论文标题
双曲线和振荡PDE的准确且时平行的有理指数积分器
An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs
论文作者
论文摘要
有理指数积分器（REXI）是一类数值方法，非常适合将线性部分微分方程与虚构特征值集成的时间。由于这些方法可以随时间并行（除了通常执行的空间并行化之外），因此非常适合利用现代高性能计算系统。在本文中，我们提出了一种新型的REXI方案，可大大提高准确性和效率。所选方法还将使我们能够轻松确定近似中需要多少个项，以获得准确的结果。我们为浅水方程提供了比较数值模拟，该层次强调了我们方法的效率，并证明可以在图形处理单元上有效实施REXI方案。
Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in addition to the spatial parallelization that is commonly performed) they are well suited to exploit modern high performance computing systems. In this paper, we propose a novel REXI scheme that drastically improves accuracy and efficiency. The chosen approach will also allow us to easily determine how many terms are required in the approximation in order to obtain accurate results. We provide comparative numerical simulations for a shallow water equation that highlight the efficiency of our approach and demonstrate that REXI schemes can be efficiently implemented on graphic processing units.
