Abstract In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data exchange gives the global method a strong explicit component. Globally, such an explicit co-simulation schemes exchange time step can be seen as a step of an one-step method which is explicit in some solution components. Exploiting this structure, we give a convergence proof for such schemes. As flows of conserved quantities are passed across subsystem boundaries, it is not ensured that system-wide balances are fulfilled: the system is not solved as one single equation system. These balance errors can accumulate and make simulation results inaccurate. Use of higher-order extrapolation in exchanged data can reduce this problem but cannot solve it. The remaining balance error has been handled in past work by recontributing it to the input signal in next coupling time step, a technique labeled balance correction methods. Convergence for that method is proven. Further, the lack of stability for co-simulation schemes with and without balance correction is stated.

中文翻译：

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显式耦合仿真工具的收敛（协同仿真）

摘要 在工程中，通过将来自子系统的信息作为参数传递给受影响的子系统，将现有的仿真工具耦合到一个大系统中是一种普遍的愿望。在固定时间点执行时，此数据交换为全局方法提供了强大的显式组件。在全球范围内，这种显式的联合仿真方案交换时间步长可以看作是在某些解决方案组件中显式的一步法的一个步骤。利用这种结构，我们给出了此类方案的收敛性证明。当守恒量流跨越子系统边界时，不能确保满足系统范围的平衡：系统不是作为一个单一方程系统求解的。这些平衡误差会累积并使仿真结果不准确。在交换数据中使用高阶外推可以减少这个问题，但不能解决它。在过去的工作中，剩余的平衡误差已通过在下一个耦合时间步长中将其重新分配给输入信号来处理，这种技术称为平衡校正方法。证明了该方法的收敛性。此外，还指出了有和没有平衡校正的联合仿真方案缺乏稳定性。