Research

Department consists of three groups working in different but closely related fields:

• Numerical linear algebra and theory of matrices
• Numerical methods of smooth and nonsmooth optimisation, nonlinear programming and solving nonlinear algebraic systems
• Mathematical modelling of problems in elastoplasticity

Research effort in the first group has been recently focused on development, analysis, implementation and application of scalable algorithms for solving extremely large generally sparse linear algebraic systems including preconditioning and implementation on parallel computer systems (Tuma, Rozloznik); theory of convergence and numerical behaviour of Krylov subspace methods (Strakos, Rozloznik, Tichy); mathematical foundations and numerical methods in error-in- variables modeling (Strakos); mathematical properties of special matrices (Fiedler); theoretical and computational aspects of problems with interval data (Rohn).

In the second group the research work is recently oriented towards computational methods for solving nonsmooth large scale systems of nonlinear equations, which are applied to nonlinear complementarity problems and variational inequalities as well as efficient globally convergent variable metric methods for nonsmooth optimization and large scale nonlinear programming. Sequential quadratic programming and interior point methods for large scale nonlinear programming are also investigated and implemented and special preconditioners for indefinite KKT systems are investigated. As an accompanying activity, an extensive software system for universal functional optimization UFO is being developed. (Luksan, Vlcek)

Third group focuses on mathematical modeling of contact problems with friction in elasticity and thermoelasticity Theoretical results are applied in several important areas in mechanics, geomechanics and technology. (Nedoma, Hlavacek)

In addition to theoretical research our department is involved in important applications. The project on remediation of environmental problems due to the chemical mining of uranium in Straz pod Ralskem represents the typical example.

Our department runs regular Computational Mathematics Seminar (founded in 1992), organizes international conferences, e.g. Computational Linear Algebra with Applications (MILOVY 2002) and Modeling: a series of IMACS conferences on Mathematical Modeling and Computational Methods in Mechanics, Physics and Geodynamics. Its members cooperate with several universities and research institutions in CR (TU Liberec (Strakos, Tuma, Rozloznik, Luksan), MFF UK Prague (Strakos, Tuma), FJFI CVUT Prague (Tuma, Drkosova)) and abroad (Emory University, Atlanta (Strakos), Los Alamos National Laboratory (Tuma)).