Hermite方法的Leapfrog时间步进
Leapfrog time-stepping for Hermite methods
AI总结：
本文提出Hermite-leapfrog方法用于一阶波系统，结合Leapfrog时间步进与Hermite方法，实现高阶精度，并在单空间维度中保持变量量。
摘要：
我们介绍了用于一阶波系统的Hermite-leapfrog方法。新的Hermite-leapfrog方法将Leapfrog时间步进与Goodrich等人的Hermite方法相结合。新的方案在时间和空间上都 stagger 场变量，并具有高阶精度。我们详细描述了该方法，并证明了在单空间维度中该方法保持变量量。通过张量积构造构建了更高维度的版本。单空间维度中的数值证据和严格分析证明了稳定性和高阶收敛性。还展示了在图形处理单元上的高效实现实验。
英文摘要：
We introduce Hermite-leapfrog methods for first order wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors. The new schemes stagger field variables in both time and space and are high-order accurate. We provide a detailed description of the method and demonstrate that the method conserves variable quantities in one-space dimension. Higher dimensional versions of the method are constructed via a tensor product construction. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.
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