Developing A Large Time Step, Robust, and Low Communication MultiMoment PDE Integration Scheme for Exascale Applications
Abstract
The Boundary Averaged Multimoment Constrained finiteVolume (BAMCV) method is de rived, explained, and evaluated for 1D transport to assess accuracy, maximum stable time step (MSTS), oscillations for discontinuous data, and parallel communication burden. The BAMCV 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 highorder the scheme is, giving significantly larger time steps than Galerkin methods, for which the MSCFL decreases nearly quadratically with in creasing order. The BAMCV method is compared against a SE method at varying order, both using the ADERDT time discretization. BAMCV error for a sine wave was comparable to the same order of accuracy for a SE method. The resulting large time step, multimoment, low communication scheme is of great interest for exascale architectures.
 Authors:

 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:
 AC0500OR22725
 Resource Type:
 Conference
 Resource Relation:
 Journal Volume: 51; Conference: International Conference on Computational Science 2015  Reykjavik, , Iceland  6/1/2015 8:00:00 AM6/3/2015 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 MultiMoment 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 MultiMoment 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 MultiMoment 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 MultiMoment PDE Integration Scheme for Exascale Applications},
author = {Norman, Matthew R.},
abstractNote = {The Boundary Averaged Multimoment Constrained finiteVolume (BAMCV) method is de rived, explained, and evaluated for 1D transport to assess accuracy, maximum stable time step (MSTS), oscillations for discontinuous data, and parallel communication burden. The BAMCV 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 highorder the scheme is, giving significantly larger time steps than Galerkin methods, for which the MSCFL decreases nearly quadratically with in creasing order. The BAMCV method is compared against a SE method at varying order, both using the ADERDT time discretization. BAMCV error for a sine wave was comparable to the same order of accuracy for a SE method. The resulting large time step, multimoment, low communication scheme is of great interest for exascale architectures.},
doi = {10.1016/j.procs.2015.05.413},
journal = {},
issn = {18770509},
number = ,
volume = 51,
place = {United States},
year = {2015},
month = {6}
}