Numerical methods for evolving curves and surfaces and their applicationsSupervisor: prof. RNDr. Karol Mikula, DrSc.
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|Project description:||The main goal of the proposed project is to build novel mathematical models and stable, efficient and accurate numerical methods for real-world applications involving evolving curves and surfaces. The targeted fundamental scientific breakthrough is to develop novel ideas in mathematical modelling, numerical analysis and scientific computing, yielding innovative numerical algorithms and efficient software solutions that will go far beyond scientific state-of-the-art and current simulation technology standards from the worldwide point of view. On the application site, the proposed project targets emerging topics as diverse as the reconstruction of living organisms morphogenesis in developmental biology, image segmentation and cell tracking in biomedical applications and drug screening, complex 3D point cloud surface reconstruction from laser scanning and photogrammetry in the digitization of cultural heritage, filtering and segmentation of a large-scale Earth satellite observation data used for the high-resolution Earth gravity field modelling, design of optimal architectural structures in the form of minimal surfaces, design of optimal computational meshes and surface discretization in computational geometry,numerical analysis, scientific computing and CAD systems, real-time forest fire front propagation modelling and simulation, and accurate and physically plausible combustion engine simulations. The success in such transversal applications must have common basis, new mathematical modelling approaches and stable, efficient and accurate numerical algorithms and software. Building such common base is the aim of the proposed project and will be achieved by development of new Lagrangian (parametric) and Eulerian (level set) numerical algorithms for evolving curves and surfaces, carefully tested and validated on real data provided by applied sciences and research and industrial cooperation.|
|Kind of project:||APVV - Všeobecná výzva ()|
|Department:||Department of Mathematics and Constructive Geometry (FCE)|
|Project status:||In process of execution|
|Project start date :||01. 07. 2016|
|Project close date:||30. 06. 2020|
|Number of workers in the project:||2|
|Number of official workers in the project:||0|