Analytical Method of Nested Algebraic Loops in Co-simulation System

Aiming at the nested algebraic loop problem in the co-simulation system, the Kosaraju algorithm and the DFS (Depth First Search) algorithm are combined to construct the Kosaraju-DFS method to detect the nested algebraic loop in the simulation system. On this basis, the Newton down-hill method and Newton-PHSS (Preconditioned Hermitian and Skew-Hermitian Splitting) iterative method are introduced, and the nested algebraic loop is disassembled and transformed into the problem of solving nonlinear equations in mathematics, and the iterative result of the nested loop is obtained. It is applied to the FMI (Functional Mock-up Interface) co-simulation system to solve the communication deadlock problem caused by the nested algebraic loop in the simulation system. The results show that the Kosaraju-DFS method can accurately detect the nested algebraic loops in the directed graph, and it can effectively improve the accuracy and robustness of the simulation through the Newton down-hill method and the Newton-PHSS iterative method.