More doc.

diff --git a/doc/doxygen/figures/NonOverlapping.fig b/doc/doxygen/figures/NonOverlapping.fig
new file mode 100644 (file)
index 0000000..5493cdd
--- /dev/null
+++ b/doc/doxygen/figures/NonOverlapping.fig
@@ -0,0 +1,45 @@
+#FIG 3.2  Produced by xfig version 3.2.5b
+Landscape
+Center
+Inches
+Letter  
+100.00
+Single
+-2
+1200 2
+2 2 0 4 1 7 50 -1 -1 0.000 0 0 -1 0 0 5
+        3600 4800 7200 4800 7200 6000 3600 6000 3600 4800
+2 2 2 1 4 7 50 -1 -1 3.000 0 0 -1 0 0 5
+        7425 4200 8700 4200 8700 4725 7425 4725 7425 4200
+2 2 0 0 0 2 0 -1 15 0.000 0 0 -1 0 0 5
+        4800 3900 6000 3900 6000 4050 4800 4050 4800 3900
+2 2 0 4 4 7 50 -1 -1 0.000 0 0 -1 0 0 5
+        6000 3900 4800 3900 4800 5700 6000 5700 6000 3900
+2 2 0 4 1 7 50 -1 -1 0.000 0 0 -1 0 0 5
+        3600 450 7200 450 7200 4050 3600 4050 3600 450
+2 2 2 1 2 7 50 -1 -1 3.000 0 0 -1 0 0 5
+        2250 3000 3225 3000 3225 3375 2250 3375 2250 3000
+2 1 0 1 2 7 50 -1 -1 0.000 0 0 -1 1 0 2
+       1 1 1.00 60.00 120.00
+        3225 3150 4800 3975
+2 2 0 0 0 2 1 -1 15 0.000 0 0 -1 0 0 5
+        4800 4800 6000 4800 6000 5700 4800 5700 4800 4800
+2 1 0 1 2 7 50 -1 -1 0.000 0 0 -1 1 0 2
+       1 1 1.00 60.00 120.00
+        3231 4489 4806 5314
+2 2 2 1 2 7 50 -1 -1 3.000 0 0 -1 0 0 5
+        2250 4275 3225 4275 3225 4650 2250 4650 2250 4275
+2 2 2 1 1 7 50 -1 -1 3.000 0 0 -1 0 0 5
+        7350 1725 8625 1725 8625 2625 7350 2625 7350 1725
+2 2 2 1 1 7 50 -1 -1 3.000 0 0 -1 0 0 5
+        7425 5100 8700 5100 8700 5925 7425 5925 7425 5100
+4 0 1 50 -1 0 12 0.0000 4 135 1170 7425 1950 Source Cell#0\001
+4 0 1 50 -1 0 12 0.0000 4 135 600 7425 2175 Area=9\001
+4 0 4 50 -1 0 12 0.0000 4 135 750 7500 4650 Area=1.5\001
+4 0 4 50 -1 0 12 0.0000 4 180 1140 7500 4425 Target Cell#0\001
+4 0 2 50 -1 0 12 0.0000 4 135 885 2325 3225 S00=0.125\001
+4 0 2 50 -1 0 12 0.0000 4 135 780 2325 4500 S01=0.75\001
+4 0 1 50 -1 0 12 0.0000 4 135 1170 7500 5325 Source Cell#1\001
+4 0 1 50 -1 0 12 0.0000 4 135 600 7500 5550 Area=3\001
+4 0 1 50 -1 0 12 0.0000 4 135 465 7425 2475 F0=4.\001
+4 0 1 50 -1 0 12 0.0000 4 135 675 7500 5775 F1=100.\001

diff --git a/doc/doxygen/figures/NonOverlapping.png b/doc/doxygen/figures/NonOverlapping.png
new file mode 100644 (file)
index 0000000..471b47d
Binary files /dev/null and b/doc/doxygen/figures/NonOverlapping.png differ

diff --git a/doc/doxygen/interptheory.dox b/doc/doxygen/interptheory.dox
index 1d16d001a7e9b97c440d14991a981b1dab82b113..bedf92e802256b272dc1d0c98c60da1b9b905ba3 100644 (file)
--- a/doc/doxygen/interptheory.dox
+++ b/doc/doxygen/interptheory.dox
@@ -39,12 +39,12 @@ mesh T the aspect of overlapping is important. In fact if any cell of
 of S is fully overlapped by cells of T and inversely any cell of T is
 fully overlapped by cells of S that is
 \f[
-\sum_{S_j} Vol(T_i\cap S_j) = Vol(T_i) and \sum_{T_i} Vol(S_j\cap T_i) = Vol(S_j)
+\sum_{S_j} Vol(T_i\cap S_j) = Vol(T_i),\hspace{1cm} and \hspace{1cm} \sum_{T_i} Vol(S_j\cap T_i) = Vol(S_j)
 \f]
 then the meshes S and T are said to be \b
 overlapping and all the algorithms will return the same results.
 
-The ideal interpolation algorithm should be conservative and respect the maximum principle. However such an algorithm can be impossible to design if the two meshes do not overlap. When the meshes do not overlap, using either \f$Vol(T_i)\f$ or \f$\sum_{S_j} Vol(T_i\cap S_j)\f$ in the formula one obtains an algorithm that respects either conservativity either the maximum principle.
+The ideal interpolation algorithm should be conservative and respect the maximum principle. However such an algorithm can be impossible to design if the two meshes do not overlap. When the meshes do not overlap, using either \f$Vol(T_i)\f$ or \f$\sum_{S_j} Vol(T_i\cap S_j)\f$ in the formula one obtains an algorithm that respects either conservativity either the maximum principle (see the nature of field \ref TableNatureOfField "summary table").
 
 
 \section InterpKerRemapInt Linear conservative remapping of P0 (cell based) fields
@@ -56,8 +56,8 @@ This value can represent either
 
 \section InterpKerP0P0Int cell-cell (P0->P0) conservative remapping of intensive fields
 
-In the \ref InterpKerGenralEq "general interpolation equation" the
-left hand side becomes :
+For intensive fields such as mass density or power density, the
+left hand side in the \ref InterpKerGenralEq "general interpolation equation" becomes :
 
 \f[
 \int_{T_i} \phi = Vol(T_i).\phi_{T_i}. 
@@ -113,10 +113,157 @@ In the case of fields with P0 representation, if the meshes do not overlap the s
 
  * <TABLE BORDER=1 >
  * <TR><TD> </TD><TD>Intensive</TD><TD> extensive </TD></TR>
- * <TR><TD> Conservation</TD><TD> \f[\frac{Vol(T_i\cap S_j)}{ Vol(T_i)}\f] <br />ConservativeVolumic </TD><TD>\f[ \frac{Vol(T_i\cap S_j)}{ \sum_{T_i} Vol(S_j\cap T_i) }\f] <br />IntegralGlobConstraint</TD></TR>
- * <TR><TD> Maximum principle </TD><TD> \f[\frac{Vol(T_i\cap S_j)}{ \sum_{S_j} Vol(T_i\cap S_j)}\f] <br /> RevIntegral</TD><TD> \f[\frac{Vol(T_i\cap S_j)}{  Vol(S_j) }\f] <br /> Integral </TD></TR>
+ * <TR><TD> Conservation</TD><TD> \f[\frac{Vol(T_i\cap S_j)}{ Vol(T_i)}\f] <br /> \ref TableNatureOfFieldExampleRevIntegral "RevIntegral" </TD><TD> \f[ \frac{Vol(T_i\cap S_j)}{ \sum_{T_i} Vol(S_j\cap T_i) }\f] <br /> \ref TableNatureOfFieldExampleIntegralGlobConstraint "IntegralGlobConstraint" </TD></TR>
+ * <TR><TD> Maximum principle </TD><TD> \f[\frac{Vol(T_i\cap S_j)}{ \sum_{S_j} Vol(T_i\cap S_j)}\f] <br /> \ref TableNatureOfFieldExampleConservVol "ConservativeVolumic" </TD><TD>  \f[\frac{Vol(T_i\cap S_j)}{  Vol(S_j) }\f] <br /> \ref TableNatureOfFieldExampleIntegral "Integral"</TD></TR>
  *</TABLE>
 
+\section TableNatureOfFieldExample Illustration of a non overlapping P0P0 interpolation
+
+Let's consider the following case with a source mesh containing two cells and a target mesh containing one cell.
+Let's consider a field FS on cells on the source mesh that we want to interpolate on the target mesh.
+
+The value of FS on the cell#0 is 4 and the value on the cell#1 is 100.
+
+The aim here is to compute the interpolated field FT on the target mesh of field FS depending on the \ref NatureOfField "nature of the field".
+
+\anchor TableNatureOfFieldEx1
+\image html NonOverlapping.png "An example of non overlapping intersection of two meshes."
+
+The first step of the interpolation leads to the following M1 matrix :
+
+\f[
+    M1=\begin{tabular}{|cc|}
+    0.125 & 0.75 \\
+    \end{tabular}
+    \f]
+ 
+\subsection TableNatureOfFieldExampleConservVol Conservative volumic case
+
+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|}
+    0.14286 & 0.85714 \\
+    \end{tabular}
+\f]
+\f[
+    FT=\begin{tabular}{|cc|}
+    $\frac{0.125}{0.875} & $\frac{0.75}{0.875} \\
+    \end{tabular}.\begin{tabular}{|c|}
+    4 \\
+    100 \\
+    \end{tabular}
+    =\begin{tabular}{|c|}
+    86.28571\\
+    \end{tabular}
+\f]
+
+As we can see here the maximum principle is respected.This nature of field is particulary recommended to interpolate an intensive
+field such as \b temperature or \b pression.
+
+\subsection TableNatureOfFieldExampleIntegral Integral case
+
+If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ M_{Integral} \f$ matrix :
+
+\f[
+    M_{Integral}=\begin{tabular}{|cc|}
+    $\frac{0.125}{9} & $\frac{0.75}{3} \\
+    \end{tabular}=\begin{tabular}{|cc|}
+    0.013888 & 0.25 \\
+    \end{tabular}
+\f]
+\f[
+    FT=\begin{tabular}{|cc|}
+    $\frac{0.125}{9} & $\frac{0.75}{3} \\
+    \end{tabular}.\begin{tabular}{|c|}
+    4 \\
+    100 \\
+    \end{tabular}
+    =\begin{tabular}{|c|}
+    25.055\\
+    \end{tabular}
+\f]
+
+This type of interpolation is typically recommended for the interpolation of \b power (\b NOT \b power \b density !) for
+a user who wants to conserve the quantity \b only on the intersecting part of the source mesh (the green part on the \ref TableNatureOfFieldEx1 "example")
+
+This type of interpolation is equivalent to the computation of \f$ 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} \\
+    $\frac{100}{3} \\
+    \end{tabular}
+\f]
+
+In the particular case treated \ref TableNatureOfFieldEx1 "here", it means that only a power of 25.055 W is intercepted by the target cell !
+
+So from the 104 W of the source field \f$ FS \f$, only 25.055 W are transmited in the target field using this nature of field.
+In order to treat differently a power field, another policy, \ref TableNatureOfFieldExampleIntegralGlobConstraint "integral global constraint nature" is available. 
+
+\subsection TableNatureOfFieldExampleIntegralGlobConstraint Integral with global constraints case
+
+If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ M_{IntegralGlobConstraint} \f$ matrix :
+
+\f[
+    M_{IntegralGlobConstraint}=\begin{tabular}{|cc|}
+    $\frac{0.125}{0.125} & $\frac{0.75}{0.75} \\
+    \end{tabular}=\begin{tabular}{|cc|}
+    1 & 1 \\
+    \end{tabular}
+\f]
+\f[
+    FT=\begin{tabular}{|cc|}
+    1 & 1 \\
+    \end{tabular}.\begin{tabular}{|c|}
+    4 \\
+    100 \\
+    \end{tabular}
+    =\begin{tabular}{|c|}
+    104\\
+    \end{tabular}
+\f]
+
+This type of interpolation is typically recommended for the interpolation of \b power (\b NOT \b power \b density !) for
+a user who wants to \b conserve \b all \b the \b power in its source field. Here we have 104 W in source field, we have 104 W too,
+in the output target interpolated field.
+
+\b BUT, As we can see here, the maximum principle is \b not respected here, because the target cell #0 has a value higher than the two
+intercepted source cells.
+
+\subsection TableNatureOfFieldExampleRevIntegral Reverse integral case
+
+If we apply the formula \ref TableNatureOfField "above" it leads to the following \f$ 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|}
+    0.083333 & 0.5 \\
+    \end{tabular}
+\f]
+\f[
+    FT=\begin{tabular}{|cc|}
+    $\frac{0.125}{1.5} & $\frac{0.75}{1.5} \\
+    \end{tabular}.\begin{tabular}{|c|}
+    4 \\
+    100 \\
+    \end{tabular}
+    =\begin{tabular}{|c|}
+    50.333\\
+    \end{tabular}
+\f]
+
+This type of nature is particulary recommended to interpolate an intensive \b density
+field (moderator density, power density).
+The difference with \ref TableNatureOfFieldExampleConservVol "conservative volumic" seen above is that here the
+target field is homogeneized to the \b whole target cell. It explains why this nature of field does not follow the maximum principle.
+
+To illustrate the case, let's consider that \f$ FS \f$ is a power density field in \f$ W/m^2 \f$.
+With this nature of field the target cell #0 cumulates 0.125*4=0.5 W of power from the source cell #0 and 0.75*100=75 W of power from the source cell #1.
+It leads to 75.5 W of power on the \b whole target cell #0. So, the final power density is equal to 75.5/1.5=50.333 W/m^2.
 
 */
 

diff --git a/doc/doxygen/medcoupling.dox b/doc/doxygen/medcoupling.dox
index 3a86a1bde90922a637c85a76c85b5a6ab1f6b3a8..5ec89d0d0f01db4c9b61ac45ceded3bb45a3a171 100644 (file)
--- a/doc/doxygen/medcoupling.dox
+++ b/doc/doxygen/medcoupling.dox
@@ -570,7 +570,7 @@ It has five possible values:
 -      "IntegralGlobConstraint", for extensive fields with conservativity favored over the maximum principle
 -      "RevIntegral", for intensive field with the maximum principle favored over conservativity
 
-By an intensive field we mean a field that represent volumetric or intensive physical variable such as density (\f$kg.m^{-3}\f$), temperature (\f$\circ K\f$) or pressure (\f$Pa\f$).
+By an intensive field we mean a field that represent volumetric or intensive physical variable such as density (\f$kg.m^{-3}\f$), power density (\f$W.m^{-3}\f$), temperature (\f$K\f$) or pressure (\f$Pa\f$).
 By extensive (or integral) field we mean a field that represents an extensive physical quantity sych as mass (\f$kg\f$), volume (\f$m^3\f$), a momentum (\f$kg.m.s^{-1}\f$) or power \f$(W\f$).
 For fields with a P0 representation, conservativity formulas are different depending on whether the field is extensive or intensive (see \ref InterpKerP0P0Int and \ref InterpKerP0P0Ext).
 In some cases such a non \ref MeshOverlap "overlapping meshes", it is impossible to fulfill both conservation and maximum principle during the interpolation. The nature of the fields determines the formula to be used for non overlapped cells and thus the property that we will be satisfied.
@@ -605,4 +605,4 @@ sourceField->setNature(ConservativeVolumic);
 ...
 \endcode
 
-*/
\ No newline at end of file
+*/