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diff --git a/doc/IGE351/SectDtrivac.tex b/doc/IGE351/SectDtrivac.tex new file mode 100644 index 0000000..41667db --- /dev/null +++ b/doc/IGE351/SectDtrivac.tex @@ -0,0 +1,469 @@ +\subsection{The \moc{trivat} dependent records on a +\dir{tracking} directory}\label{sect:trivatrackingdir} + +A TRIVAC--type tracking data structure is holding the information related to +the ADI partitionning of the system matrices in 1D, 2D or 3D. A one-speed +discretization of the diffusion equation leads to a matrix system of the form + +\begin{equation} +\bf{A} \ \vec\Phi = \vec S +\label{eq:tratr1} +\end{equation} + +\noindent where $\Phi$ may contains different types of unknowns: flux values, +current values, polynomial coefficients, etc. + +\vskip 0.2cm + +The matrix $\bf{A}$ can be splitted in different ways. Many TRIVAC discretizations in +Cartesian geometry are based on the following ADI splitting: + +\begin{equation} +\bf{A} = \bf{U} + \bf{P}_x\bf{X}\bf{P}_x^\top + \bf{P}_y\bf{Y}\bf{P}_y^\top + \bf{P}_z\bf{Z}\bf{P}_z^\top +\label{eq:tratr2} +\end{equation} + +\noindent where + +\begin{tabular}{rl} +$\bf{U}=$ & matrix containing the diagonal elements of $\bf{A}$\\ +$\bf{X},\bf{Y},\bf{Z}=$ & symetrical matrices containing the nondiagonal elements of $\bf{A}$\\ +$\bf{P}_x,\bf{P}_y,\bf{P}_z=$ & permutation matrices that ensure a minimum bandwidth for matrices $\bf{X}$, $\bf{Y}$ and $\bf{Z}$.\\ +\end{tabular} + +\vskip 0.2cm + +Similarly, many discretizations in hexagonal geometry are based on the following ADI splitting: +\begin{equation} +\bf{A} = \bf{U} + \bf{P_w}\bf{W}\bf{P}_w^\top + \bf{P}_x\bf{X}\bf{P}_x^\top + \bf{P}_y\bf{Y}\bf{P}_y^\top + \bf{P}_z\bf{Z}\bf{P}_z^\top \ \ \ . +\label{eq:tratr3} +\end{equation} + +The diffusion equation can also be solved using a Thomas-Raviart polynomial basis together with a mixte-dual +variational formulation. In this case, the following splitting will be used in Cartesian geometry: + +\begin{equation} +\bf{A} = \left(\matrix{\bf{A}_x & \bf{0} & \bf{0} & -\bf{R}_x \cr + \bf{0} & \bf{A}_y & \bf{0} & -\bf{R}_y \cr + \bf{0} & \bf{0} & \bf{A}_z & -\bf{R}_z \cr + -\bf{R}_x^\top & -\bf{R}_y^\top & -\bf{R}_z^\top & -\bf{T} \cr}\right) +\label{eq:tratr4} +\end{equation} + +\vskip 0.2cm + +Similarly, we use the following ADI splitting in hexagonal geometry: + +\begin{equation} +\bf{A} = \left(\matrix{\bf{A}_w & \bf{C}_{xw}^\top & \bf{C}_{wy} &\bf{0} & -\bf{R}_w \cr + \bf{C}_{xw} & \bf{A}_x & \bf{C}_{yx}^\top & \bf{0} & -\bf{R}_x \cr + \bf{C}_{wy}^\top & \bf{C}_{yx} & \bf{A}_y & \bf{0} & -\bf{R}_y \cr + \bf{0} & \bf{0} & \bf{0} & \bf{A}_z & -\bf{R}_z \cr + -\bf{R}_w^\top & -\bf{R}_x^\top & -\bf{R}_y^\top & -\bf{R}_z^\top & -\bf{T} \cr}\right) +\label{eq:tratr5} +\end{equation} + +\vskip 0.2cm + +When the \moc{TRIVAT:} operator is used ($\mathsf{CDOOR}$={\tt 'TRIVAC'}), 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 TRIVAC geometry: +\begin{displaymath} +\mathcal{S}^{t}_{6} = \left\{ +\begin{array}{rl} + 2 & \textrm{Cartesian 1-D geometry} \\ + 3 & \textrm{Tube 1-D geometry} \\ + 5 & \textrm{Cartesian 2-D geometry} \\ + 6 & \textrm{Tube 2-D geometry} \\ + 7 & \textrm{Cartesian 3-D geometry} \\ + 8 & \textrm{Hexagonal 2-D geometry} \\ + 9 & \textrm{Hexagonal 3-D geometry} +\end{array} \right. +\end{displaymath} + +\item $\mathcal{S}^{t}_{7}$: ({\tt IHEX}) Type of hexagonal symmetry if $\mathcal{S}^{t}_{6}\ge 8$: +\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 IDIAG}) Diagonal symmetry flag if $\mathcal{S}^{t}_{6}=5$ or $=7$. +$\mathcal{S}^{t}_{8}=1$ if diagonal symmetry is present. + +\item $\mathcal{S}^{t}_{9}$: ({\tt IELEM}) Type of finite elements: +\begin{displaymath} +\mathcal{S}^{t}_{9} = \left\{ +\begin{array}{rl} + <0 & \textrm{Order $-\mathcal{S}^{t}_{9}$ primal finite elements} \\ + >0 & \textrm{Order $\mathcal{S}^{t}_{9}$ dual finite elements} +\end{array} \right. +\end{displaymath} + +\item $\mathcal{S}^{t}_{10}$: ({\tt ICOL}) Type of quadrature used to integrate +the mass matrix: +\begin{displaymath} +\mathcal{S}^{t}_{10} = \left\{ +\begin{array}{rl} + 1 & \textrm{Analytical integration} \\ + 2 & \textrm{Gauss-Lobatto quadrature (finite difference/collocation method)} \\ + 3 & \textrm{Gauss-Legendre quadrature (superconvergent 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 ICHX}) Type of discretization algorithm: +\begin{displaymath} +\mathcal{S}^{t}_{12} = \left\{ +\begin{array}{rl} + 1 & \textrm{Variational collocation method (mesh-corner finite differences or primal finite} \\ + & \textrm{elements with Gauss-Lobatto quadrature). \Eq{tratr2} or \Eq{tratr3} is used.} \\ + 2 & \textrm{Dual finite element approximation (Thomas-Raviart or Thomas-Raviart-Schneider} \\ + & \textrm{polynomial basis). \Eq{tratr4} or \Eq{tratr5} is used.} \\ + 3 & \textrm{Nodal collocation method with full tensorial products (mesh-centered finite} \\ + & \textrm{differences or dual finite elements with Gauss-Lobatto quadrature). \Eq{tratr2} or} \\ + & \textrm{\Eq{tratr3} is used.} \\ + 4 & \textrm{Coarse mesh finite differences (CMFD) method.} \\ + 5 & \textrm{Nodal expansion method (NEM).} \\ + 6 & \textrm{Analytic nodal method (ANM).} +\end{array} \right. +\end{displaymath} + +\item $\mathcal{S}^{t}_{13}$: ({\tt ISPLH}) Type of hexagonal mesh splitting if $\mathcal{S}^{t}_{6}\ge 8$: +\begin{displaymath} +\mathcal{S}^{t}_{13} = \left\{ +\begin{array}{rl} + 1 & \textrm{No mesh splitting (full hexagons)}; \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 $\mathcal{S}^{t}_{14}$: ({\tt LX}) Number of elements along the $X$ axis in Cartesian geometry or number of +hexagons in one axial plane. + +\item $\mathcal{S}^{t}_{15}$: ({\tt LY}) Number of elements along the $Y$ axis. + +\item $\mathcal{S}^{t}_{16}$: ({\tt LZ}) Number of elements along the $Z$ axis. + +\item $\mathcal{S}^{t}_{17}$: ({\tt ISEG}) Number of components in a vector +register (used +for supervectorial operations). Equal to zero for operations in scalar mode. + +\item $\mathcal{S}^{t}_{18}$: ({\tt IMPV}) Print parameter for supervectorial operations. + +\item $\mathcal{S}^{t}_{19}$: ({\tt LTSW}) Maximum bandwidth for supervectorial operations ($=2$ for +tridiagonal matrices). + +\item $\mathcal{S}^{t}_{20}$: ({\tt LONW}) number of groups of linear systems for matrices +$\bf{W}+\bf{P}_w^\top \bf{U}\bf{P}_w$ or $\bf{A}_w+\bf{R}_w\bf{T}^{-1}\bf{R}_w^\top$ (used +for supervectorial operations) + +\item $\mathcal{S}^{t}_{21}$: ({\tt LONX}) number of groups of linear systems for matrices +$\bf{X}+\bf{P}_x^\top \bf{U}\bf{P}_x$ or $\bf{A}_x+\bf{R}_x\bf{T}^{-1}\bf{R}_x^\top$ (used +for supervectorial operations) + +\item $\mathcal{S}^{t}_{22}$: ({\tt LONY}) number of groups of linear systems for matrices +$\bf{Y}+\bf{P}_y^\top \bf{U}\bf{P}_y$ or $\bf{A}_y+\bf{R}_y\bf{T}^{-1}\bf{R}_y^\top$ (used +for supervectorial operations) + +\item $\mathcal{S}^{t}_{23}$: ({\tt LONZ}) number of groups of linear systems for matrices +$\bf{Z}+\bf{P}_z^\top \bf{U}\bf{P}_z$ or $\bf{A}_z+\bf{R}_z\bf{T}^{-1}\bf{R}_z^\top$ (used +for supervectorial operations) + +\item $\mathcal{S}^{t}_{24}$: ({\tt NR0}) Number of radii used with the cylindrical correction +algorithm for the albedos. Equal to zero if no cylindrical correction is applied. + +\item $\mathcal{S}^{t}_{25}$: ({\tt LL4F}) Order of matrices $\bf{T}$ if $\mathcal{S}^{t}_{12}=2$ or number of average flux components if $\mathcal{S}^{t}_{12}=4$ + +\item $\mathcal{S}^{t}_{26}$: ({\tt LL4W}) Order of matrices $\bf{A_w}$ if $\mathcal{S}^{t}_{12}=2$ + +\item $\mathcal{S}^{t}_{27}$: ({\tt LL4X}) Order of matrices $\bf{A_x}$ if $\mathcal{S}^{t}_{12}=2$ or number of $X-$directed net current components if $\mathcal{S}^{t}_{12}=4$ + +\item $\mathcal{S}^{t}_{28}$: ({\tt LL4Y}) Order of matrices $\bf{A_y}$ if $\mathcal{S}^{t}_{12}=2$ or number of $Y-$directed net current components if $\mathcal{S}^{t}_{12}=4$ + +\item $\mathcal{S}^{t}_{29}$: ({\tt LL4Z}) Order of matrices $\bf{A_z}$ if $\mathcal{S}^{t}_{12}=2$ or number of $Z-$directed net current components if $\mathcal{S}^{t}_{12}=4$ + +\item $\mathcal{S}^{t}_{30}$: ({\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 $\mathcal{S}^{t}_{31}$: ({\tt ISPN}) Type of transport approximation if {\tt NLF}$\ne 0$: +\begin{displaymath} +\mathcal{S}^{t}_{31} = \left\{ +\begin{array}{rl} + 0 & \textrm{Complete $P_n$ approximation of order {\tt NLF}$-1$ (currently not available)}\\ + 1 & \textrm{Simplified $P_n$ approximation of order {\tt NLF}$-1$} +\end{array} \right. +\end{displaymath} + +\item $\mathcal{S}^{t}_{32}$: ({\tt ISCAT}) Number of terms in the scattering sources if {\tt NLF}$\ne 0$: +\begin{displaymath} +\mathcal{S}^{t}_{32} = \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 $\mathcal{S}^{t}_{32}$ indicates that $1/3D^{g}$ values are used as $\Sigma_1^{g}$ cross sections. + +\item $\mathcal{S}^{t}_{33}$: ({\tt NADI}) Number of ADI iterations at the inner +iterative level. + +\item $\mathcal{S}^{t}_{34}$: ({\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}_{34} = \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} + +\item $\mathcal{S}^{t}_{39}$: ({\tt IGMAX}) Hyperbolic nodal expansion functions are used in energy groups indices $\ge$ {\tt IGMAX}. +\end{itemize} + +The following records will also be present on the main level of a \dir{tracking} directory. + +\clearpage + +\begin{DescriptionEnregistrement}{The \moc{trivat} 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; =8 CYLI.} +\RealEnr + {ZCODE\blank{7}}{$6$}{$1$} + {Record containing the albedo value (real number) on each surface.} +\OptRealEnr + {SIDE\blank{8}}{$1$}{$\mathcal{S}^{t}_{6}\ge 8$}{cm} + {Side of a hexagon.} +\OptRealEnr + {XX\blank{10}}{$\mathcal{S}^{t}_{1}$}{$\mathcal{S}^{t}_{6}<8$}{cm} + {Element-ordered $X$-directed mesh spacings after mesh-splitting for type 2, 5 + or 7 geometries. Element-ordered radius after mesh-splitting for type 3 + or 6 geometries.} +\OptRealEnr + {YY\blank{10}}{$\mathcal{S}^{t}_{1}$}{$\mathcal{S}^{t}_{6}=5, \ 6 \ {\rm or} \ 7$}{cm} + {Element-ordered $Y$-directed mesh spacings after mesh-splitting for type 5, 6 + or 7 geometries.} +\OptRealEnr + {ZZ\blank{10}}{$\mathcal{S}^{t}_{1}$}{$\mathcal{S}^{t}_{6}=7 \ {\rm or} \ 9$}{cm} + {Element-ordered $Y$-directed mesh spacings after mesh-splitting for type 7 + or 9 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 cylindrical 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. $N_{\rm surf}=6$ in Cartesian geometry and $=8$ in hexagonal geometry.} +\IntEnr + {IQFR\blank{8}}{$N_{\rm surf}\times\mathcal{S}^{t}_{1}$} + {Element-ordered physical albedo indices. $N_{\rm surf}=6$ in Cartesian geometry and $=8$ in hexagonal geometry.} +\OptIntEnr + {MUW\blank{9}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{26}$}{$\mathcal{S}^{t}_{6}\ge 8$} + {Indices used with compressed diagonal storage mode matrices $\bf{W}+\bf{P}_w^\top \bf{U}\bf{P}_w$ or $\bf{A}_w+\bf{R}_w\bf{T}^{-1}\bf{R}_w^\top$.} +\OptIntEnr + {IPW\blank{9}}{$\mathcal{S}^{t}_{11}$}{$\mathcal{S}^{t}_{6}\ge 8$} + {Permutation vector ensuring minimum bandwidth for matrices $\bf{W}+\bf{P}_w^\top \bf{U}\bf{P}_w$ or $\bf{A}_w+\bf{R}_w\bf{T}^{-1}\bf{R}_w^\top$.} +\OptIntEnr + {MUX\blank{9}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{27}$}{$\mathcal{S}^{t}_{8}=0$} + {Indices used with compressed diagonal storage mode matrices $\bf{X}+\bf{P}_x^\top \bf{U}\bf{P}_x$ or $\bf{A}_x+\bf{R}_x\bf{T}^{-1}\bf{R}_x^\top$.} +\IntEnr + {IPX\blank{9}}{$\mathcal{S}^{t}_{11}$} + {Permutation vector ensuring minimum bandwidth for matrices $\bf{X}+\bf{P}_x^\top \bf{U}\bf{P}_x$ or $\bf{A}_x+\bf{R}_x\bf{T}^{-1}\bf{R}_x^\top$.} +\OptIntEnr + {MUY\blank{9}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{28}$}{$\mathcal{S}^{t}_{6}\ge 5$} + {Indices used with compressed diagonal storage mode matrices $\bf{Y}+\bf{P}_y^\top \bf{U}\bf{P}_y$ or $\bf{A}_y+\bf{R}_y\bf{T}^{-1}\bf{R}_y^\top$.} +\OptIntEnr + {IPY\blank{9}}{$\mathcal{S}^{t}_{11}$}{$\mathcal{S}^{t}_{6}\ge 5$} + {Permutation vector ensuring minimum bandwidth for matrices $\bf{Y}+\bf{P}_y^\top \bf{U}\bf{P}_y$ or $\bf{A}_y+\bf{R}_y\bf{T}^{-1}\bf{R}_y^\top$.} +\OptIntEnr + {MUZ\blank{9}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{29}$}{$\mathcal{S}^{t}_{6}=7$ or $9$} + {Indices used with compressed diagonal storage mode matrices $\bf{Z}+\bf{P}_z^\top \bf{U}\bf{P}_z$ or $\bf{A}_z+\bf{R}_z\bf{T}^{-1}\bf{R}_z^\top$.} +\end{DescriptionEnregistrement} + +\begin{DescriptionEnregistrement}{The \moc{trivat} records in \dir{tracking} (contd.)}{8.0cm} +\OptIntEnr + {IPZ\blank{9}}{$\mathcal{S}^{t}_{11}$}{$\mathcal{S}^{t}_{6}=7$ or $9$} + {Permutation vector ensuring minimum bandwidth for matrices $\bf{Z}+\bf{P}_z^\top \bf{U}\bf{P}_z$ or $\bf{A}_z+\bf{R}_z\bf{T}^{-1}\bf{R}_z^\top$.} +\DirEnr + {BIVCOL\blank{6}} + {Sub-directory containing the unit matrices (mass, stiffness, nodal coupling, + etc.) for a finite element discretization. + The specification of this directory is given in \Sect{bivactrackingdir}} +\end{DescriptionEnregistrement} + +The following records will also be present on the main level of a \dir{tracking} +directory in cases where a nodal method is used ($\mathcal{S}^{t}_{12}\ge 4$): + +\begin{DescriptionEnregistrement}{The \moc{trivat} records in \dir{tracking} (contd.)}{8.0cm} +\OptRealEnr + {XXX\blank{9}}{$\mathcal{S}^{t}_{14}+1$}{$\mathcal{S}^{t}_{12}=6$}{cm} + {The $x-$directed mesh position $X_{i}$} +\OptRealEnr + {YYY\blank{9}}{$\mathcal{S}^{t}_{15}+1$}{$\mathcal{S}^{t}_{12}=6$ and $\mathcal{S}^{t}_{6}\ge 5$}{cm} + {The $y-$directed mesh position $Y_{i}$} +\OptRealEnr + {ZZZ\blank{9}}{$\mathcal{S}^{t}_{16}+1$}{$\mathcal{S}^{t}_{12}=6$ and $\mathcal{S}^{t}_{6}=7$}{cm} + {The $z-$directed mesh position $Z_{i}$} +\OptIntEnr + {IMAX\blank{8}}{$\mathcal{S}^{t}_{25}$}{$\mathcal{S}^{t}_{12}=6$} + {$X-$oriented position of each first non-zero column element.} +\OptIntEnr + {IMAY\blank{8}}{$\mathcal{S}^{t}_{25}$}{$\mathcal{S}^{t}_{12}=6$ and $\mathcal{S}^{t}_{6}\ge 5$} + {$Y-$oriented position of each first non-zero column element.} +\OptIntEnr + {IMAZ\blank{8}}{$\mathcal{S}^{t}_{25}$}{$\mathcal{S}^{t}_{12}=6$ and $\mathcal{S}^{t}_{6}=7$} + {$Z-$oriented position of each first non-zero column element.} +\end{DescriptionEnregistrement} + +The following records will also be present on the main level of a \dir{tracking} +directory in cases where a Thomas-Raviart or Thomas-Raviart-Schneider polynomial basis is used ($\mathcal{S}^{t}_{12}=2$): + +\begin{DescriptionEnregistrement}{The \moc{trivat} records in +\dir{tracking} (contd.)}{8.0cm} +\OptIntEnr + {IPF\blank{9}}{$\mathcal{S}^{t}_{25}$}{$\mathcal{S}^{t}_{25}\ne 0$} + {Localization vector for flux values in unknown vector.} +\OptIntEnr + {IPBBW\blank{7}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{26}$}{$\mathcal{S}^{t}_{26}\ne 0$} + {Perdue sparse storage indices for matrices $\bf{R}_w$.} +\OptIntEnr + {IPBBX\blank{7}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{27}$}{$\mathcal{S}^{t}_{27}\ne 0$} + {Perdue sparse storage indices for matrices $\bf{R}_x$.} +\OptIntEnr + {IPBBY\blank{7}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{28}$}{$\mathcal{S}^{t}_{28}\ne 0$} + {Perdue sparse storage indices for matrices $\bf{R}_y$.} +\OptIntEnr + {IPBBZ\blank{7}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{29}$}{$\mathcal{S}^{t}_{29}\ne 0$} + {Perdue sparse storage indices for matrices $\bf{R}_z$.} +\OptRealEnr + {WB\blank{10}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{26}$}{$\mathcal{S}^{t}_{26}\ne 0$}{~} + {Matrix component $\bf{R}_w$ in Perdue sparse storage mode.} +\OptRealEnr + {XB\blank{10}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{27}$}{$\mathcal{S}^{t}_{27}\ne 0$}{~} + {Matrix component $\bf{R}_x$ in Perdue sparse storage mode.} +\OptRealEnr + {YB\blank{10}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{28}$}{$\mathcal{S}^{t}_{28}\ne 0$}{~} + {Matrix component $\bf{R}_y$ in Perdue sparse storage mode.} +\OptRealEnr + {ZB\blank{10}}{$2 \, \mathcal{S}^{t}_{9} \times \mathcal{S}^{t}_{29}$}{$\mathcal{S}^{t}_{29}\ne 0$}{~} + {Matrix component $\bf{R}_z$ in Perdue sparse storage mode.} +\OptIntEnr + {IPERT\blank{7}}{$N_{\rm los}$}{$\mathcal{S}^{t}_{6}\ge 8$} + {Mixture permutation index. $N_{\rm los}=\mathcal{S}^{t}_{14}\times \mathcal{S}^{t}_{15}\times (\mathcal{S}^{t}_{13})^2$} +\OptDbleEnr + {CTRAN\blank{7}}{$N_{\rm pio}\times N_{\rm pio}$}{$\mathcal{S}^{t}_{6}\ge 8$}{~} + {Piolat current coupling matrix. $N_{\rm pio}=(\mathcal{S}^{t}_{9}+1)\times \mathcal{S}^{t}_{9}$} +\OptRealEnr + {FRZ\blank{9}}{$\mathcal{S}^{t}_{16}$}{$\mathcal{S}^{t}_{6}\ge 8$}{~} + {Volume fractions related to the SYME boundary condition in $Z$.} +\end{DescriptionEnregistrement} + +The following records will also be present on the main level of a \dir{tracking} +directory in cases where supervectorial operations are used ($\mathcal{S}^{t}_{17}\ne 0$): + +\begin{DescriptionEnregistrement}{The \moc{trivat} records in +\dir{tracking} (contd.)}{8.0cm} +\IntEnr + {LL4VW\blank{7}}{$1$} + {Order of a reordered $W-$matrix, including supervectorial fill-in. Multiple of $\mathcal{S}^{t}_{17}$} +\IntEnr + {LL4VX\blank{7}}{$1$} + {Order of a reordered $X-$matrix, including supervectorial fill-in. Multiple of $\mathcal{S}^{t}_{17}$} +\IntEnr + {LL4VY\blank{7}}{$1$} + {Order of a reordered $Y-$matrix, including supervectorial fill-in. Multiple of $\mathcal{S}^{t}_{17}$} +\IntEnr + {LL4VZ\blank{7}}{$1$} + {Order of a reordered $Z-$matrix, including supervectorial fill-in. Multiple of $\mathcal{S}^{t}_{17}$} +\OptIntEnr + {NBLW\blank{8}}{$\mathcal{S}^{t}_{20}$}{$\mathcal{S}^{t}_{20}\ne 0$} + {Number of linear systems per supervector group for $W-$matrices} +\OptIntEnr + {NBLX\blank{8}}{$\mathcal{S}^{t}_{21}$}{$\mathcal{S}^{t}_{21}\ne 0$} + {Number of linear systems per supervector group for $X-$matrices} +\OptIntEnr + {NBLY\blank{8}}{$\mathcal{S}^{t}_{22}$}{$\mathcal{S}^{t}_{22}\ne 0$} + {Number of linear systems per supervector group for $Y-$matrices} +\OptIntEnr + {NBLZ\blank{8}}{$\mathcal{S}^{t}_{23}$}{$\mathcal{S}^{t}_{23}\ne 0$} + {Number of linear systems per supervector group for $Z-$matrices} +\OptIntEnr + {LBLW\blank{8}}{$\mathcal{S}^{t}_{20}$}{$\mathcal{S}^{t}_{20}\ne 0$} + {Number of unknowns per supervector group for $W-$matrices} +\OptIntEnr + {LBLX\blank{8}}{$\mathcal{S}^{t}_{21}$}{$\mathcal{S}^{t}_{21}\ne 0$} + {Number of unknowns per supervector group for $X-$matrices} +\OptIntEnr + {LBLY\blank{8}}{$\mathcal{S}^{t}_{22}$}{$\mathcal{S}^{t}_{22}\ne 0$} + {Number of unknowns per supervector group for $Y-$matrices} +\OptIntEnr + {LBLZ\blank{8}}{$\mathcal{S}^{t}_{23}$}{$\mathcal{S}^{t}_{23}\ne 0$} + {Number of unknowns per supervector group for $Z-$matrices} +\OptIntEnr + {MUVW\blank{8}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{26}$}{$\mathcal{S}^{t}_{6}\ge 8$} + {Indices used with $W-$directed compressed diagonal storage mode matrices in supervector mode} +\OptIntEnr + {MUVX\blank{8}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{27}$}{$\mathcal{S}^{t}_{8}=0$} + {Indices used with $X-$directed compressed diagonal storage mode matrices in supervector mode} +\OptIntEnr + {MUVY\blank{8}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{28}$}{$\mathcal{S}^{t}_{6}\ge 5$} + {Indices used with $Y-$directed compressed diagonal storage mode matrices in supervector mode} +\OptIntEnr + {MUVZ\blank{8}}{$\mathcal{S}^{t}_{11}$ or $\mathcal{S}^{t}_{29}$}{$\mathcal{S}^{t}_{6}=7$ or $9$} + {Indices used with $Z-$directed compressed diagonal storage mode matrices in supervector mode} +\OptIntEnr + {IPVW\blank{8}}{$\mathcal{S}^{t}_{11}$}{$\mathcal{S}^{t}_{6}\ge 8$} + {$W-$directed ADI permutation matrix in supervector mode} +\IntEnr + {IPVX\blank{8}}{$\mathcal{S}^{t}_{11}$} + {$X-$directed ADI permutation matrix in supervector mode} +\OptIntEnr + {IPVY\blank{8}}{$\mathcal{S}^{t}_{11}$}{$\mathcal{S}^{t}_{6}\ge 5$} + {$Y-$directed ADI permutation matrix in supervector mode} +\OptIntEnr + {IPVZ\blank{8}}{$\mathcal{S}^{t}_{11}$}{$\mathcal{S}^{t}_{6}=7$ or $9$} + {$Z-$directed ADI permutation matrix in supervector mode} +\end{DescriptionEnregistrement} + +The following records will also be present on the main level of a \dir{tracking} +directory in cases where a cylindrical correction of the albedos is used ($\mathcal{S}^{t}_{24}\ne 0$): + +\begin{DescriptionEnregistrement}{The \moc{trivat} records in +\dir{tracking} (contd.)}{8.0cm} +\OptRealEnr + {RR0\blank{9}}{$\mathcal{S}^{t}_{24}$}{$\mathcal{S}^{t}_{24}\ne 0$}{cm} + {Radii of the cylindrical boundaries in the cylindrical correction} +\OptRealEnr + {XR0\blank{9}}{$\mathcal{S}^{t}_{24}$}{$\mathcal{S}^{t}_{24}\ne 0$}{cm} + {Coordinates on principal axis in the cylindrical correction} +\OptRealEnr + {ANG\blank{9}}{$\mathcal{S}^{t}_{24}$}{$\mathcal{S}^{t}_{24}\ne 0$}{1} + {Angles for applying the cylindrical correction} +\end{DescriptionEnregistrement} + +\eject |