论文标题
时空DG-SEM实施的理论和实际方面
Theoretical and Practical Aspects of Space-Time DG-SEM Implementations
论文作者
论文摘要
我们讨论了两种方法，用于制定和实施时空不连续的盖尔金光谱元素方法（DG-SEM）。一方面，时间被视为附加的坐标方向，并将盖金方法应用于整个问题。在另一个中，线路的方法在空间中与DG-SEM一起使用，并在时间上使用完全隐式的runge-kutta方法lobatto IIIC。这两种方法在数学上是等效的，因为它们导致了相同的离散解决方案。但是，实际上它们在几个重要方面有所不同，包括用于描述它们的术语，所得软件的结构以及与非线性求解器的相互作用。讨论了两种方法的挑战和优点，目的是为从业者提供足够的考虑来选择遵循哪种途径。此外，提供两种方法的实现是进一步开发的起点。数值实验验证了这些代码的理论准确性，并证明了它们的实用性，即使对于4D问题也是如此。
We discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire problem. In the other, the method of lines is used with DG-SEM in space and the fully implicit Runge-Kutta method Lobatto IIIC in time. The two approaches are mathematically equivalent in the sense that they lead to the same discrete solution. However, in practice they differ in several important respects, including the terminology used to describe them, the structure of the resulting software, and the interaction with nonlinear solvers. Challenges and merits of the two approaches are discussed with the goal of providing the practitioner with sufficient consideration to choose which path to follow. Additionally, implementations of the two methods are provided as a starting point for further development. Numerical experiments validate the theoretical accuracy of these codes and demonstrate their utility, even for 4D problems.
