From 98e9f3fa878a4c3db80d77d98fb87f5109b545d2 Mon Sep 17 00:00:00 2001 From: ageay Date: Fri, 14 Oct 2011 15:10:06 +0000 Subject: [PATCH] *** empty log message *** --- doc/doxygen/interptheory.dox | 90 ++++++++++++++++++------------------ 1 file changed, 45 insertions(+), 45 deletions(-) diff --git a/doc/doxygen/interptheory.dox b/doc/doxygen/interptheory.dox index bedf92e80..4d1d13a50 100644 --- a/doc/doxygen/interptheory.dox +++ b/doc/doxygen/interptheory.dox @@ -132,9 +132,9 @@ The aim here is to compute the interpolated field FT on the target mesh of field The first step of the interpolation leads to the following M1 matrix : \f[ - M1=\begin{tabular}{|cc|} + M1=\left[\begin{tabular}{cc} 0.125 & 0.75 \\ - \end{tabular} + \end{tabular}\right] \f] \subsection TableNatureOfFieldExampleConservVol Conservative volumic case @@ -142,22 +142,22 @@ The first step of the interpolation leads to the following M1 matrix : If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ M_{Conservative Volumic} \f$ matrix : \f[ - M_{Conservative Volumic}=\begin{tabular}{|cc|} - $\frac{0.125}{0.125+0.75} & $\frac{0.75}{0.125+0.75} \\ - \end{tabular}=\begin{tabular}{|cc|} + M_{Conservative Volumic}=\left[\begin{tabular}{cc} + $\displaystyle\frac{0.125}{0.125+0.75}$ & $\displaystyle\frac{0.75}{0.125+0.75}$ \\ + \end{tabular}\right]=\left[\begin{tabular}{cc} 0.14286 & 0.85714 \\ - \end{tabular} + \end{tabular}\right] \f] \f[ - FT=\begin{tabular}{|cc|} - $\frac{0.125}{0.875} & $\frac{0.75}{0.875} \\ - \end{tabular}.\begin{tabular}{|c|} + FT=\left[\begin{tabular}{cc} + $\displaystyle\frac{0.125}{0.875}$ & $\displaystyle\frac{0.75}{0.875}$ \\ + \end{tabular}\right].\left[\begin{tabular}{c} 4 \\ 100 \\ - \end{tabular} - =\begin{tabular}{|c|} + \end{tabular}\right] + =\left[\begin{tabular}{c} 86.28571\\ - \end{tabular} + \end{tabular}\right] \f] As we can see here the maximum principle is respected.This nature of field is particulary recommended to interpolate an intensive @@ -168,22 +168,22 @@ field such as \b temperature or \b pression. If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ M_{Integral} \f$ matrix : \f[ - M_{Integral}=\begin{tabular}{|cc|} - $\frac{0.125}{9} & $\frac{0.75}{3} \\ - \end{tabular}=\begin{tabular}{|cc|} + M_{Integral}=\left[\begin{tabular}{cc} + $\displaystyle\frac{0.125}{9}$ & $\displaystyle\frac{0.75}{3}$ \\ + \end{tabular}\right]=\left[\begin{tabular}{cc} 0.013888 & 0.25 \\ - \end{tabular} + \end{tabular}\right] \f] \f[ - FT=\begin{tabular}{|cc|} - $\frac{0.125}{9} & $\frac{0.75}{3} \\ - \end{tabular}.\begin{tabular}{|c|} + FT=\left[\begin{tabular}{cc} + $\displaystyle\frac{0.125}{9}$ & $\displaystyle\frac{0.75}{3}$ \\ + \end{tabular}\right].\left[\begin{tabular}{c} 4 \\ 100 \\ - \end{tabular} - =\begin{tabular}{|c|} + \end{tabular}\right] + =\left[\begin{tabular}{c} 25.055\\ - \end{tabular} + \end{tabular}\right] \f] This type of interpolation is typically recommended for the interpolation of \b power (\b NOT \b power \b density !) for @@ -192,10 +192,10 @@ a user who wants to conserve the quantity \b only on the intersecting part of th This type of interpolation is equivalent to the computation of \f$ FS_{vol} \f$ followed by a multiplication by \f$ M1 \f$ where \f$ FS_{vol} \f$ is given by : \f[ - FS_{vol}=\begin{tabular}{|c|} - $\frac{4}{9} \\ - $\frac{100}{3} \\ - \end{tabular} + FS_{vol}=\left[\begin{tabular}{c} + $\displaystyle\frac{4}{9}$ \\ + $\displaystyle\frac{100}{3}$ \\ + \end{tabular}\right] \f] In the particular case treated \ref TableNatureOfFieldEx1 "here", it means that only a power of 25.055 W is intercepted by the target cell ! @@ -208,22 +208,22 @@ In order to treat differently a power field, another policy, \ref TableNatureOfF If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ M_{IntegralGlobConstraint} \f$ matrix : \f[ - M_{IntegralGlobConstraint}=\begin{tabular}{|cc|} - $\frac{0.125}{0.125} & $\frac{0.75}{0.75} \\ - \end{tabular}=\begin{tabular}{|cc|} + M_{IntegralGlobConstraint}=\left[\begin{tabular}{cc} + \displaystyle\frac{0.125}{0.125} & \displaystyle\frac{0.75}{0.75} \\ + \end{tabular}\right]=\left[\begin{tabular}{cc} 1 & 1 \\ - \end{tabular} + \end{tabular}\right] \f] \f[ - FT=\begin{tabular}{|cc|} + FT=\left[\begin{tabular}{cc} 1 & 1 \\ - \end{tabular}.\begin{tabular}{|c|} + \end{tabular}\right].\left[\begin{tabular}{c} 4 \\ 100 \\ - \end{tabular} - =\begin{tabular}{|c|} + \end{tabular}\right] + =\left[\begin{tabular}{c} 104\\ - \end{tabular} + \end{tabular}\right] \f] This type of interpolation is typically recommended for the interpolation of \b power (\b NOT \b power \b density !) for @@ -238,22 +238,22 @@ intercepted source cells. If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ M_{RevIntegral} \f$ matrix : \f[ - M_{RevIntegral}=\begin{tabular}{|cc|} - $\frac{0.125}{1.5} & $\frac{0.75}{1.5} \\ - \end{tabular}=\begin{tabular}{|cc|} + M_{RevIntegral}=\left[\begin{tabular}{cc} + $\displaystyle\frac{0.125}{1.5}$ & $\displaystyle\frac{0.75}{1.5}$ \\ + \end{tabular}\right]=\left[\begin{tabular}{cc} 0.083333 & 0.5 \\ - \end{tabular} + \end{tabular}\right] \f] \f[ - FT=\begin{tabular}{|cc|} - $\frac{0.125}{1.5} & $\frac{0.75}{1.5} \\ - \end{tabular}.\begin{tabular}{|c|} + FT=\left[\begin{tabular}{cc} + $\displaystyle\frac{0.125}{1.5}$ & $\displaystyle\frac{0.75}{1.5}$ \\ + \end{tabular}\right].\left[\begin{tabular}{c} 4 \\ 100 \\ - \end{tabular} - =\begin{tabular}{|c|} + \end{tabular}\right] + =\left[\begin{tabular}{c} 50.333\\ - \end{tabular} + \end{tabular}\right] \f] This type of nature is particulary recommended to interpolate an intensive \b density -- 2.39.2