Hierarchical, Multimodel, Multiscale Parallel-In-Time

Project Overview

Many physical systems of interest to LLNL and the wider scientific community are modeled by high-dimensional kinetic partial differential equations (PDEs) that feature widely varying time-scales. The combination of high dimensionality and multiple scales makes simulations of such systems extremely computationally intensive. Examples include magnetic and inertial confinement fusion simulations, rarefied gas dynamics, and thermal radiative transfer. Parallel-in-time (PIT) methods would seem to be a natural candidate to accelerate such simulations. These methods classically treat time integration as an iterative process, generating cheap estimates on a grid that has been coarsened in time and/or space, which are iteratively corrected by parallel computations on finer grids. However, due to their enormous expense, multiscale kinetic codes are typically run at a bare minimum of spatiotemporal resolution. Further coarsening will often step over physically relevant time-scales, qualitatively changing the solution or, in the worst case, making the code unstable.

This project explored the feasibility of obtaining parallel speedups using PIT schemes that coarsen the model, not the resolution. Specifically, we found that it is possible, within a parareal PIT framework, to leverage computationally advantageous fluid models arising from the kinetic equations, closed via kinetic data computed in parallel, to accelerate the time-to-solution for multi-scale kinetic systems. We have demonstrated parallel speed-up on the classical two-stream instability problem of kinetic plasma dynamics.

This work has received follow-on funding through the ASCR Mathematical Multifacted Integrated Capability Center (MMICC) program, where it will continue to be refined so that larger speed-ups can be achieved on a wider variety of problems.

Mission Impact

The work presented here can be leveraged to accelerate many of the computationally intensive multi-physics and multi-scale simulations that are ubiquitous in LLNL's mission focus areas. Examples of core missions and competencies include Stockpile Stewardship, ICF, All-WMD Threat Reduction, HPC, and High-Energy Density Science. The proposed methodology holds the potential to accelerate time-to-solution of high-fidelity simulations across each of these mission areas.

Publications, Presentations, and Patents

Tranquilli, P. et al., 2022. "Hierarchical, Multimodel, Multiscale Parallel-In-Time." Poster (https://meetings.aps.org/Meetings/DPP22/Session/TP11.112) American Physics Society Division of Plasma Physics, Spokane, WA. October 20, 2022.