  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.
