在 Octree 网格上扩展的本地时间步长（CS）

米琳达·费尔南多 ， 哈里·桑达尔

双曲偏微分方程（PDES）的数值解在科学和工程中随处可见。行法是一种在时空定义时对 PED 进行离散化的通俗方法，其中空间和时间是独立离散的。在自适应网格上使用显式时间步长时，使用由最佳网格间距决定的全局时间步长会导致较粗区域效率低下。尽管自适应空间离散化在计算科学中被广泛使用，但由于时间适应性复杂，时间适应性并不常见。本文提出了高度可扩展的算法，用于在完全自适应的八进制上实现显式时间步进（LTS）的显式时间步进方案。在 TACC Frontera 中，我们展示了我们方法的准确性以及我们框架跨 16K 内核的可扩展性。我们还提出了LTS的加速估计模型，该模型预测的加速与全局时间步长（GTS）相比平均误差仅为0.1。

Scalable Local Timestepping on Octree Grids

Milinda Fernando, Hari Sundar

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.