Modern methods of geometric modeling and its applications

The research is devoted to the study of novel mathematical methods of geometric modelling for a purpose of suitable description, data representation, modification and presentation of curves and surfaces with respect to their application in technical practice. The team deals with the recognition of significant curves and surfaces given by exact and approximate representations, with the development and implementation of algorithms based on a hybrid approach combining symbolic and numeric computations by which the current challenging problems of geometric modelling are subsequently addressed. As a highly innovative research and development topic with a high application potential are studied methods of isogeometric analysis for the numerical solution of equations describing the stationary and various self-exciting nonstationary (including turbulent) flows, especially with regard to the optimization of hydraulic profile shapes of water turbines in order to increase their utility properties. Finally, the team is interested in advanced topics of approximate algebraic geometry, namely in the study of exact geometrical operations with algebraic varieties determined by perturbed coefficients.