论文标题
高阶隐式时间集成方案，具有基于混合订单膨胀的可控数值耗散
High-order implicit time integration scheme with controllable numerical dissipation based on mixed-order Padé expansions
论文作者
论文摘要
提出了一个在高频下具有可控数值耗散的单步高阶隐式时间整合方案，用于对结构动态问题的瞬态分析。数值耗散的量由高频限制中的光谱半径$ρ_\ infty $的用户指定值控制。使用此用户指定的参数作为权重系数，通过混合对角线和亚对角线的扩展来构建运动方程矩阵指数解的addé扩展。设计了有效的时间播放方案，其中方程式与标准Newmark方法的复杂性相似，可以递归地解决。结果表明，所提出的高级方案实现了高频耗散，同时最大程度地减少了低频耗散和周期误差。数值示例证明了提供的耗散控制和计划效率的有效性。提供了选择控制参数和时间步长大小的简单指南。用MATLAB和FORTRAN编写的源代码可下载：https：//github.com/chongminsong/chongminsong/highordertimeintegration。
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled by a user-specified value of the spectral radius $ρ_\infty$ in the high frequency limit. Using this user-specified parameter as a weight factor, a Padé expansion of the matrix exponential solution of the equation of motion is constructed by mixing the diagonal and sub-diagonal expansions. An efficient timestepping scheme is designed where systems of equations, similar in complexity to the standard Newmark method, are solved recursively. It is shown that the proposed high-order scheme achieves high-frequency dissipation, while minimizing low-frequency dissipation and period errors. The effectiveness of the provided dissipation control and the efficiency of the scheme are demonstrated by numerical examples. A simple guideline for the choice of the controlling parameter and time step size is provided. The source codes written in MATLAB and FORTRAN are available for download at: https://github.com/ChongminSong/HighOrderTimeIntegration.
