The main idea of the proposed project is to increase the efficiency of mathematical modeling and simulation for complex dynamic systems that are described by systems of differential equations. For this, parallel algorithms for obtaining numerical solutions will be developed. Potential fields of application for the developed algorithms are renewable energy resources, environmental protection, the design of new materials, tracking climate change, biomedical research for diagnosis, risk prediction, etc.
The scientific and methodological basis of the proposed research are the works, devoted to the problems of modeling dynamic systems, increasing the efficiency of numerical implementations. Recently, according to numerous testimonies of researchers, the most promising research directions are approaches such as unstructured grids, adaptability, multigrid methods, and parallelism.
The described study devoted to improve the efficiency of parallel computing. It will be achieved by developing new and restructuring well-known methods for parallelizing computational processes of finding numerical solutions that arise when simulating complex dynamic systems. Application areas for the proposed methods are parallel simulating of dynamic objects with lumped parameters, as well as objects with distributed parameters, for which partial differential equations can be discretized using the method of lines.
The proposed work will install the completely new concept of multi-point block schemes for parallel time integration. These new schemes will be more efficient (better accuracy and adaptive convergence order) than existing, simpler block schemes, and the new schemes will be equipped with total error control for installing adaptivity.
