Preconditioned dynamic iteration for coupled differential-algebraic systems
Preconditioned dynamic iteration for coupled differential-algebraic systems
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DOI：
10.1023/a:1021909032551
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发表时间：
2001-01-01
期刊：
影响因子：
1.5
通讯作者：
Günther, M
中科院分区：
文献类型：
--
作者：
Arnold, M;Günther, M
复杂技术系统建模的网络方法经常导致一组由耦合条件连接的微分代数系统。这种耦合问题的数值解的一种常见方法是基于子系统的标准时间积分方法的耦合。作为一个统一的框架，这种多速率，多方法或动态迭代方法的收敛性分析，我们研究在本文中的收敛性的动态迭代方法与（小）有限数目的迭代步骤，在每个窗口。预处理用于保证耦合数值方法的稳定性。理论结果适用于电路模拟和指数3系统中产生的多体动力学的准线性问题。
The network approach to the modelling of complex technical systems results frequently in a set of differential-algebraic systems that are connected by coupling conditions. A common approach to the numerical solution of such coupled problems is based on the coupling of standard time integration methods for the subsystems. As a unified framework for the convergence analysis of such multi-rate, multi-method or dynamic iteration approaches we study in the present paper the convergence of a dynamic iteration method with a (small) finite number of iteration steps in each window. Preconditioning is used to guarantee stability of the coupled numerical methods. The theoretical results are applied to quasilinear problems from electrical circuit simulation and to index-3 systems arising in multibody dynamics.