We are developing methods and algorithms that can effectively use modern supercomputers for modeling of physical and other similar processes described by differential equations. Particular attention is paid to optimal algorithms, or nearly optimal, in two aspects. For one thing that with increasing number of unknowns grows computational work only linearly, and for another that the computational work can be divided among a large number of computational processors or cores without loss of effectiveness.
In addition to the numerical modeling of individual processes, we focus on solving problems of next level of the complexity, such as the role of multiphysics, where we simultaneously model the multiple interacting processes; solutions of the multiscale tasks when we consider the interaction of processes in the micro -and macro- structure; inverse problems for the identification of physical parameters solving and shape or material optimization tasks solving.
Application currently mainly concern the following areas:
- modeling of plastic and quasi-brittle behavior of materials;
- solution of coupled fluid flow and deformation of porous jobs and geological environments with applications in projects of underground storage of nuclear waste , the use of geothermal energy , etc.;
- methods for solving contact problems;
- shape optimization - modeling of the ideal product shape with given properties;
- micromechanics with using input from tomographic images;
- inverse problems solution to find the material properties and diagnostic equipment;
- analysis and vibration control;
- financial economics troubleshooting.
- Radim Blaheta
Deputy head of research programme
- Dalibor Lukáš
- Marek Lampart
- Jiří Bouchala
- Pavel Burda
- Petr Kovář
- Radek Kučera
- Jan Valdman
- Jan Zeman
- Zdeněk Zmeškal
- Petr Beremlijski
- Martin Čermák
- Václav Šátek
- Tomáš Tichý
- Lukáš Malý
- Lukáš Pospíšil
- Alena Vašatová
- Jan Zapletal
KUČERA, R.; KOZUBEK, T.; MARKOPOULOS, A. On large-scale generalized inverses in solving two-by-two block linear systems, Linear Algebra and its Applications. Volume 438, Issue 7, p. 3011-3029. Doi: http://dx.doi.org/ 10.1016/j.laa.2012.09.027. 2013.
NOVÁK, J.; KUČEROVÁ, A.; ZEMAN, J. Microstructural enrichment functions based on stochastic Wang tilings. In Modelling and Simulation in Materials Science and Engineering. Volume 21, No. 2. Doi: http://dx.doi.org/10.1088/0965-0393/21/2/025014. 2013.
AXELSSON, O. Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I. In Springer Proceedings in Mathematics & Statistics. Volume 45, p. 45 – 67. 2013.
AXELSSON, O.; BLAHETA, R.; SYSALA, S.; AHMAD, B. On the solution of high order stable time integration methods. In Boundary Value Problems, Springer Verlag. Doi: http://dx.doi.org/10.1186/1687-2770-2013-108. 2013.
BLAHETA, R.; JAKL, O.; STARÝ, J.; TURAN, E. Parallel Solvers for Numerical Upscaling. P. Manninen and P. Oster (Eds.): PARA 2012, LNCS 7782. Volume 7782, p. 375 – 386. 2013
HASLINGER, J.; KUČERA, R. T-FETI based algorithm for 3D contact problems with orthotropic friction. In Lecture Notes in Applied and Computational Mechanics. Volume 56, p. 131-149. Doi: http://dx.doi.org/10.1007/978-3-642-33968-4_9. 2013
LAMPART, M.; ZAPOMĚL, J. Dynamics of the electromechanical system with impact element. In Journal of Sound and Vibration. Volume 332, Issue 4, p. 701 – 713. Doi: http://dx.doi.org/10.1016/j.jsv.2012.10.013. 2013
GARCIA GUIRAO, J. L; LAMPART, M.; ZHANG, G. H. On the dynamics of a 4d local Cournot model. In Applied mathematics & information sciences. Volume 7, No. 3, p. 857-865.Doi: http://dx.doi.org/10.12785/amis/070303. 2013
KUČERA, R.; KOZUBEK, T.; MARKOPOULOS, A.; MACHALOVÁ, J. On the Moore-Penrose inverse in solving saddle-point systems with singular diagonal blocks, Numerical Linear Algebra with Applications. Volume 19, Issue 4, p. 677-699, doi: http://dx.doi.org/10.1002/nla.798. 2012.
LAMPART, M. Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors. In Chaos, Solitons & Fractals . Volume 45, Issues 9 – 10, p. 1081-1085. Doi: http://dx.doi.org/10.1016/j.chaos.2012.05.007. 2012.
SYSALA, S. Application of a modified semismooth Newton method to some elasto-plastic problems. In Mathematics and Computers in Simulation. Volume 82, Issue 10, p. 2004-2021. Doi: http://dx.doi.org/10.1016/j.matcom.2012.03.012. 2012.
TICHÝ, T. An Application of an n-dimensional Fuzzy Smoothing Filter in Financial Modeling. In BEIAC 2012 - 2012 IEEE Business, Engineering and Industrial Applications Colloquium. p. 231-236.2012.