May 23, 2019   10:49 a.m. Želmíra
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Geometrical partial differential equations - numerical analysis and applications

Supervisor: prof. RNDr. Karol Mikula, DrSc.


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Project description:The project is devoted to a design, numerical analysis and serial and parallel implementation of new efficient, stable and precise numerical methods for solving nonlinear geometrical partial differential equations (PDEs) arising in image processing and computer vision applications in biology, bioengineering and medicine, in nonlinear conservation laws, transport and advection-diffusion equations of computational fluid dynamics and porous media flow with free boundaries, in wind-driven forest fire front spreading modelled by evolving plane curves, and in solution of geodetic boundary value problems and geodetic data filtering by nonlinear PDEs on surfaces given by the Earth topography. New numerical schemes for solving inverse problems will be also designed and analysed. New efficient and stable higher-order level-set methods and Lagrangean schemes for motion of curves and surfaces dependent on mean curvature, anisotropy and external velocity will be developed. The proposed methods will be based on original semi-implicit and explicit/fully-implicit time discretizations and on finite volume, finite element and boundary element space discretizations adjusted to uniform and unstructured adaptive grids in 2D, 3D and to grids on 3D surfaces. The numerical methods will be analysed with respect to stability, efficiency of computations and regarding convergence to the exact solutions of the nonlinear partial differential equations.
Kind of project:APVV - Všeobecná výzva ()
Department:Department of Mathematics and Constructive Geometry (FCE)
Project identification:APW-0184-10
Project status:Successfully completed
Project start date :01. 05. 2011
Project close date:31. 10. 2014
Number of workers in the project:2
Number of official workers in the project:0