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Fix placement of normalization factor. Fix link in depletion methods

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Paul Romano 2020-04-20 11:50:34 -05:00
parent ac8b5e574f
commit 17a3aadfa5
2 changed files with 12 additions and 11 deletions
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13
docs/source/methods/depletion.rst
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@ -132,9 +132,10 @@ more matrix exponentials. OpenMC uses the Chebyshev rational approximation
method (CRAM), which was introduced in a series of papers by Pusa (`1
<https://doi.org/10.13182/NSE09-14>`_, `2
<https://doi.org/10.13182/NSE10-81>`_), to evaluate matrix exponentials. In
particular, OpenMC utilizes an `incomplete partial fraction <cram_ipf>`_ (IPF)
form of CRAM that provides a good balance of numerical stability and efficiency.
In this representation the matrix exponential is approximated as
particular, OpenMC utilizes an `incomplete partial fraction
<https://doi.org/10.13182/NSE15-26>`_ (IPF) form of CRAM that provides a good
balance of numerical stability and efficiency. In this representation the matrix
exponential is approximated as
.. math::
@ -147,8 +148,8 @@ where :math:`k` is the order of the approximation and :math:`\alpha_0`,
have been tabulated for orders up to :math:`k=48`. Rather than computing the
full approximation and then multiplying it by a vector, the following algorithm
is used to incrementally apply the terms within the product (note that the
original description of the algorithm presented by `Pusa <cram_ipf>`_ contains a
typo):
original description of the algorithm presented by `Pusa
<https://doi.org/10.13182/NSE15-26>`_ contains a typo):
1. :math:`\mathbf{n} \gets \mathbf{n_0}`
2. For :math:`\ell = 1, 2, \dots, k/2`
@ -162,8 +163,6 @@ The :math:`k`\ th order approximation for CRAM requires solving :math:`k/2`
sparse linear systems. OpenMC relies on functionality from
:mod:`scipy.sparse.linalg` for solving the linear systems.
.. _cram_ipf: https://doi.org/10.13182/NSE15-26
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Data Considerations
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