Mihhail Berezovski


My research interests center on two disciplines: computational mathematics for material science and data-enabled industrial mathematics.

Data- Enabled Industrial Mathematics

One of my significant accomplishments at ERAU has been the establishment of a new research path in the subject of Data- Enabled Industrial Mathematics (DEIM). Industrial mathematics is a relatively new subject that focuses on converting technological, organizational, and data-enabled challenges offered by business, industry, or government into mathematical problems. I have set up a number of externally funded academia and industry partnerships.

I was successful in obtaining a National Science Foundation grant for the establishment of a Research Experiences for Undergraduates (REU) site at ERAU. The REU site allows undergraduate students to participate in real-world research projects in data-enabled industrial mathematics. The goals of this one-of-a-kind research experience are to educate students for challenges in data-driven industrial mathematics and to provide them with the abilities needed to navigate successfully in today's data-rich environment. The ultimate goal is to simulate a real-world industrial research experience, with an emphasis on student development and encouraging students to interact with content at a level that goes beyond the usual classroom. Students collaborate on challenges presented to them directly by business, government, and industry.

Computational mathematics for material science

My long-term research interest in computational mathematics for material science is focused on adaptive algorithms for numerical simulations of dynamic energy redistribution in advanced and novel materials such as spatio-temporal composites and micro-structured, multifunctional, and hierarchical metamaterials. My research in this field can be separated into the three following major categories:

Numerical methods for hyperbolic PDEs:
  • Development of higher-order finite-volume algorithms for wave propagation in linear and nonlinear media, including thermo-elastic, electromagnetic, and shallow water waves.
  • Higher-order finite-volume algorithms for dispersive waves in materials with microstructure, periodic and functionally graded media.
  • Font tracking algorithms for shock waves and phase-transition fronts.
Mathematical Material Science:
  • Analysis and implementation of constitutive models for wave propagation in heterogeneous and anisotropic material with microstructure at different time and space scales.
Computational Solid Mechanics:
  • Numerical analysis of dynamic response under impact loading of advanced and novel materials such as micro-structured, bio-inspired, hierarchical, and dynamic materials.
  • Numerical simulation of wave propagation in acoustic metamaterials (phononic crystals) with focus on negative index materials and acoustic diode.
  • Dynamic energy redistribution by wave handling in complex material structures.


Published Conference Abstracts
Print A. Berezovski, J. Engelbrecht, M. Berezovski, Numerical simulation of elastic wave diffraction, 13th European Mechanics of Materials Conference, Warsaw, Poland, September 8th - 11th, 2013, Book of Abstracts, p. 201.
Print A. Berezovski, M. Berezovski, Dispersive wave propagation in solids with microstructure, SIAM Conference on Computational Science & Engineering (CSE13), The Westin Boston Waterfront, Boston, Massachusetts, USA, February 25 - March 1, 2013, Book of Abstracts, p. 141.
Print A. Berezovski, J. Engelbrecht, M. Berezovski, Influence of internal structures on wave dispersion in solids, EUROMECH Colloquium 540 - Advanced Modelling of Wave Propagation in Solids, 1-3 October 2012, Prague, Czech Republic, Book of Abstracts, 31-32.
Print M. Berezovski, A. Berezovski, J. Engelbrecht, Wave propagation in heterogeneous materials with secondary substructure, The 3rd International Conference for Heterogeneous Materials Mechanics (ICHMM), Shanghai University, China, 22-29 May, 2011, Book of Abstracts.
Print M. Berezovski, A. Berezovski, J. Engelbrecht, Two-scale macroscopic dynamics of materials with microstructure, The 20th International Workshop on Computational Mechanics of Materials (IWCMM 2010). Loughborough University, UK, 8-10 September 2010, Book of Abstracts, pp. 13–14.
Print A. Berezovski, M. Berezovski, and J. Engelbrecht, Multiscale Microstructure Dynamics, International Symposium on Trends in Applications of Mathematics to Mechanics (STAMM 2010), Berlin (Germany), August 30th - September 2nd, 2010, Book of Abstracts, p. 1.
Print A. Berezovski, M. Berezovski, J. Engelbrecht, Dispersive wave equations for microstructured solids, CPEA’10 - Course and Conference on Continuum Physics and Engineering Applications, Rackeve (Budapest), Hungary, May 29- June 7 2010, Programme and Abstracts, p. 35.
Print M. Berezovski, A. Berezovski, J. Engelbrech, Numerical simulation of wave propagation in materials with microstructure, SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia, Pennsylvania, May 23-26, 2010, MS10 Abstracts, 57–58.
Print M. Berezovski, A. Berezovski, J. Engelbrecht, Numerical simulations of one-dimensional microstructure dynamics, 2nd Int. Symp. on Computational Mechanics (ISCM II) and 12th Int. Conf. on Enhancement and Promotion of Computational Methods in Eng. and Sci. (EPMESC XII), November 30 – December 3, 2009 Hong Kong - Macau, Book of Abstracts, p. 193.
Print M. Berezovski, A. Berezovski, J. Engelbrecht, Waves in materials with microstructure: Numerical simulation, in: A.Berezovski and T.Soomere (eds.) Int. Conf. Complexity of Nonlinear Waves. Book of abstracts, TUT, Tallinn, 2009, p. 9.
Print M. Rousseau, G.A. Maugin, M. Berezovski, Elements of wave propagation in dynamic materials. Proc. of 7th EUROMECH Solid Mech. Conf., September 7–11, 2009, Lisbon, Portugal, p. 55.
Print J. Engelbrecht, A. Berezovski, M. Berezovski, Deformation waves in microstructured materials: Theory and Numerics, IUTAM Symp. on Recent Advances of Acoustic Waves in Solids, May 25–28, 2009, Taipei, Taiwan. Abstracts Book, 21–22.