Mathematical modeling and methods for high performance computing

Mathematical modeling and methods for high performance computing

Mathematical modeling aims to describe and study various phenomena using the language of mathematics. It represents an indispensable tool in natural sciences, engineering, life and also social sciences. Mathematical modeling in mechanics and thermodynamics of continuous media is the research subject of the mathematical modeling group at Mathematical Institute of Charles University and the computational mathematics group at Department of Numerical Mathematic, Faculty of Mathematics and Physics of Charles University. The key members of the team include Vít Dolejší, Josef Málek, Zdeněk Strakoš, Miroslav Tůma, Petr Knobloch, Milan Pokorný, and Miroslav Bulíček, and the team includes also very promissing young scientists Iveta Hnětýnková, Jaroslav Hron, Václav Kučera, Vít Průša, Ondřej Souček, and Petr Tichý. Eduard Feireisl from Mathematical Institute of the Academy of Sciences of the Czech Republic and Martin Vohralík from INRIA, Paris-Rocquencourt, are collaborating (part time) members of the team. The activities are closely linked with the ERC-CZ AdG project MORE (PI Josef Málek), as well as with the ERC AdG project MATHEF (PI Eduard Feireisl) and the ERC CoG project GATIPOR (PI Martin Vohralík).

The uniqueness of this research group consists in the fact that it is able to cover – at a very high scientific level – all aspects of the mathematical modeling workflow, in particular development of mathematical models, mathematical analysis of their properties, development and analysis of the suitable numerical methods, and implementation of the numerical methods optimally exploiting the available computational power of the current and near future high performance computing systems.

Selected outputs

  • Dolejší, V., Feistauer, M., Discontinuous Galerkin Method - Analysis and Applications to Compressible Flow, Springer-Verlag, 2015.

  • Málek J., Strakoš Z., Preconditioning and the Conjugate Gradient Method in the Context of Solving Partial Differential Equations, SIAM, Philadelphia, 2015.

  • Liesen, J., Strakoš, Z., Krylov Subspace Methods, Principals and Analysis, Oxford University Press, Oxford, 2013.

  • Bulíček M., Málek J., Süli E.: Existence of global weak solutions to implicitly constituted kinetic models of incompressible homogeneous dilute polymers, Comm. Partial Differential Equations 38 (2013), 882-924.

  • Dolejší V., Ern A., Vohralík M.: A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems, SIAM J. Numer. Anal. 51 (2013), 773-793.

  • Bulíček M., Gwiazda P., Málek J., Świerczewska-Gwiazda A.: On unsteady flows of implicitly constituted incompressible fluids, SIAM J. Math. Anal. 44 (2012), 2756-2801.

  • Souček O., Průša V., Málek J., Rajagopal K.R.: On the natural structure of thermodynamical potentials and fluxes in the theory of chemically non-reacting binary mixtures, Acta Mech. 225 (2014), 3157-3186.

  • Knobloch, P., Tobiska, L., On the stability of finite-element discretizations of convection-diffusion-reaction equations, IMA Journal of Numerical Analysis 31 (2011), 147-164.

Last change: December 15, 2015 10:57 
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