In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper focuses on operator-splitting techniques for coupled systems and aims at preserving the structure in the port-Hamiltonian framework. The study explores two decomposition strategies: one considering the underlying coupled subsystem structure and the other addressing energy-associated properties such as conservation and dissipation. We show that for coupled index-$1$ DAEs with and without private index-2 variables, the splitting schemes on top of a dimension-reducing decomposition achieve the same convergence rate as in the case of ordinary differential equations. Additionally, we discuss an energy-associated decomposition for index-1 pH-DAEs and introduce generalized Cayley transforms to uphold energy conservation. The effectiveness of both strategies is evaluated using port-Hamiltonian benchmark examples from electric circuits.

翻译：在微分代数方程的仿真中，必须采用考虑其内在结构、保持显式或隐式代数约束而不加以改变的数值方案。本文聚焦于耦合系统的算子分裂技术，旨在端口-汉密尔顿框架内保持结构特性。研究探讨了两种分解策略：其一基于底层耦合子系统结构，其二针对能量相关特性（如守恒与耗散）。我们证明，对于含或不含私有指标-2变量的耦合指标-1微分代数方程，基于降维分解的分裂方案可达到常微分方程情形下的相同收敛阶。此外，针对指标-1 pH-微分代数方程，我们讨论了能量相关分解，并引入广义凯莱变换以保持能量守恒。通过来自电路的端口-汉密尔顿基准算例，评估了两种策略的有效性。