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Mathematics Colloquium - Efficient Time-Integration Strategies for Non-hydrostatic Atmospheric Models

October 22, 2019 @ 4:00 pm - 5:00 pm MDT

Dr. Frank Giraldo
Professor of Applied Mathematics
Naval Postgraduate School
Oct. 22, 2019, 4:00-5:00pm, ILC 402

Efficient Time-Integration Strategies for Non-hydrostatic Atmospheric Models

The Non-hydrostatic Unified Model of the Atmosphere (NUMA) is a compressible Navier-Stokes solver that sits inside of the U.S. Navy’s NEPTUNE weather model based on high-order continuous and discontinuous Galerkin (CG/DG) methods.
Therefore, it is imperative that NUMA runs as efficiently as possible without sacrificing accuracy and conservation. One of the last places to squeeze out more performance is in the time-integration strategy used in the model. In this talk, I will review the various time-integration strategies currently available in NUMA such as: fully explicit methods with large
stability regions, fully implicit methods, implicit-explicit methods, and multirate methods. With multirate methods, the idea is to partition the processes with different speeds (or stiffness) in some hierarchical way in order to use time-steps commensurate with the wave speed of each process. However, to gain all the benefits of this approach requires fully embracing this idea at the code level which then means that the time-integrators and spatial discretization methods have to be fully aware of each other (complicates the code). In this talk, I will discuss our recent results on time-integrators and possible preconditioning strategies for the implicit solvers and our experience shows that IMEX time-integrators are only competitive with explicit time-integrators if and only if the Schur complement is used.


Dr. Frank Giraldo is professor of Applied Mathematics at the Naval Postgraduate School and director of the Center for Computational Mathematics. Dr. Giraldo serves on various national boards such as the National Earth Systems Prediction Capability (ESPC) High-Performance Computing Working Group and the National Unified Operational Prediction Capability (NUOPC) group. In addition, he serves on various panels such as the DOE’s E3SM review panel (past 5 years), and the DOE’s INCITE panel in Earth Sciences (for the past 4 years, having chaired the panel for the past two years). Dr. Giraldo also served on the Scientific Advisory Committee for the Korea Institute of Atmospheric Prediction System when it was first founded in 2011.

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