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rad.txt
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"Return to Steve Plimpton's home page"_main.html :c
:line
Radiation Transport via the Discrete Ordinates form of the Boltzmann
equation :h3
The absorption, emission, and transport of radiative energy is an
important effect in many kinds of simulations. Two cases of interest
to Sandia are shown in these images -- simulating the effect of a fire
on a waste or weapon container in an accident scenario, and simulating
the implosion of a fuel pellet at the center of Sandia's Z-Pinch
machine which is a prototype device for producing energy from nuclear
fusion.
:c,image(images/rad_fire.gif)
:c,image(images/rad_zpinch.gif)
The radiation effects in these phenomena are described by the discrete
ordinates form of the Boltzman equation. When discretized for a finite
element grid, it describes the radiation flux of a particular energy
as it passes through a grid cell with accompanying absorption,
emission, and scattering. Including these effects is a large
computational task because the radiative flux is a 3 dimensional
quantity -- 2 angular directions and energy -- which must be solved
for in each grid cell of the normal fluid or shock hydrodynamics
model. This introduces as many as a few thousand extra unknowns per
grid cell to solve for at each timestep.
On an unstructured grid, one way to solve the Boltzmann equation is to
sweep the flux solution across the mesh in the direction of an
individual discretized ordinate (angle). As shown in this figure, that
gives rise to a directed graph where each vertex in the graph is a
grid cell in the mesh, and edges point in the downwind direction
between 2 adjacent grid cells.
:c,image(images/rad_mesh2graph.gif)
We've developed a parallel Boltzmann solver which allows multiple
angles to be swept simultaneously on a grid/graph that is distributed
across processors. This gives rise to an asynchronous parallel
algorithm where small messages are passed from one processor to
another as dependencies in the graphs are satisfied. The algorithm's
scalability and load-balance is a function of how the grid is
distributed across processors and the order in which work on each
processor is scheduled. We are currently working to determine what
options produce optimal parallel sweeping algorithms.
For deformed meshes such as those that occur in a Lagrangian
hydrodynamics code (e.g. for the Z-Pinch simulations), these sweeping
techinques also require that cycles in the directed graphs be detected
and eliminated. Finding cycles in distributed directed graphs is an
interesting algorithmic challenge that we have also been working on
recently with collaborators at Texas A&M University. One of the
papers below addresses this problem.
Collaborators on this project:
Bruce Hendrickson, Sandia
Kent Budge, Sandia
Shawn Burns, Sandia
Will McLendon, Texas A&M
Marv Adams, Texas A&M
Shawn Pautz, LANL
Randy Baker, LANL
Paul Nowak, LLNL :ul
:line
This paper overviews all of the parallel algorithms we developed, and
highlights their performance on 2 large parallel machines:
[Parallel Sn Sweeps on Unstructured Grids: Algorithms for
Prioritization, Grid Partitioning, and Cycle-Detection],
S. J. Plimpton, B. Hendrickson, S. Burns, W. Mclendon III, L.
Rauchwerger, Nuclear Science and Engineering, 150, 267-283 (2005).
("abstract"_art3)
:link(art3,abstracts/nse05.html)
This paper gives greater details about the parallel graph traversal
algorithms:
[Finding Strongly Connected Components in Distributed Graphs],
W. McLendon, B. Hendrickson, S. J. Plimpton, L. Rauchwerger, J
Parallel and Distributed Computing, 65, 901-910 (2005).
("abstract"_art4)
:link(art4,abstracts/jpdc05.html)
This is a paper with details of our initial parallel sweeping
algorithm for solving the Boltzmann equation and some performance
results on the Intel Tflops machine:
[Parallel Algorithms for Radiation Transport on Unstructured Grids],
S. J. Plimpton, B. A. Hendrickson, S. P. Burns, W. McLendon III, Proc
of SuperComputing 2000 (SC2000), Dallas, TX, November
2000. ("abstract"_abs1)
:link(abs1,abstracts/sc00.html)
This paper discusses out initial parallel algorithm for cycle
detection:
[Identifying Strongly Connected Components in Parallel], W. McLendon
III, B. Hendrickson, S. J. Plimpton, L. Rauchwerger, in Proc of SIAM
Parallel Processing for Scientific Computing Conf, March
2001. ("abstract"_abs2)
:link(abs2,abstracts/siam01a.html)