On Numerical Solution of Block-Structured Discrete Systems

The paper presents a numerical methodology for solving high-dimensional discrete dynamical systems characterized by a block structure with boundary conditions that are non-separated between blocks. Direct application of classical methods of transferring boundary conditions is inefficient, since the block structure of the conditions, as for many other classes of problems, allows to speed up their solution considerably. In this approach the decomposition of complex processes into simpler sub-processes with known mathematical models is used, and the decomposition of a complex process is performed in such a way that the intermediate states of sub-processes do not affect each other, i.e. they are independent, and the connection between sub-processes is implemented only through their input and output states. In this case, as a rule, the conditions determining the links between sub-processes are characterized by poorly occupied Jacobi matrices. In the paper formulas that perform transferring of non-separated boundary conditions are presented and practical results demonstrating the efficacy of the proposed approach on a test problem are provided.