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Title: Developing A Large Time Step, Robust, and Low Communication Multi-Moment PDE Integration Scheme for Exascale Applications

Abstract

The Boundary Averaged Multi-moment Constrained finite-Volume (BA-MCV) method is de- rived, explained, and evaluated for 1-D transport to assess accuracy, maximum stable time step (MSTS), oscillations for discontinuous data, and parallel communication burden. The BA-MCV scheme is altered from the original MCV scheme to compute the updates of point wise cell boundary derivatives entirely locally. Then it is altered such that boundary moments are replaced with the interface upwind value. The scheme is stable at a maximum stable CFL (MSCFL) value of one no matter how high-order the scheme is, giving significantly larger time steps than Galerkin methods, for which the MSCFL decreases nearly quadratically with in- creasing order. The BA-MCV method is compared against a SE method at varying order, both using the ADER-DT time discretization. BA-MCV error for a sine wave was comparable to the same order of accuracy for a SE method. The resulting large time step, multi-moment, low communication scheme is of great interest for exascale architectures.

Authors:
ORCiD logo [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1462911
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Journal Volume: 51; Conference: International Conference on Computational Science 2015 - Reykjavik, , Iceland - 6/1/2015 8:00:00 AM-6/3/2015 8:00:00 AM
Country of Publication:
United States
Language:
English

Citation Formats

Norman, Matthew R. Developing A Large Time Step, Robust, and Low Communication Multi-Moment PDE Integration Scheme for Exascale Applications. United States: N. p., 2015. Web. doi:10.1016/j.procs.2015.05.413.
Norman, Matthew R. Developing A Large Time Step, Robust, and Low Communication Multi-Moment PDE Integration Scheme for Exascale Applications. United States. doi:10.1016/j.procs.2015.05.413.
Norman, Matthew R. Mon . "Developing A Large Time Step, Robust, and Low Communication Multi-Moment PDE Integration Scheme for Exascale Applications". United States. doi:10.1016/j.procs.2015.05.413. https://www.osti.gov/servlets/purl/1462911.
@article{osti_1462911,
title = {Developing A Large Time Step, Robust, and Low Communication Multi-Moment PDE Integration Scheme for Exascale Applications},
author = {Norman, Matthew R.},
abstractNote = {The Boundary Averaged Multi-moment Constrained finite-Volume (BA-MCV) method is de- rived, explained, and evaluated for 1-D transport to assess accuracy, maximum stable time step (MSTS), oscillations for discontinuous data, and parallel communication burden. The BA-MCV scheme is altered from the original MCV scheme to compute the updates of point wise cell boundary derivatives entirely locally. Then it is altered such that boundary moments are replaced with the interface upwind value. The scheme is stable at a maximum stable CFL (MSCFL) value of one no matter how high-order the scheme is, giving significantly larger time steps than Galerkin methods, for which the MSCFL decreases nearly quadratically with in- creasing order. The BA-MCV method is compared against a SE method at varying order, both using the ADER-DT time discretization. BA-MCV error for a sine wave was comparable to the same order of accuracy for a SE method. The resulting large time step, multi-moment, low communication scheme is of great interest for exascale architectures.},
doi = {10.1016/j.procs.2015.05.413},
journal = {},
issn = {1877-0509},
number = ,
volume = 51,
place = {United States},
year = {2015},
month = {6}
}

Conference:
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