On the convergence rate of dynamic iteration for coupled problems with multiple subsystems
On the convergence rate of dynamic iteration for coupled problems with multiple subsystems
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DOI：
10.1016/j.cam.2013.07.031
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
A. Bartel;Markus Brunk;S. Schöps
中科院分区：
文献类型：
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作者：
A. Bartel;Markus Brunk;S. Schöps
在多物理体建模中自然会出现耦合问题。每个子问题通常用一组偏微分代数方程来表示。应用直线法，得到了耦合微分代数方程（DAEs）。带窗口的动态迭代是这类系统瞬态仿真的标准技术。与常微分方程系统的动态迭代不同，DAEs的收敛性一般不能保证，除非满足某些收缩条件。在收敛的情况下，它是线性的。在本文中，我们用窗口大小来量化收敛速率，即收缩的斜率。我们研究了DAE和ODE系统以及两个或多个子系统的耦合结构的收敛速度。我们发现（对于某些耦合结构）比以前已知的速率更高（即，窗口大小呈线性），并给出了速率的精确估计。此外，还揭示了速率如何依赖于子系统的数量。
In multiphysical modeling coupled problems naturally occur. Each subproblem is commonly represented by a system of partial differential-algebraic equations. Applying the method of lines, this results in coupled differential-algebraic equations (DAEs). Dynamic iteration with windowing is a standard technique for the transient simulation of such systems. In contrast to the dynamic iteration of systems of ordinary differential equations, convergence for DAEs cannot be generally guaranteed unless some contraction condition is fulfilled. In the case of convergence, it is a linear one.In this paper, we quantify the convergence rate, i.e., the slope of the contraction, in terms of the window size. We investigate the convergence rate with respect to the coupling structure for DAE and ODE systems and also for two and more subsystems. We find higher rates (for certain coupling structures) than known before (that is, linear in the window size) and give sharp estimates for the rate. Furthermore it is revealed how the rate depends on the number of subsystems.