Variational space–time elements for large-scale systems
Variational space–time elements for large-scale systems
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DOI：
10.1016/j.cma.2017.08.020
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发表时间：
2017-11
影响因子：
7.2
通讯作者：
C. Hesch;S. Schuß;M. Dittmann;S. Eugster;M. Favino;R. Krause
中科院分区：
文献类型：
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作者：
C. Hesch;S. Schuß;M. Dittmann;S. Eugster;M. Favino;R. Krause
本文引入了一种新的基于伽辽金的瞬态连续问题的空间和时间偏微分方程公式。因此，我们的目标是对时空进行直接的有限元离散化，适用于出现大规模问题的大规模并行分析。提出的公式适用于热、机械和流体系统，以及Kuramoto-Sivashinsky问题，代表了材料科学中使用NURBS形状函数的一般高阶公式。只要可能，我们就验证这个公式的守恒性质。最后，通过一系列实例验证了本文所提出的所有系统的适用性。
In this paper, we introduce a new Galerkin based formulation for transient continuum problems, governed by partial differential equations in space and time. Therefore, we aim at a direct finite element discretization of the space–time, suitable for massive parallel analysis of the arising large-scale problem. The proposed formulation is applied to thermal, mechanical and fluid systems, as well as to a Kuramoto–Sivashinsky problem, representing the general class of higher-order formulations in material science using NURBS based shape functions. We verify whenever possible the conservation properties of the formulation. Finally, a series of examples demonstrate the applicability to all systems presented in this paper.