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Update documentation to reflect no use of union energy grid.

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Paul Romano 2014-10-25 13:46:58 -04:00
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docs/source/methods/cross_sections.rst
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@ -47,45 +47,30 @@ there would be for burnup calculations. Thus, there is a strong motive to
implement a method of reducing the number of energy grid searches in order to
speed up the calculation.
Unionized Energy Grid
---------------------
-------------------
Logarithmic Mapping
-------------------
The most naïve method to reduce the number of energy grid searches is to
construct a new energy grid that consists of the union of the energy points of
each nuclide and use this energy grid for all nuclides. This method is
computationally very efficient as it only requires one energy grid search at
each collision as well as one interpolation between cross section values since
the interpolation factor can be used for all nuclides. However, it requires
redundant storage of cross section values at points which were added to each
nuclide grid. This additional burden on memory storage can become quite
prohibitive. To lessen that burden, the unionized energy grid can be thinned
with cross sections reconstructed on the thinned energy grid. This method is
currently used by default in the Serpent Monte Carlo code.
To speed up energy grid searches, OpenMC uses logarithmic mapping technique
[Brown]_ to limit the range of energies that must be searched for each
nuclide. The entire energy range is divided up into equal-lethargy segments, and
the bounding energies of each segment are mapped to bounding indices on each of
the nuclide energy grids. By default, OpenMC uses 8000 equal-lethargy segments
as recommended by Brown.
Unionized Energy Grid with Nuclide Pointers
-------------------------------------------
-------------
Other Methods
-------------
While having a unionized grid that is used for all nuclides allows for very fast
lookup of cross sections, the burden on memory is in many circumstances
unacceptable. The OpenMC Monte Carlo code utilizes a method that allows for a
single energy grid search to be performed at every collision while avoiding the
redundant storage of cross section values. Instead of using the unionized grid
for every nuclide, the original energy grid of each nuclide is kept and a list
of pointers (of the same length as the unionized energy grid) is constructed for
each nuclide that gives the corresponding grid index on the nuclide grid for a
given grid index on the unionized grid. One must still interpolate on cross
section values for each nuclide since the interpolation factors will generally
be different. The figure below illustrates this method. All values within the
dashed box would need to be stored on a per-nuclide basis, and the union grid
would need to be stored once. This method is also referred to as *double
indexing* and is available as an option in Serpent (see paper by Leppanen_).
A good survey of other energy grid techniques, including unionized energy grids,
can be found in a paper by Leppanen_.
.. figure:: ../_images/uniongrid.*
:width: 600px
:align: center
:figclass: align-center
----------
References
----------
Mapping of union energy grid to nuclide energy grid through pointers.
.. [Brown] Forrest B. Brown, "New Hash-based Energy Lookup Algorithm for Monte
Carlo codes," LA-UR-14-24530, Los Alamos National Laboratory (2014).
.. _MCNP: http://mcnp.lanl.gov
.. _Serpent: http://montecarlo.vtt.fi