unbounded Domains
Mathematical Theory of Gases and Fluids and Related Applications (Seoul). Presentation: On the Lipschitz continuity on data of weak solutions to 1D viscous compressible heat-conducting gas equations and its applications
International Congress of Mathematicians 2014 (Seoul). Presentation: Higher order numerical methods for solving the time-dependent Schrödinger equation in unbounded domains
XX Всероссийская конференция «Теоретические основы и конструирование численных алгоритмов и решения задач математической физики», посвященная памяти К.И. Бабенко (Дюрсо). Presentation: Пространственная дискретизация одномерной квазигазодинамической системы уравнений с общими уравнениями состояния и уравнение баланса энтропии
6th International Conference on Computational Methods in Applied Mathematics (Strobl). Presentation: Error estimates for numerical methods with discrete transparent boundary conditions for the time-dependent Schrödinger equation in unbounded domains
Актуальные проблемы математической физики (Москва). Presentation: Методы с расщеплением по потенциалу и дискретными ПГУ для численного решения нестационарного уравнения Шрёдингера в неограниченном параллелепипеде
- 2013
Numerical Computations: Theory and Algorithms 2013 (Фалерна). Presentation: A New Space Discretization of the 1D Quasi-Gas Dynamic System of Equations and the Entropy Balance Equation
The Mathematics of Finite Elements and Applications 2013 (Лондон). Presentation: FEM with discrete transparent boundary conditions for the Cauchy problem for the Schrödinger equation on the whole axis
ENUMATH 2013 (лозанна). Presentation: The Crank-Nicolson scheme with splitting and discrete transparent boundary conditions for the Schrodinger equation on an infinite strip
SciCADE 2013 (Вальядолид). Presentation: Finite-difference schemes with splitting and discrete TBCs for the 2D Schrödinger equation in a strip
- 2012
17th International Conference on Mathematical Modelling and Analysis (Tallinn). Presentation: The space discretization of the 1d quasi-gas dynamic systems of equations and the entropy and energy balance equations
5th Conference on Computational Methods in Applied Mathematics (Берлин). Presentation: The space discretization of the 1d quasi-gas dynamic systems of equations and the entropy and energy balance equations
Supervisor of the following Doctoral theses
- 1
1. Lomonosov Timofey Aleksandrovich. Dissipativity analysis of explicit linearized finite-difference methods with regularization for gas dynamics equations. The dissertation of the Philosophy Doctor in Applied Mathematics. M.: NRU HSE, 2020.
2. Gavrilin Vladimir Alekseevich. Conservative discretizations of one-dimensional quasi-gas and quasi-hydrodynamic systems of equations. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.07 - computational mathematics. Moscow, MPEI, 2016.
3. Kireeva Olga Ilyinichna. Projection-grid methods for stationary and non-stationary equations of the 4th order with nonsmooth data. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.07 - computational mathematics. Moscow, MPEI, 2002.
4. Zaitseva Svetlana Borisovna. Sharp error estimates for locally one-dimensional and vector methods for solving the heat equation. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.07 - computational mathematics. Moscow, MPEI, 1999.
5. Nguyen Zha Bao. Questions of the qualitative theory of equations of one-dimensional motion of a viscous gas in the presence of free boundaries. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.02 - differential equations. Moscow, 1998.
- 2A. Fedchenko Regularized equations for multicomponent compressible gasmixture flows and their finite-defference approximations, 2024
- 3T. Lomonosov Dissipativity analysis of explicit linearized finite-difference methods with regularization for gas dynamics equations, 2020
Grants
Participation in RFBR and RSF projects in 2009-2024.
23-21-00061 RSF Construction and analysis of higher-accuracy numerical methods for solving some problems of wave physics (head)
22-11-00126 RSF "Development of molecular-gas-dynamic algorithms for solving coupled problems of heat and mass transfer on the surface of high-speed aero vehicles"
19-11-00169 RSF “Development and application of parallel quasi-gas and quasi-hydrodynamic algorithms and technologies” for 2019-2021 (main performer).
19-11-00104 RSF “New approaches to the development of algorithms for solving problems of continuum mechanics for ultra-high-performance computing systems” for 2019-2021.
19-01-00262 “Quasi-gasdynamic algorithms on modern computing platforms and modeling of actual problems of gas and hydrodynamics” for 2019-2021.
18-01-00587 “Theoretical research and application of a quasi-gasdynamic system of equations for solving problems of gas and hydrodynamics” for 2018-2020.
16-01-00048 "Development and new applications of quasi-gasdynamic numerical methods" for 2016-2018 (head)
14-11-00549 RSF "Development of a quasi-hydrodynamic approach for mathematical modeling of multiphase flows using supercomputers" in 2016.
13-01-00703 “Development and improvement of quasi-gasdynamic methods and their applications” for 2013-2015 (head).
14-01-90009-Bel-a "Development and study of grid algorithms for efficient calculations of some evolutionary problems of mathematical physics, hydrodynamics and dynamics of traffic flows" for 2014-2015.
12-01-90008-Bel_a “Development, analysis and application of new effective difference methods for solving multidimensional filtration and convection-diffusion problems” for 2012-2013.
10-01-90005-Bel_a “Development and research of effective grid algorithms and mathematical modeling of some problems of hydro- and gasdynamics” for 2010-2011.
10-01-00136-a “Development and applications of quasi-gas and quasi-hydrodynamic systems of equations” for 2010-2012.
09-01-12166-ofi_m “Asymptotic methods in some problems of mechanics of viscous compressible media and heat transfer by radiation” for 2009-2010 (co-head).
Editorial board membership
Employment history
2011 - present time: HSE University, Faculty of Economic Sciences, Department of Mathematics, 2011-2020 professor, since 2020 professor-researcher
2019- present time: Keldysh Institute of Applied Mathematics of the RAS, leading researcher (part-time)
Research and lecturing abroad
- Ecole Normale Superieure Assia Djebar of Constantine, Algerie, October-November, 2017
- Tianjin University of Finance and Economics, P.R. China, April-May, 2017
- Technische Universität München, Germany, February 2014, March 2015
- Centre de recherche scientifique du Commissariat à l'énergie atomique et aux énergies alternatives, Département de Physique Théorique et Appliquée, Ile-de-France, 2002-2007 and 2009-2012
- Zhejiang University, Hangzhou, P.R. China, August 2008
- Institute of Applied Physics and Computational Mathematics, Beijing, P.R. China, December 2001
- Università di Torino, Facoltà di Matematica “Giuseppe Peano”, Torino, Italy, October 2001
- Université Paris 7 Denis Didro, Paris, France, April 2001
- Institute of Mathematics, Czech Academy of Sciences, Prague, September 2000-January 2001 and July-August 2001
- Université Paris 6 Pierre et Marie Curie, Paris, France, March 2000
- Institut Mittag-Leffler of the Royal Swedish Academy of Sciences, Stockholm, May 1998
Membership in dissertation councils
Member of the Council for the review of dissertations for the scientific degrees
Candidate of Science and Doctor of Science in the specialties 1.1.2 Differential Equations and Mathematical Physics and 1.1.6 Computational Mathematics at National Research University "Moscow Power Engineering Institute"
Reviewer of papers for scientific journals:
• Applicable Analysis, • Applied Mathematics and Computation, • Applied Numerical Mathematics, • Boundary Value Problems, • Computer Physics Communications, • Computers and Fluids, • Computers and Mathematics with Applications, • Computational Methods in Applied Mathematics, • Discrete and Continuous Dynamical Systems – A, • Entropy, • Heliyon, • Journal of Computational and Applied Mathematics, • Journal of Computational Physics, • Journal of Differential Equations, • Journal of Dynamical and Control Systems, • Journal of Function Spaces, • Journal of Mathematical Physics, • Lithuanian Mathematical Journal, • Mathematical Methods in the Applied Sciences, • Mathematical Modelling and Analysis, • Mathematics (Switzerland), • Mathematics and Computers in Simulation, • Methods and Applications of Analysis, • Nonlinearity, • Numerical Algorithms, • Numerical Methods for Partial Differential Equations, • The Royal Society of Edinburgh: Proceedings A, • Russian Journal on Numerical Analysis and Mathematical Modelling, • SIAM Journal on Mathematical Analysis, • SIAM Journal of Numerical Analysis, • Symmetry, • Zeitschrift für angewandte Mathematik und Physik (ZAMP), • Zeitschrift für Naturforschung A (A Journal of Physical Sciences)
and • Differential Equations, • Computational Mathematics and Mathematical Physics, • Izvestiya: Mathematics, • Russian Mathematics (Iz. VUZ), • Mathematical Notes, • Mathematical Models and Computer Simulation, • Numerical Analysis and Applications, • Proceedings of Institute for System Programming of the Russian Academy of Sciences, • The HSE Economic Journal