论文标题
构造时空帐篷的意识
Structure aware Runge-Kutta time stepping for spacetime tents
论文作者
论文摘要
我们引入了一种新的Runge-Kutta类型方法，适合于时间步进，以在帐篷形时段内传播双曲线解决方案。与标准的runge-kutta方法不同，当使用标准高阶空间（不连续的盖尔金）离散化时，新方法会产生预期的收敛性。在提出了这些方法的非标准顺序条件的推导后，我们显示了非线性双曲系统的数值示例，以证明最佳收敛速率。我们还报告了应用于线性双曲方程的这些方法的离散稳定性。
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta methods, the new methods yield expected convergence properties when standard high order spatial (discontinuous Galerkin) discretizations are used. After presenting a derivation of nonstandard order conditions for these methods, we show numerical examples of nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We also report on the discrete stability properties of these methods applied to linear hyperbolic equations.
