无网格时域自适应算法在振动问题中的应用

为了提高无网格方法计算振动问题时的计算效率和计算精度,开发了无网格时域自适应算法。该方法在时域内采用时域自适应算法,将每个变量在每个时间步内离散成关于时间的展开形式,通过控制展开阶数保证自适应算法的精度,可以更准确的描述变量随时间的变化;同时将时空耦合的初值问题转化为一系列的空间边值问题,并采用无网格方法递推求解。该方法可以提高计算效率并弥补时间步长较多或较大时造成的精度损失,并通过数值算例验证了其准确性。

Application of the meshless time domain adaptive method in solving vibration problems

To increase the computational efficiency and accuracy of the meshless method for solving vibration problems, a new meshless time domain adaptive algorithm was developed.In the method, a time domain adaptive algorithm was used and variables were expanded in terms of time within each time interval.The variables could be more accurately described over time by adopting higher expansion order.The time-space problem of vibration would be transformed into a series of boundary value problems solved by the meshless method.The method can improve the computational efficiency and compensate for the loss of precision caused by different time steps, and its efficiency and accuracy were verified by numerical examples.