This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody dynamics, mechatronics and many other branches of sciences and technologies. By deecting the algebraic equations the second-order index-3 system can be altered into an equivalent standard second-order system. This can be done by projecting the system onto the null space of the constraint matrix. However, creating the projector is computationally expensive and it yields huge bottleneck during the implementation. This paper shows how to find a reduce order model without projecting the system onto the null space of the constraint matrix explicitly. To show the efficiency of the theoretical works we apply them to several data of second-order index-3 models and experimental resultants are discussed in the paper.
翻译:本文讨论了通过应用超逻辑理性Krylov Algorithm(IRKA)减少大型稀散二阶指数-3差异代数方程式(DAEs)的示范订单减少模式,一般而言,这类二阶指数3系统产生于制约力机械学、多体动态学、中观力学以及科学和技术的许多其他分支。通过分解代数方程式,第二阶指数-3系统可以改变为同等的标准二阶系统。这可以通过将系统投射到制约矩阵的空格上来完成。然而,创建投影器在计算上费用昂贵,在执行过程中会产生巨大的瓶颈。本文说明了如何找到一个降序模型,而不将系统投射到约束矩阵的空格上。为了显示理论工作的效率,我们在文件中讨论了第二阶指数-3模型和实验结果模型的若干数据中应用这些理论工作。