Scalable Local Timestepping on Octree Grids

TL;DR

This paper introduces scalable algorithms for local timestepping on adaptive octree grids, improving efficiency in solving hyperbolic PDEs by enabling temporal adaptivity alongside spatial adaptivity.

Contribution

It presents novel scalable algorithms for local timestepping on fully adaptive octree grids, addressing a gap in temporal adaptivity for explicit schemes.

Findings

Achieved accurate solutions with the proposed methods.

Demonstrated scalability across 16,000 cores.

Developed a speedup estimation model with 0.1 average error.

Abstract

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.