论文标题
OCTREE网格上的可扩展本地时间播放
Scalable Local Timestepping on Octree Grids
论文作者
论文摘要
双曲线部分微分方程（PDE）的数值解在科学和工程中无处不在。线方法是一种流行的方法，可以离散在时空定义的PDE，其中空间和时间是独立离散的。当在自适应网格上使用明确的时间播放器时，使用最好的网格间距规定的全局时间段尺寸会导致较粗区域的效率低下。即使自适应空间离散化被广泛用于计算科学中，由于其复杂的性质，时间适应性不太常见。在本文中，我们提出了高度可扩展的算法，以实现本地时间播放（LTS），以便在完全自适应的机器人上进行明确的时间播放方案。我们证明了我们方法的准确性以及跨TACC的Frontera中16K内核的框架的可扩展性。我们还提出了LTS的加快估计模型，该模型预测了与全局时间播放（GTS）相比的加速度，平均相对误差为0.1。
Numerical solutions of hyperbolic partial differential equations(PDEs) are ubiquitous in science and engineering. Method of lines is a popular approach to discretize PDEs defined in spacetime, where space and time are discretized independently. When using explicit timesteppers on adaptive grids, the use of a global timestep-size dictated by the finest grid-spacing leads to inefficiencies in the coarser regions. Even though adaptive space discretizations are widely used in computational sciences, temporal adaptivity is less common due to its sophisticated nature. In this paper, we present highly scalable algorithms to enable local timestepping (LTS) for explicit timestepping schemes on fully adaptive octrees. We demonstrate the accuracy of our methods as well as the scalability of our framework across 16K cores in TACC's Frontera. We also present a speed up estimation model for LTS, which predicts the speedup compared to global timestepping (GTS) with an average of 0.1 relative error.
