May 19, 2019   4:29 p.m. Gertrúda
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Modern methods of mathematical and computational modelling in engineering applications.

Supervisor: prof. RNDr. Karol Mikula, DrSc.


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Project description:Mathematical and computational modelling is a rapidly growing scientific discipline nowadays. It brings consistent mathematical models derived from the first principles and allows testing and application of the mathematical methods in complex real situations studied by many applied sciences by means of computer simulations. The aim of this project is to study mathematical models and to develop efficient computational methods and computer simulations in the engineering applications like the nonlinear diffusion, heat conduction, free boundary problems and related motion of interfaces modelled by the elastic curves, flow in porous media and contaminant transport, dislocations motion in material solidification, precise determination of the Earth geoid and quasigeoid, filtration and analysis of large data sets, image processing and segmentation and visualization of large scale computer simulations. The project puts together scientists working in mathematical and engineering disciplines in order to make a significant progress in mathematical and computational methods used in engineering sciences and applications. The main objective is to study the mathematical models and their numerical solution described by the nonlinear partial differential equations using stable and efficient time discretizations and spatial discretizations by the finite element and finite volume methods. The computational methods are studied with regard to efficiency, possibility of the parallelization, stability of computations and convergence to variational solutions of corresponding initial-boundary value problems.
Kind of project:VEGA ()
Department:Department of Mathematics and Constructive Geometry (FCE)
Project identification:1/3321/06
Project status:Successfully completed
Project start date :01. 01. 2006
Project close date:31. 12. 2008
Number of workers in the project:1
Number of official workers in the project:0