Publication Date

Summer 7-15-2024

Abstract

Despite the fact that Parallel-in-Time (PinT) methods are predicted to become necessary to fully utilize next-generation exa- and zettascale machines, there are currently no known practical methods which scale well with the length of the time-domain for chaotic problems, due to exponential dependence of the condition number on the fastest chaotic timescale. I present modifications to the coarse-grid equations along with a novel rediscretization approach which together greatly improve convergence of the multigrid reduction in time (MGRIT) algorithm and allow the first known PinT speedup for a chaotic PDE. The novel Local Shadowing Relaxation (LSR) is presented as an alternative to classical FCF-relaxation for MGRIT and demonstrated to be a convergent, PinT smoother for chaotic PDE systems. Promising preliminary analytical results and numerical experiments with the Lorenz system indicate that LSR may solve the scaling problem for chaotic systems, potentially allowing space-time parallelization of turbulent computational fluid dynamics.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Jacob B. Schroder

Second Committee Member

Jehanzeb Chaudhary

Third Committee Member

Amanda Bienz

Fourth Committee Member

Stefanie Guenther

Project Sponsors

Funded by the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344

Language

English

Keywords

chaos, parallel-in-time, MGRIT, multigrid, dynamical systems

Document Type

Dissertation

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