| engl. Beschreibung/ Kurzkommentar |
A growing complexity of modern engineering problems requires advanced numerical algorithms for a correct treatment of the corresponding boundary value problems. Therefore, methods working directly with discrete mathematical structures, such as methods of discrete potential theory, discrete function theory, and finite element exterior calculus, are gaining more and more popularity nowadays. Independent of a chosen method, the solution procedure starts with a discretisation of a given domain to construct discrete geometrical setting, i.e. with discrete geometric modelling. Thus, this project deals with discrete geometric modelling of different domain in two- and three-dimensional setting. The general idea of the project is to develop a software tool allowing consistent discretisation of a given arbitrary domain. Thus, project participants will study different approaches to discretisation and their influence on the results of computer simulations with known numerical methods. Moreover, an efficient computer implementation is desired, and therefore, studying of several strategies for speeding up computations with discrete structure will be performed during the project. Practical realisation of the project can be done in any programming language depending on skills and desires of participants, e.g. C++, Phyton, Matlab etc. |
