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\subsection{The \moc{bivact} dependent records on a
\dir{tracking} directory}\label{sect:bivactrackingdir}
When the \moc{BIVACT:} operator is used ($\mathsf{CDOOR}$={\tt 'BIVAC'}), the following elements in the vector
$\mathcal{S}^{t}_{i}$ will also be defined.
\begin{itemize}
\item $\mathcal{S}^{t}_{6}$: ({\tt ITYPE}) Type of BIVAC geometry:
\begin{displaymath}
\mathcal{S}^{t}_{6} = \left\{
\begin{array}{rl}
2 & \textrm{Cartesian 1-D geometry} \\
3 & \textrm{Tube 1-D geometry} \\
4 & \textrm{Spherical 1-D geometry} \\
5 & \textrm{Cartesian 2-D geometry} \\
6 & \textrm{Tube 2-D geometry} \\
8 & \textrm{Hexagonal 2-D geometry}
\end{array} \right.
\end{displaymath}
\item $\mathcal{S}^{t}_{7}$: ({\tt IHEX}) Type of hexagonal symmetry if $\mathcal{S}^{t}_{6}= 8$:
\begin{displaymath}
\mathcal{S}^{t}_{7} = \left\{
\begin{array}{rl}
0 & \textrm{non-hexagonal geometry} \\
1 & \textrm{S30} \\
2 & \textrm{SA60} \\
3 & \textrm{SB60} \\
4 & \textrm{S90} \\
5 & \textrm{R120} \\
6 & \textrm{R180} \\
7 & \textrm{SA180} \\
8 & \textrm{SB180} \\
9 & \textrm{COMPLETE}
\end{array} \right.
\end{displaymath}
\item $\mathcal{S}^{t}_{8}$: ({\tt IELEM}) Type of finite elements:
\begin{displaymath}
\mathcal{S}^{t}_{8} = \left\{
\begin{array}{rl}
<0 & \textrm{Order $-\mathcal{S}^{t}_{8}$ primal finite elements} \\
>0 & \textrm{Order $\mathcal{S}^{t}_{8}$ dual finite elements. The Thomas-Raviart or Thomas-Raviart-Schneider} \\
& \textrm{method is used except if $\mathcal{S}^{t}_{9}=4$ in which case a mesh-centered finite difference} \\
& \textrm{approximation is used}
\end{array} \right.
\end{displaymath}
\item $\mathcal{S}^{t}_{9}$: ({\tt ICOL}) Type of quadrature used to integrate
the mass matrix:
\begin{displaymath}
\mathcal{S}^{t}_{9} = \left\{
\begin{array}{rl}
1 & \textrm{Analytical integration} \\
2 & \textrm{Gauss-Lobatto quadrature (finite difference/collocation method)} \\
3 & \textrm{Gauss-Legendre quadrature (superconvergent approximation)} \\
4 & \textrm{mesh-centered finite difference approximation in hexagonal geometry}
\end{array} \right.
\end{displaymath}
\item $\mathcal{S}^{t}_{10}$: ({\tt ISPLH}) Type of hexagonal mesh splitting:
\begin{displaymath}
\mathcal{S}^{t}_{10} = \left\{
\begin{array}{rl}
1 & \textrm{No mesh splitting}; \emph{or} \\
& \textrm{$3$ lozenges per hexagon with Thomas-Raviart-Schneider approximation} \\
K & \textrm{$6\times(K-1)\times(K-1)$ triangles per hexagon with finite-difference approximations} \\
& \textrm{$3\times K \times K$ lozenges per hexagon with Thomas-Raviart-Schneider approximation}
\end{array} \right.
\end{displaymath}
\item $\mathcal{S}^{t}_{11}$: ({\tt LL4}) Order of the group-wise matrices.
Generally equal to
$\mathcal{S}^{t}_{2}$ except in cases where averaged fluxes are appended to the
unknown vector. $\mathcal{S}^{t}_{11}\le\mathcal{S}^{t}_{2}$.
\item $\mathcal{S}^{t}_{12}$: ({\tt LX}) Number of elements along the $X$ axis in Cartesian geometry or number of
hexagons.
\item $\mathcal{S}^{t}_{13}$: ({\tt LY}) Number of elements along the $Y$ axis.
\item $\mathcal{S}^{t}_{14}$: ({\tt NLF}) Number of components in the angular expansion of the flux. Must be a positive
even number. Set to zero for diffusion theory. Set to 2 for $P_1$ method.
\item $\mathcal{S}^{t}_{15}$: ({\tt ISPN}) Type of transport approximation if {\tt NLF}$\ne 0$:
\begin{displaymath}
\mathcal{S}^{t}_{15} = \left\{
\begin{array}{rl}
0 & \textrm{Complete $P_n$ approximation of order {\tt NLF}$-1$} \\
1 & \textrm{Simplified $P_n$ approximation of order {\tt NLF}$-1$}
\end{array} \right.
\end{displaymath}
\item $\mathcal{S}^{t}_{16}$: ({\tt ISCAT}) Number of terms in the scattering sources if {\tt NLF}$\ne 0$:
\begin{displaymath}
\mathcal{S}^{t}_{16} = \left\{
\begin{array}{rl}
1 & \textrm{Isotropic scattering in the laboratory system} \\
2 & \textrm{Linearly anisotropic scattering in the laboratory system} \\
$n$ & \textrm{order $n-1$ anisotropic scattering in the laboratory system}
\end{array} \right.
\end{displaymath}
\noindent A negative value of $\mathcal{S}^{t}_{16}$ indicates that $1/3D^{g}$ values are used as $\Sigma_1^{g}$ cross sections.
\item $\mathcal{S}^{t}_{17}$: ({\tt NVD}) Number of base points in the Gauss-Legendre quadrature used to integrate
void boundary conditions if {\tt ICOL} $=3$ and {\tt NLF}$\ne 0$:
\begin{displaymath}
\mathcal{S}^{t}_{17} = \left\{
\begin{array}{rl}
0 & \textrm{Use a ({\tt NLF}$+1$)--point quadrature consistent with $P_{{\rm NLF}-1}$ theory} \\
1 & \textrm{Use a {\tt NLF}--point quadrature consistent with $S_{\rm NLF}$ theory} \\
2 & \textrm{Use an analytical integration consistent with diffusion theory}
\end{array} \right.
\end{displaymath}
\end{itemize}
\goodbreak
The following records will also be present on the main level of a \dir{tracking}
directory.
\begin{DescriptionEnregistrement}{The \moc{bivact} records in
\dir{tracking}}{8.0cm}
\IntEnr
{NCODE\blank{7}}{$6$}
{Record containing the types of boundary conditions on each surface. =0 side
not used; =1 VOID; =2 REFL; =4 TRAN; =5 SYME; =7 ZERO. {\tt NOODE(5)} and
{\tt NOODE(6)} are not used.}
\RealEnr
{ZCODE\blank{7}}{$6$}{$1$}
{Record containing the albedo value (real number) on each surface. {\tt ZOODE(5)}
and {\tt ZOODE(6)} are not used.}
\OptRealEnr
{SIDE\blank{8}}{$1$}{$\mathcal{S}^{t}_{6}=8$}{cm}
{Side of a hexagon.}
\OptRealEnr
{XX\blank{10}}{$\mathcal{S}^{t}_{1}$}{$\mathcal{S}^{t}_{6}\ne 8$}{cm}
{Element-ordered $X$-directed mesh spacings after mesh-splitting for type 2
and 5 geometries. Element-ordered radius after mesh-splitting for type 3
and 6 geometries.}
\OptRealEnr
{YY\blank{10}}{$\mathcal{S}^{t}_{1}$}{$\mathcal{S}^{t}_{6}=5 \ {\rm or} \ 6$}{cm}
{Element-ordered $Y$-directed mesh spacings after mesh-splitting for type 5
and 6 geometries.}
\OptRealEnr
{DD\blank{10}}{$\mathcal{S}^{t}_{1}$}{$\mathcal{S}^{t}_{6}=3 \ {\rm or} \ 6$}{cm}
{Element-ordered position used with type 3 and 6 geometries.}
\IntEnr
{KN\blank{10}}{$N_{\rm kn}\times\mathcal{S}^{t}_{1}$}
{Element-ordered unknown list. $N_{\rm kn}$ is the number of unknowns per element.}
\RealEnr
{QFR\blank{9}}{$N_{\rm surf}\times\mathcal{S}^{t}_{1}$}{}
{Element-ordered boundary condition. $N_{\rm surf}=4$ in Cartesian geometry and $=6$ in hexagonal geometry.}
\IntEnr
{IQFR\blank{8}}{$N_{\rm surf}\times\mathcal{S}^{t}_{1}$}
{Element-ordered physical albedo indices. $N_{\rm surf}=4$ in Cartesian geometry and $=6$ in hexagonal geometry.}
\RealEnr
{BFR\blank{9}}{$N_{\rm surf}\times\mathcal{S}^{t}_{1}$}{}
{Element-ordered boundary surface fractions.}
\IntEnr
{MU\blank{10}}{$\mathcal{S}^{t}_{11}$}
{Indices used with compressed diagonal storage mode matrices.}
\OptIntEnr
{IPERT\blank{7}}{$\mathcal{S}^{t}_{12}\times (\mathcal{S}^{t}_{10})^2$}{*}
{Mixture permutation index. This information is provided if and only if $\mathcal{S}^{t}_{6}=8, \ \mathcal{S}^{t}_{8}>0 \ {\rm and} \
\mathcal{S}^{t}_{9}\le 3$.}
\DirEnr
{BIVCOL\blank{6}}
{Sub-directory containing the unit matrices (mass, stiffness, nodal coupling,
etc.) for a finite element discretization.}
\end{DescriptionEnregistrement}
\goodbreak
The following records will be present on the \moc{/BIVCOL/} sub-directory:
\begin{DescriptionEnregistrement}{Description of the \moc{/BIVCOL/} sub-directory}{8.0cm}
\RealEnr
{T\blank{11}}{$L$}{}
{Cartesian linear product vector. $L=|\mathcal{S}^{t}_{8}|+1$}
\RealEnr
{TS\blank{10}}{$L$}{}
{Cylindrical linear product vector.}
\RealEnr
{R\blank{11}}{$L\times L$}{}
{Cartesian mass matrix.}
\RealEnr
{RS\blank{10}}{$L\times L$}{}
{Cylindrical mass matrix.}
\RealEnr
{Q\blank{11}}{$L\times L$}{}
{Cartesian stiffness matrix.}
\RealEnr
{QS\blank{10}}{$L\times L$}{}
{Cylindrical stiffness matrix.}
\RealEnr
{V\blank{11}}{$L\times (L-1)$}{}
{Nodal coupling matrix.}
\RealEnr
{H\blank{11}}{$L\times (L-1)$}{}
{Piolat transform coupling matrix (used with Thomas-Raviart-Schneider method).}
\RealEnr
{E\blank{11}}{$L\times L$}{}
{Polynomial coefficients.}
\RealEnr
{RH\blank{10}}{6$\times$6}{}
{Hexagonal mass matrix.}
\RealEnr
{QH\blank{10}}{6$\times$6}{}
{Hexagonal stiffness matrix.}
\RealEnr
{RT\blank{10}}{3$\times$3}{}
{Triangular mass matrix.}
\RealEnr
{QT\blank{10}}{3$\times$3}{}
{Triangular stiffness matrix.}
\end{DescriptionEnregistrement}
\eject
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