Runge--Kutta--Nyström methods with maximized stability domain in structural dynamics
Runge--Kutta--Nyström methods with maximized stability domain in structural dynamics
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DOI：
10.1016/j.apnum.2004.09.003
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发表时间：
2005-05
影响因子：
2.8
通讯作者：
Christoph Lunk;B. Simeon
中科院分区：
文献类型：
--
作者：
Christoph Lunk;B. Simeon
结构动力学应用的特点是一种特殊类型的二阶刚性方程，通常与右侧的低光滑度，大尺寸和非线性强迫项相结合。作为隐式格式的替代方案，显式Runge-Kutta-Nyström方法进行了分析，重点是低阶和最大化的稳定域，因为不需要解决虚假的高频振荡。事实证明，可以构造具有在虚轴上延伸到hω=2s的稳定域的方法，其中h是步长，ω是系统中的最大频率，s是级数。FEMLAB仿真算例表明，该方法具有较强的竞争力.
Structural dynamics applications feature a particular type of second order stiff equations, often in combination with low smoothness of the right side, large dimension and non-linear forcing terms. As alternative to implicit schemes, explicit Runge–Kutta–Nyström methods are analysed, with focus on low order and maximized stability domain since spurious high frequency oscillations need not be resolved. It turns out that it is possible to construct methods with a stability domain that stretches up to hω=2s on the imaginary axis where h is the stepsize, ω the largest frequency in the system, and s the stage number. Simulation examples generated by FEMLAB show that the methods are competitive.