Research interests

• Numerical methods for differential equations (spectral collocation method, finite element method)
• Nonlinear dynamical systems and bifurcation analysis
• Elastic solids, Newtonian and non-Newtonian fluids, viscoelastic fluids (numerical simulations, thermodynamics)
• Reduced-order models and machine learning for fluid mechanics

Multiple steady states of viscoelastic fluid in a sudden expansion channel

Education

• 09/2025-present PhD student, Institute of Science and Technology Austria (ISTA)

• 09/2022-06/2025 Master’s degree with honours, Mathematical Modelling in Physics and Technology, Charles University, Faculty of Mathematics and Physics
  • Thesis title: Bifurcation analysis of viscoelastic flows using deflation method
  • Supervisor: Doc. Mgr. Vít Průša, Ph.D.
• 09/2019-06/2022 Bachelor’s degree with honours, Mathematical Modelling, Charles University, Faculty of Mathematics and Physics
  • Thesis title: Spectral collocation methods in solid mechanics
  • Supervisor: Doc. Mgr. Vít Průša, Ph.D.

Deflection of a semi-infinite elastic solid by a surface load

Publications

• Vít Průša and Ladislav Trnka. Numerical bifurcation analysis using deflated continuation method—cross-slot flow of FENE-CR viscoelastic fluid. AIP Conference Proceedings, 2025. doi.org/10.1063/5.0282408

• Vít Průša, K. R. Rajagopal, Casey Rodriguez, Ladislav Trnka, and Martin Vejvoda. Modeling metamaterials by second-order rate-type constitutive relations between only the macroscopic stress and strain, 2025. URL arxiv.org/abs/2502.10045

• Jan Blechta, Vít Průša, Ladislav Trnka, and Karel Tůma. Fast construction of the discrete green operator for a second order ordinary differential equation, 2024. URL arxiv.org/abs/2412.06242

• Vít Průša and Ladislav Trnka. Mechanical response of elastic materials with density dependent Young modulus. Applications in Engineering Science, 2023. doi:10.1016/j.apples.2023.100126

Extension of a right circular cylinder, prediction by the standard linearised elasticity model (red), prediction by the model with density dependent Young modulus (yellow)

Research experience

• 08-09/2025 Scientific intern at the Hof group, Prof. Björn Hof, Institute of Science and Technology Austria

• 02/2023-03/2025 Team researcher, Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics, Czech Science Foundation, EXPRO 20-11027X, Principal investigator Doc. RNDr. Miroslav Bulíček, Ph.D.

• 09-11/2022 Principal investigator, Elastic bodies with density dependent material moduli, Student Faculty Grants, Charles University, Faculty of Mathematics and Physics

Recent talks, posters

• 2025 Novel Trends in Rheology X, Faculty of Technology, Tomas Bata University in Zlín, July 30-31, Zlín, Czech Republic, poster

• 2024 Modelling, PDE Analysis and Computational Mathematics in Materials Science, Faculty of Mathematics and Physics, Charles University, September 22-27, Prague, Czech Republic, poster

• 2024 High Performance Computing in Science and Engineering Conference, IT4Innovations National Supercomputing Center, VSB (Technical University of Ostrava), May 20-23, Karolinka, Czech Republic, poster

• 2024 EMS School, Mathematical Aspects of Fluid Flows, EMS (European Mathematical Society), Faculty of Mathematics and Physics, Charles University, May 12-17, Kácov, Czech Republic,
  slides

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