Explicit co-simulation with interface Jacobian approximation

Explicit co-simulation denotes a weak coupling of subsystems without iteration between the communication time points (macro-time points). Extrapolated polynomials are commonly used to represent coupling variables. The error introduced by the polynomials can induce instability. Partial derivatives of the interface variables are used in the iterative co-simulation (implicit or semi-implicit co-simulation) to enhance stability. However, repetition of macro-time step becomes a main drawback especially for practical applications. In this manuscript we approximate the interface Jacobian using a truncated matrix exponential and study the numerical behavior in the framework of explicit co-simulations. The stability is greatly improved compared to the classical explicit method. The error of the interface Jacobian approximation has been investigated. A supported pendulum is used to validate the proposed co-simulation method.