The main idea of the proposed project is to improve the efficiency of mathematical modeling and simulation for complex dynamic systems 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 include renewable energy resources, environmental protection, the design of new materials, tracking climate change, and biomedical research for diagnosis and risk prediction.
The scientific and methodological basis of the proposed research is the works devoted to the problems of modeling dynamic systems and increasing the efficiency of numerical implementations. Recently, according to numerous researchers' testimonies, the most promising research directions include unstructured grids, adaptivity, multigrid methods, and parallelism.
The described study is devoted to improving the efficiency of parallel computing. It will be achieved by developing new methods and restructuring well-known methods for parallelizing the computational processes used to find numerical solutions arising in the simulation of complex dynamic systems. Application areas for the proposed methods are parallel simulation 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 a completely new concept of multi-point block schemes for parallel time integration. These new schemes will be more efficient (with better accuracy and adaptive convergence order) than existing, simpler block schemes, and will be equipped with total error control for adaptive convergence.
