High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling.
High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling.
复制标题
DOI：
10.1002/nme.4631
复制
发表时间：
2014-04-13
影响因子：
2.9
通讯作者：
Whiteman, John R.
中科院分区：
文献类型：
--
作者：
Banks, H. T.;Birch, Malcolm J.;Brewin, Mark P.;Greenwald, Stephen E.;Hu, Shuhua;Kenz, Zackary R.;Kruse, Carola;Maischak, Matthias;Shaw, Simon;Whiteman, John R.
关键词：
我们重新审视最初由Werder等人介绍的方法。方法应用机械工程，190：6685-6708，2001）用于应用于抛物型偏微分方程的时间不连续Galerkin FEM。在这种方法中，块系统的出现是因为空间系统通过时间基函数的内积的耦合。如果空间有限元空间的维数为D，并且在时间上使用r次多项式，则块系统的维数为（r + 1）D，并且当r > 1时通常被认为太大。Werder等人发现时空耦合矩阵在r = 100时是可对角化的，这意味着在一个时间步长内的时间耦合计算实际上是可以解耦的。通过在空间中使用连续Galerkin或谱元方法，我们应用这种DG在时间上的方法，第一次，二阶波动方程，包括弹性动力学和不Kelvin-Voigt和Maxwell-Zener粘弹性。给出了一组数值结果的例子，以证明适度高阶（高达7度）的时间和时空近似的误差和计算工作的有利影响，我们还触及了这种方法的应用程序的一个雄心勃勃的问题有关的冠状动脉疾病的诊断。版权所有© 2014作者。International Journal for Numerical Methods in Engineering（英语：International Journal for Numerical Methods in Engineering），John Wiley & Sons Ltd.
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
登录
查看更多内容
DOI：
10.1016/0045-7825(93)90172-t
发表时间：
1993-08-01
影响因子：
7.2
作者：
FRENCH, DA
通讯作者：
FRENCH, DA
影响因子：
2
作者：
French, DA;Peterson, TE
通讯作者：
Peterson, TE
DOI：
10.3934/mbe.2014.11.427
发表时间：
2014-06
期刊：
Mathematical biosciences and engineering : MBE
影响因子：
--
作者：
Banks HT;Hu S;Kenz ZR;Kruse C;Shaw S;Whiteman J;Brewin MP;Greenwald SE;Birch MJ
通讯作者：
Birch MJ
DOI：
10.1016/0045-7825(88)90006-0
发表时间：
1988-02-01
影响因子：
7.2
作者：
HUGHES, TJR;HULBERT, GM
通讯作者：
HULBERT, GM
影响因子：
2.5
作者：
Ainsworth, M.;Monk, P.;Muniz, W.
通讯作者：
Muniz, W.