ABSTRACT The term co-simulation denotes the coupling of some simulation tools for dynamical systems into one big system by having them exchange data at points of a fixed time grid and extrapolating the received data into the interval, while none of the steps is repeated for iteration. From the global perspective, the simulation thus has a strong explicit component. Frequently, among the data passed across subsystem boundaries there are flows of conserved quantities, and as there is no iteration of steps, system-wide balances may not be fulfilled: the system is not solved as one monolithic equation system. If these balance errors accumulate, simulation results become inaccurate. Balance correction methods which compensate these errors by adding corrections for the balances to the signal in the next coupling time step have been considered in past research. But establishing the balance of one quantity a posteriori due to the time delay in general cannot establish the balances of quantities that depend on the exchanged quantities, usually energy. In most applications from physics, the balance of energy is equivalent to stability. In this paper, a method is presented which allows users to choose the quantity that should be balanced to be that energy, and to accurately balance it. This establishes also numerical stability for many classes of stable problems.

中文翻译：

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解决联合仿真中的能量平衡误差

摘要 术语协同仿真表示将一些用于动力系统的仿真工具耦合到一个大系统中，方法是让它们在固定时间网格的点交换数据并将接收到的数据外推到间隔中，而不重复任何步骤进行迭代. 因此，从全局角度来看，模拟具有很强的显式组件。通常，在跨子系统边界传递的数据中存在守恒量流，并且由于没有步骤的迭代，可能无法实现系统范围的平衡：系统不是作为一个整体方程系统求解的。如果这些平衡误差累积，仿真结果就会变得不准确。在过去的研究中已经考虑了通过在下一个耦合时间步长中向信号添加平衡校正来补偿这些误差的平衡校正方法。但是，由于时间延迟，后验建立一个量的平衡通常不能建立依赖于交换量（通常是能量）的量的平衡。在物理学的大多数应用中，能量平衡等同于稳定性。在本文中，提出了一种方法，允许用户选择应该平衡的数量作为该能量，并准确地平衡它。这也为许多类别的稳定问题建立了数值稳定性。但是，由于时间延迟，后验建立一个量的平衡通常不能建立依赖于交换量（通常是能量）的量的平衡。在物理学的大多数应用中，能量平衡等同于稳定性。在本文中，提出了一种方法，允许用户选择应该平衡的数量作为该能量，并准确地平衡它。这也为许多类别的稳定问题建立了数值稳定性。但是，由于时间延迟，后验建立一个量的平衡通常不能建立依赖于交换量（通常是能量）的量的平衡。在物理学的大多数应用中，能量平衡等同于稳定性。在本文中，提出了一种方法，允许用户选择应该平衡的数量作为该能量，并准确地平衡它。这也为许多类别的稳定问题建立了数值稳定性。