Numerical solution and applications of the nonlinear partial differential equationsSupervisor: prof. RNDr. Karol Mikula, DrSc.
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|Project description:||Project deals with design of original numerical methods for solving nonlinear partial differential equations, study of their stability, convergence,, computational efficiency and parallelization, for the mathematical models describing- nonlinear thermomechanics, groundwater flow, dislocation dynamics and fluid dynamics with free boundaries modelled by evolving curves and surfaces driven by the external velocity field, anisotropy, surface and elastic energies,- filtering of 2D and 3D images and image sequences based on the nonlinear anisotropic and geometrical diffusion equations,- segmentation of 2D and 3D images using evolving geodesic and elastic curves and surfaces in Lagrangean and level-set formulations,-flow, diffusion and transport with adsorption in porous media, related contaminant transport in groundwater flow and solution of direct and inverse problems for the model parameter estimation,-geodetic boundary value problems formulated on the Earth surface as fixed or free boundary, and, their solution using finite and boundary element method.|
|Kind of project:||APVV ()|
|Department:||Department of Mathematics and Constructive Geometry (FCE)|
|Project status:||Successfully completed|
|Project start date :||01. 06. 2008|
|Project close date:||30. 06. 2011|
|Number of workers in the project:||2|
|Number of official workers in the project:||0|