Technical Area: Time Integration

As scientific models improve in physical fidelity, their simulations increasingly couple large-scale, stiff, and temporally disparate interacting processes. FASTMath efforts, therefore, focus on software delivery and application support for implicit, explicit, and implicit/explicit time integration methods and development of next-generation time integrator software for multi-rate problems. Methods involved in this work include adaptive linear multistep methods and additive multistage Runge-Kutta methods.

Planned work includes the development of adaptive multirate and structure-exploiting time integration software tailored to efficient solution of problems arising in the context of multiphysics and multiscale simulations and making our time integration techniques more accessible to the machine-learning community.

The temperature field in the baroclinic wave test after 30 days of evolution. The results were generated using the Tempest nonhydrostatic atmospheric dynamics model and a second order implicit-explicit additive Runge-Kutta method from the ARKODE package in the SUNDIALS library.

Simulation results from the MGK fusion SciDAC project showing electron-scale turbulence in a multiscale ion+electron plasma turbulence simulation. Electron-scale effects must be resolved at a finer time scale than ion-scale turbulence, necessitating multiscale treatment in time. FASTMath time integration researchers are working with MGK researchers to apply multirate time integration methods to accurately capture these effects.

Solution to Gray-Scott reaction-diffusion pattern formation test problem using the SUNDIALS multirate integrators to capture the fine scale in time with the AMReX adaptive mesh refinement framework to capture the fine scale in space.