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© 2000 - 2010   Jiri Stary        Česky  English

Department of applied mathematics and computer science

Personnel
  • Doc. RNDr. Josef Malik, CSc.
    head of the department
  • RNDr. Ondrej Jakl, CSc.
    deputy head of the department
  • Prof. RNDr. Radim Blaheta, CSc.
  • Mgr. Petr Byczanski
  • Ing. Petr Harasim
  • RNDr. Roman Kohut, CSc.
  • Mgr. Alexej Kolcun, CSc.
  • Ing. Jiri Stary, Ph.D.
  • Mgr. Stanislav Sysala
  • Jaroslava Vavrova
Main research topics

The topics correspond to the research plan Effective Methods of Numerical Modeling of Physical Phenomena in Geological Environment. This orientation includes several research fields. The first of them is numerical modelling of heat (T), hydraulic (H), and mechanical (M) processes in rocks, which is done both separately, neglecting the mutual influences, and jointly as a coupled multiphysics modelling. The research in this area includes development of numerical methods and high performance solvers that enable solution of large-scale 3D problems, considering more complicated nonlinear behaviour of geomaterials as well as analyzing and reducing influence of uncertainty in input data. The described field of modelling brings a lot of motivation to applied computer science. More precisely, it motivates the research in code optimization, in parallel and distributed computing or computer graphics and the work in effective methods for preparing input data and visualization of the computed physical fields. The methods for multi-scale modelling of problems with high heterogeneity or microstructure and methods of identification of material parameters are newly opened research topics. A specific field is the modelling of special reinforcement and geotechnical elements (bolts, geosynthetic materials) for geomechanics and civil engineering and modelling of behaviour of cable stayed and suspension bridges.

Important scientific achievements

  • Modelling of THM processes in rocks

    The in-house finite element software GEM3 is developed for modelling of thermo-mechanical processes and testing of numerical methods. The code has been applied for solving large scale problems with millions of nodal points. Originally the code was used for the solution of geomechanical problems, newly it is used also for thermo-mechanical analysis with application to assessment of repositories of the spent nuclear fuel. Application of iterative methods and parallel programming techniques developed in the department allows to solve large scale problems of huge dimensions.

  • Schwarz domain decomposition methods

    A series of new results came from analysis and application of the Schwarz method for parallel solution of boundary value problems of heat conduction and elasticity. This method uses decomposition of the original domain into overlapping subdomains. We showed that for efficient solution of elasticity problems, it is necessary to complete the domain decomposition with some coarse approximate solution of the original problem, e.g. a solution of a coarser discretization of the problem. We also demonstrated that such approximate solution can be obtained by inexact solution of an algebraically constructed aggregated problem using inner iterations. Moreover, it is possible to use correctly nonsymmetric variants of the preconditioning. For evolutionary heat conduction problem, we showed that the coarse solution is not required. Newly, we have proposed a variant of the Schwarz methods for the solution of underground water flow problems by the mixed finite element method.

  • Aggregation and algebraic multigrid

    A lot of useful numerical methods can be based on a nested coarse and fine division of the problem domain into finite elements. But sometimes, it is difficult to use such nested divisions and there are many reasons why to think about an algebraic construction of the coarse discretization. One possible algebraic construction of a coarse grid discretization is aggregation which we have been dealing with for longer time. New results are connected with a combination of aggregation and hierarchical preconditioning, the use of aggregation in the framework of nonconforming finite element methods and with Schwarz aggregation methods for solving elliptic problems.

  • Parallel computations

    The development of parallel computations at the Institute was started in 1995 already, in the context of two EC projects called High Performance Computing in Geosciences I, II. At present, we focus on the efficient implementation of the Schwarz methods for the solution of T, H, M problems on parallel computers. The parallel codes themselves are based on current standards for parallel processing, namely on MPI for platforms with distributed memory, e.g. clusters, and OpenMP for platforms with shared memory, symmetric multiprocessors in particular. The Institute owns smaller parallel systems of both types. Thanks to the involvement of the Institute in the fast academic network infrastructure, larger parallel computations, which make use of tens of processors, can be carried out externally. For example, a great number of computations were completed in the UPPMAX computing centre at the Uppsala University, supported by the joint project Parallel Computing in Geosciences.

  • Hierarchical methods

    Standard hierarchical finite element methods use approximation on nested grids and corresponding decomposition of the stiffness matrix. Our results are connected with the analysis of efficiency of hierarchical decompositions, robustness with respect to anisotropy, application to nonconforming finite element methods and construction of aposteriori estimates of the discretization error.

  • Homogenization techniques

    Homogenization techniques are used in continuum mechanics problems to obtain coefficients describing the behavior of environments with some microstructure. Our results are mainly connected with the modelling of rock mass reinforced with bolt anchoring and heat conduction together with mechanics of porous media in the case of nonlinear behaviour of material. The technique connected with homogenization of bolt anchoring was implemented in the code GEM2 and successfully tested in practical problems.

  • Analysis of cable stayed and suspension bridges

    Cable stayed and suspension bridges are modelled as a one dimensional beam suspended by a cable system. For cable stayed bridges the main attention was paid to asymptotic stability in lateral wind. As well, the influence of eigenvalues corresponding to vertical and torsion oscillations on the stability of bridges was studied. For suspension bridges the main attention was paid to the nonlinearity of cable systems, where cable stays are attached to the main cable, which is freely flexible. This nonlinearity is the source of instability influencing the behavior of such bridges.

Technical equipment
  • Thea - Beowulf-type computer cluster, 1 interactive and 8 computing nodes with processors AMD Athlon/1400, memory 1.5 GB, disk 20 GB and 2 FastEthernet interfaces, file server with 2 processors AMD Athlon MP/1900, memory 1 GB and disk capacity 100 GB.
  • Natan - Symmetric multiprocessor IBM e-server xSeries 455, 8 processors Intel Itanium 2/1300, shared memory 16 GB, RAID controller with disk capacity 2 x 72 GB.
  • GEM - In-house FEM software for experimental purposes and practical computations.
Solved projects
  • Project D2011 Decovalex 2011 – Development of codes and their validation against experiments (2008 - 2011, coordinator: SKB - Swedish Nuclear Fuel and Waste Management Company Sweden).
  • Project RAWRA (Radioactive Waste Repository Authority CR, 2008 - 2009, cooperation: Technical University in Liberec).
  • Project of bilateral cooperation between IPP BAS and CIMFR Assessment of stability and reinforcement of underground structures through numerical modelling and back analysis (20?? - 20??, cooperation: Central Institute of Mining and Fuel Research India).
  • Grantový projekt 105/09/1830 Víceúrovňové modelování a rentgenová tomografie v geotechnice (Grantová agentura ČR, 2009 – 2011, spolupráce: České Vysoké Učení Technické v Praze).
  • Grant project 103/08/1700 Stability analysis of cable stayed and suspension bridges (Czech Science Foundation - GACR, 2008 – 2010).
  • Project of bilateral cooperation between IPP BAS and IG ASCR Microstructure and multiscale modelling in bio- and geo-environment (2008 - 2010, cooperation: Institute for Parallel Processing BAS Sofia Bulgaria).
  • Grant project 106/06/0646 The micromechanics of self-affine fractal cracks in brittle materials (Czech Science Foundation - GACR, 2006 - 2008, cooperation: VSB - Technical University Ostrava).
  • Project FT-TA3/069 Optimal design of geosynthetics for the negative impact recovery related to the mainly exploatation energetics activities - new technology development (Ministry of Industry and Trade, 2006 - 2007, cooperation: Stavebni geologie - Geotechnika Prague).
  • Project of bilateral cooperation between IPP BAS and IG ASCR Reliable modelling and large scale scientific computing in geosciences (2005 - 2007, cooperation: Institute for Parallel Processing BAS Sofia Bulgaria).
  • Grant project 1ET400300415 in framework of the program Information Society Modeling and simulation of complex technical problems: effective numerical algorithms and parallel implementation using new information technologies (Academy of Sciences CR, 2004 - 2008, cooperation: Institute of Computer Science ASCR).
  • Project of bilateral cooperation between IPP BAS and UU Parallel computing in geosciences (2004 - 2006, cooperation: Uppsala University Sweden).
  • Grant project 105/04/P036 Parallel computations for modelling of thermomechanical processes in rocks (Czech Science Foundation - GACR, 2004 - 2006).
  • Project 1N0435 in framework of the program INFRA3 Network security handling in an environment of R&D institutions (Ministry of Education, Youth and Sports CR, 2004 - 2008, cooperation: VSB - Technical University Ostrava).
  • Grant project 106/03/0771 Effects of microcracks initiation and propagation mechanisms on fracture toughness of structural steels - sectional task Computer simulation and modelling of microstructural damage processes (Czech Science Foundation - GACR, 2003 - 2005, cooperation: VSB - Technical University Ostrava).
  • Project of bilateral cooperation between IPP BAS and IG ASCR Large-scale scientific computations in geomechanics (2002 - 2004, cooperation: Institute for Parallel Processing BAS Sofia Bulgaria).
  • Project of bilateral cooperation INTAS 01-647 Prevention of environmental pollution by sewerge tunnel failures (2002 - 2004, cooperation: University of Leeds, United Kingdom).
  • Grant project 105/02/0492 Modelling of thermo-mechanical processes connected to the underground deposition of the spent nuclear fuel (Czech Science Foundation - GACR, 2002 - 2004).
  • Scholastik research project K3012103 Processes inside the Earth body, on its surface and in its environments (Academy of Sciences CR, 2001 - 2004).
  • Scholastik research project K1019101 Mathematics, computer science and cybernetics: methods, tools and applications (Academy of Sciences CR, 2001 - 2004).
  • Targeted research project S3086102 Parallel algorithms for large scale simulations on PC clusters (Academy of Sceiences CR, 2001 - 2005).
  • Grant project 105/99/1651 Mathematical modelling of optimal designs of bolt reinforcements (Czech Science Foundation - GACR, 1999 - 2001).
  • Project of bilateral cooperation between CLPP BAS and IG ASCR Large-scale scientific computations in geomechanics (1999 - 2003, cooperation: Central Laboratory for Parallel Processing BAS Sofia Bulgaria).
  • Grant project 105/99/1229 Supercomputing and shape optimization in geomechanics (Czech Science Foundation - GACR, 1999 - 2001).
  • Project LB98212 Realization of fast data interconnections at the Institute of Geonics AS CR Ostrava (Ministry of Education, Youth and Sports, 1998 - 2000).
  • Project LB98273 Rozvoj metropolitního superpočítačového centra v Ostravě - podpora výzkumu v oblasti paralelních algoritmů (Ministry of Education, Youth and Sports, 1998 - 2000, cooperation: VSB - Technical University Ostrava).
  • Project účelové dotace OK 383 High performance computing in geosciences II - support of EC Copernicus 977006 (Ministry of Education, Youth and Sports, 1999 - 2001).
  • Project of international cooperation Copernicus 977006 in framework of the program KIT High performance computing in geosciences II (EC, 1997 - 1999, cooperation: Catholic University of Nijmegen Netherlands, Universite Libre de Bruxelles Belgium, Central Laboratory for Parallel Processing BAS Bulgaria, Institute of Computer Science ASCR).
  • Targeted research project K1012601 Evaluation of rock mass physical reaction on human oriented impact - sectional task Mathematical modelling of rock mass with the aid of effective numerical methods and parallel computer implementation (Academy of Sciences CR, 1996 - 2001).
  • Project účelové dotace OK 157 High performance computing in geosciences, support of EC Copernicus 940820 (Ministry of Education, Youth and Sports, 1996 - 1998).
  • Project of international cooperation Copernicus 940820 High performance computing in geosciences (EC, 1995 - 1998, cooperation: Catholic University of Nijmegen Netherlands, Universite Libre de Bruxelles Belgium, Central Laboratory for Parallel Processing BAS Bulgaria, Institute of Computer Science ASCR).
  • Grant project 105/95/1273 Mathematical modelling in geomechanics, solving large 3D problems (Czech Science Foundation - GACR, 1995 - 1997).
  • Project 93035 in framework of the program CS-US VTP Rocks mass freezing (1994 - 1998, cooperation: National Institute for Occupational Safety and Health Spokane).
  • Grant project 201/94/1861 Iterative methods for solvin 3D problems of elasticity and plasticity (Czech Science Foundation - GACR, 1994 - 1996).
  • Grant project 21 6101 Language oriented fuzzy regulator - 2nd stage (Academy of Sciences CR, 1993 - 1994).
  • Grant project 31656 Numerical analysis of 3D nonlinear problems of geomechanics (Academy of Sciences CR, 1992 - 1994, cooperation: VSB - Technical University Ostrava).
Selected publications
  • O. Axelsson, R. Blaheta: Two simple derivations of universal bounds for the C.B.S. inequality constant. Applications of Mathematics. Vol. 49, No. 1, 2004, pp. 57-72. ISSN 0862-7940.
  • R. Blaheta: GPCG - generalized preconditioned CG method and its use with non-linear and non-symmetric displacement decomposition preconditioners. Numerical Linear Algebra with Applications. Vol. 9, No. 6/7, 2002, pp. 525-550. ISSN 1070-5325.
  • R. Blaheta: Nested tetrahedral grids and strengthened C.B.S. inequality. Numerical Linear Algebra with Applications. Vol. 10, 2003, pp. 619-637. ISSN 1070-5325.
  • R. Blaheta (ed.): Iterative methods, preconditioning and numerical PDE's, Applications of Mathematics (AS CR and Kluwer), Vol. 50, No. 3, 2005. Preface, pp. 177-178, special issue.
  • R. Blaheta, P. Byczanski, R. Kohut, A. Kolcun, R. Snuparek: Large-Scale Modelling of T-M Phenomena from Underground Reposition of the Spent Nuclear Fuel, EUROCK 2005 Impact of Human Activity on Geological Environment, P. Konecny (ed.), A.A. Balkema, Leiden, 2005, pp. 49-55.
  • R. Blaheta, S. Margenov, M. Neytcheva: Uniform estimate of the constant in the strengthened CBS inequality for anisotropic non-conforming FEM systems. Numerical Linear Algebra with Applications. Vol. 11, No. 4, 2004, pp. 309-326. ISSN 1070-5325.
  • R. Blaheta, S. Margenov, M. Neytcheva: Aggregation-based multilevel preconditioning of non-conforming FEM elasticity problems, Proc. PARA'04, Workshop on state-of –the-art in scientific computing, J. Dongarra, K. Madsen, J. Wasniewski (eds.): PARA 2004, LNCS 3732, Springer-Verlag Berlin Heidelberg, 2005, pp. 847–856.
  • R. Blaheta, M. Neytcheva, S. Margenov: Robust optimal multilevel preconditioners for nonconforming FE systems. Numerical Linear Algebra with Applications, No. 12, 2005, pp. 495-514.
  • R. Blaheta, J. Nedoma (eds.): Numerical Models in Geomechanics and Geodynamice, Future Generation Computer Systems (EIsevier). Vol. 22, No. 4, 2006, special issue.
  • R. Blaheta: Algebraic Multilevel Methods with Aggregations: An Overview, In: I. Lirkov, S. Margenov, and J. Wasniewski (eds.) LSSC 2005, LNCS 3743, Springer, Berlin, Heidelberg, 2006, pp. 3–14.
  • R. Blaheta: Multilevel iterative methods and deflation, ECCOMAS CFD 2006, European conference on Computational Fluid Dynamics, P. Wesseling, E. Onate, J. Periaux (eds.), TU Delft, 2006, 12pp.
  • R. Blaheta, P. Byczanski, O. Jakl, R. Kohut, A. Kolcun, K. Krecmer, J. Stary: Large-scale parallel FEM computations of far/near stress field changes in rocks, Future Generation Computer Systems, special issue Numerical Modelling in Geomechanics and Geodynamics. Vol. 22, No. 4, 2006, pp. 449-459.
  • R. Blaheta, P. Byczanski, R. Kohut: Composite Grid finite element method: implementation and iterative solution with inexact subproblems. Applications of Mathematics. Vol. 47, No. 2, 2002, pp. 83-100. ISSN 0862-7940.
  • R. Blaheta, P. Byczanski, O. Jakl, J. Stary: Space decomposition preconditioners and their application in geomechanics. Mathematics and Computers in Simulation. Vol. 61, 2003, pp. 409-420. ISSN 0378-4754.
  • R. Blaheta, P. Byczanski, O. Jakl, J. Stary: Parallel Schwarz Methods: Algebraic Construction of Coarse Problems, Implementation and Testing, Parallel Processing and Applied Mathematics. 6th International Conference, PPAM 2005, Poznań, Poland, September 11-14, 2005 Revised Selected Papers. Berlin : Springer, 2006 - (R. Wyrzykowski), pp. 505-512.
  • R. Blaheta, O. Jakl, J. Stary: Linear system solvers based on space decompositions and parallel computations. Engineering Mechanics / Inzenyrska mechanika. Vol. 10, No. 6, 2003, pp. 439-454. ISSN 1210-2717.
  • R. Blaheta, O. Jakl, J. Stary: Displacement Decomposition and Parallelization of the PCG Method for Elasticity Problems, International Journal of Computational Science and Engineering, Inderscience Publishers NY, USA. ISSN (Online): 1742–7193.
  • R. Blaheta, R. Kohut, M. Neytcheva, J. Stary: Schwarz Methods for Discrete Elliptic and Parabolic problems with an Application to Nuclear Waste Repository Modelling, Mathematics and Computers in Simulation (IMACS/Elsevier), in print.
  • R. Kohut, J. Stary, R. Blaheta, K. Krecmer: Parallel Computing of Thermoelasticity Problems, Large-Scale Scientific Computing. Berlin : Springer, 2006 - (I. Lirkov), pp. 671-678.
  • J. Malik: Mathematical modelling of rock bolt systems II, Appl. Math., No. 45, 2000, pp. 177-203.
  • J. Malik, P. Martinec: Inverse analysis for estimating some characteristic of stress fields and effective instalation of bolt reinforcement, Roofbolting in Mining, Aachen International Mining Symposia, RWTH Aachen, 2004. (P.N.Martens), pp. 416-423.
  • J. Malik: Generalized G-convergence of Quasilinea elliptic differential operators, Nonlinear Analysis, 2007, in print.
  • J. Malik: Mathematical modeling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems. Appl. Math., No. 49, 2004, pp. 1-38.
  • J. Malik: Oscillations in cable stayed bridges: existence, uniqueness, homogenization of cable systems. J. Math. Anal. Appl., No. 266, 2002, pp. 100-126.
  • J. Malik: Asymptotic behavior of solutions to cable stayed bridge equations. J. Math. Anal. Appl., No. 317, 2006, pp. 146-162.
  • J. Malik: Instability of oscillations in cable stayed bridges. Appl. Math., No. 50, 2005, pp. 503-52.
  • J. Malik: Nonlinear models of suspension bridges. J. Math. Anal. Appl., No. 324, 2006, pp. 1288-1296.
  • J. Malik: Generalized nonlinear models of suspension bridges. J. Math. Anal. Appl., No. 321, 2006, pp. 828-850.
  • J. Stary, R. Blaheta, O. Jakl, R. Kohut: Parallel Simulation of T-M Processes in Underground Repository of Spent Nuclear Fuel. Recent Advances in Parallel Virtual Machine and Message Passing Interface. LNCS 4192, Springer, Berlin, 2006 – (B. Mohr), pp. 391-399.
  • B. Strnadel, P. Byczanski: Micro-structural reliability design of brittle materials. Engineering Fracture Mechanics. Vol. 74, No. 11, 2007, pp. 1825-1836.