Higher order accurate discontinuous and continuous p‐Galerkin methods for linear elastodynamics
Higher order accurate discontinuous and continuous p‐Galerkin methods for linear elastodynamics
复制标题
线性弹性动力学的高阶精确间断和连续 p-Galerkin 方法
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
D. Kuhl
中科院分区：
文献类型：
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作者：
T. Gleim;D. Kuhl
本文讨论了用不同的高阶精度Galerkin时间积分格式对线性结构动力学问题进行数值积分的问题。首先，使用任意多项式次数以广义方式发展单场间断和连续p-Galerkin格式。在进一步的步骤中，两个场间断和连续的p-Galerkin格式被导出。在这两类算法中，连续Galerkin格式作为间断Galerkin格式的特例，通过强连续性条件得到。相关的时间积分方案在算法设置中以这样的方式进行调节，即实现类似于经典的Newmark方案及其α导数。所选的基准算例证明了本Galerkin积分格式的优良耗散和色散特性以及鲁棒性。此外，基于解析解和真实的当地时间积分误差，对Galerkin时间积分格式的精度阶数进行了误差分析，验证了所选多项式阶数的控制性。特别是为每一类的Galerkin积分计划的精度顺序指定。通过对经典Newmark格式和Galerkin格式的数值计算结果的比较，表明了Galerkin格式的优越性：对于给定的误差水平，高阶Galerkin格式比Newmark格式更有效。
The present paper is concerned with the numerical integration of linear structural dynamics by means of different higher order accurate Galerkin time integration schemes. Firstly the single field discontinuous and continuous p‐Galerkin schemes are developed in a generalized fashion using arbitrary polynomial degrees. In a further step the two field discontinuous and continuous p‐Galerkin schemes are derived. In both algorithmic classes continuous Galerkin schemes are obtained by the strong enforcement of the continuity condition as special case of the discontinuous Galerkin schemes. The related time integration schemes are conditioned in an algorithmic set‐up in such a manner that the implementation is similar to the classical Newmark scheme and its α derivates. Selected benchmark examples demonstrate the excellent dissipation and dispersion behavior and the robustness of the present Galerkin integration schemes. Furthermore, an error analysis, based on the analytical solution and the real local time integration error, verifies the order of accuracy of Galerkin time integration schemes controlled by the chosen polynomial degree. In particular the order of accuracy for each class of Galerkin integration schemes is specified. The comparison of the numerical effort for the classical Newmark scheme and the family of Galerkin schemes indicates advantages for Galerkin schemes: For a prescribed error level higher order Galerkin schemes are more effective than the Newmark scheme.