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<P>
 This menu is analogous to that of <b> TRACXX</b> which enables the user to define
the axis of  the cut  (it corresponds therefore to plotting a curve, which is explained in detail
in  <b> TRACXX</b>).
<P>
<P>
<P>
Once the  plot of the cut has been obtained, the following <i> graphics</i> menu appears:
<P>
<UL><LI> End of cuts (0) and return to the module's main menu,
<LI> Continue (1), re-plot the mesh,
<LI> Refresh (4) the screen,
<LI> Exit (5) from session,
<LI> Produce a softcopy (8) or hardcopy (9) of the cut on another graphics terminal; having done this,
the user is returned to the initial state (of this <i> graphics</i> menu).
</UL>
<P>
<DL COMPACT><DT>Example:
<DD> Figure <A HREF="#figtrmaco4">3.6</A> is nothing other that cut through the displacements
 in the x-direction of test 2. The cut line is vertical and passes through
the center of the circles (consult the geometry of the figures shown earlier)
which explains the presence of two holes in the cut.
<P>
The plot was obtained by typing the following sequence:
<P>
<UL><LI> figure <A HREF="#figtrmaco4">3.6</A> : -1 t2mail t2coor 10 4 t2b 0 7 7 OUI 61 'cut line'
'displacement in X, VN' 0  8 2 bw ncadre nlogo   x12 y12  ftrmaco4 v
</UL> 
 </DL>
<P>
<P><A NAME=2259>&#160;</A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img81.gif">
<BR><STRONG>Figure 3.6:</STRONG> <i> Example <b> TRMCXX</b> 2D: cut</i><A NAME=2257iExample2253bTRMCXXb22532Dcuti2257>&#160;</A><BR>
<P>
<P>
<DT>Flux:
<DD>  
<P>
This option enables the user to visualize the flux for mixed finite elements only. The flux
is represented by  arrows, as in the case of velocities, and we can consequently
consult the operating instructions corresponding to  plotting velocities.
The only difference is that of key 56 in the main menu.
<P>
<PRE> ------------------------------------------------------------
 | 56 | VISUALISATION OF FLUX     |          EVERYWHERE
 ------------------------------------------------------------
</PRE>
<P>
This choice  (by default) can be modified by activating key 56:
<P>
<PRE>    ON ALL THE REFERENCES      : 0
    EVERYWHERE                 : 1
    ON SOME REFERENCES         : 2
</PRE>
<P>
Case  2 consists of specifying only those reference numbers which we desire.
<P>
 </DL>
<P>
<P>
<P>
<H2><A NAME=SECTION04424000000000000000>3.2.4 P1 interpolation of solutions</A></H2>
<P>
<P>
<P>
When plotting the isovalues of a solution it is necessary to define exactly what we want to plot.
The finite elements used (described in D.S. <b> MAIL</b>) can be more, or less, rich
(as a function of the degree of interpolation chosen).
<P>
The plot program is purely P1 and applies to the case of  a triangular type element.
Using the solution values at
the three vertices of the triangle, the isovalues present in the triangle are calculated.
<P>
Consequently, each finite element must be decomposed into the most judicious set  of
triangles such that the quality of the interpolation is preserved:
it does not correspond to making beautiful plots but plots conforming to known
information. The decomposition must thus satisfy this concern.
It corresponds thus to interpreting  each element in terms of P1 triangles.
<P>
<P>
<P>
The choices made for the usual element are given below:
<P>
<UL><LI> a P1 triangle  (TRIA 2P1D, TRIA AP1D) is considered as such,
<LI> a P2 triangle (TRIA 2P2D or TRIA 2P2C and TRIA AP2C) is decomposed into 4 P1 sub-triangles,
<LI> a Q1 quadrilateral (QUAD 2Q1D, QUAD AQ1C)is decomposed into 4 P1 sub-triangles by creating its
barycentre,
<LI> a Q2  quadrilateral (QUAD 2Q2D or QUAD 2Q2C and QUAD AQ2C) is decomposed into 16 P1 sub-triangles in
the following manner:
<UL><LI> we decompose the  initial quadrilateral into 4 sud-quadrilaterals by creating its  barycentre, and then
decompose all these elements into 4 P1 sub-triangles.
</UL>
<LI> etc.
</UL>
<P>
Only certain elements are actually known  and thus considered by the plot module.
If an element is not known, the module will stop and indicate that it does not
 know this type of element. The user must then add it by decomposing it
in a consistent manner with the corresponding interpolation.
<P>
The decomposition is the object of subroutine RANGPQ in library UTIL. This subroutine has the following form:
<P>
<PRE>      SUBROUTINE RANGPQ(NOM1,NOM2,NCGE,NNO,NONO,NPO,NOPOI,COORP,
     +                  SOLU,XX,YY,SOL,NTRIP1)
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  AIM : DECOMPOSE THE ELEMENT INTO P1 TRIANGLES ONLY
C  ---
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  INPUT PARAMETERS :
C  ------------------
C  NOM1, NOM2 : ELEMENT NAMES
C  NCGE,NNO,NONO(*),NPO,NOPOI(*) : USUAL NOTATION
C  COORP   : POINT COORDINATES
C  SOLU    : SOLUTION ARRAY = B4(NDSMT,NDT,1:NOE)
C            WITH NDSMT : RIGHT-HAND-SIDE CONSIDERED ( BETWEEN 1 AND NDSM )
C                 NDT   : THE D.O.F. CONSIDERED ( BETWEEN 1 AND ND )
C                 B4    : ARRAY B4 CONSIDERED
C            REMARK     : SUBROUTINE CHARB4 CREATES SOLU FROM THE GLOBAL B4
C  OUTPUT PARAMETERS :
C  -------------------
C  XX(*),YY(*) : COORDINATES OF POINTS P1
C  SOL     : CORRESPONDING SOLUTIONS
C  NTRIP1  : NUMBER OF P1 ELEMENTS IN THE DECOMPOSITION OF THE ELEMENT
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C
C  SUBROUTINE TO BE COMPLETED FOR ALL NEW ELEMENTS INTERPRETED INTO P1.
C
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  PROGRAMMEUR  : PL GEORGE  INRIA  1987
C  ....................................................................
      DIMENSION NONO(*),NOPOI(*),COORP(2,*),SOLU(*),XX(*),YY(*),
     +          SOL(*),SOLP1(3),SOLP2(6),SOLQ1(4),SOLQ2(9),INDIC(4),
     +          SOLQ5(5)
      CHARACTER*4 NOM1,NOM2
  200 FORMAT(' %% ERREUR RANGPQ : ELEMENT ',A4,A4,' NON CONNU'///
     +       ' VOIR LE SP RANGPQ ET AJOUTER CET ELEMENT'///)
C
      IMPRIM = IINFO('I')
C     -------------------------------------------------------
C     ------------         THE TRIANGLES         ------------
C     -------------------------------------------------------
      IF ( NOM1 .EQ. 'TRIA'  ) THEN
C        -------------   TRIANGLE :  NOM COMMENCANT PAR TRIA
         IF( NOM2 .EQ. '2P1D' ) THEN
C        ------   TRIA 2P1D   ------
             NTRIP1 = 1
             NUMER  = 0
             DO 301 J=1,NNO
                SOLP1(J) = SOLU(NONO(J))
                INDIC(J) = J
  301        CONTINUE
             CALL RANGP1(NUMER,COORP,INDIC,SOLP1,XX,YY,SOL)
         ELSE IF( NOM2 .EQ. 'AP1D' ) THEN
C        ------   TRIA AP1D   ------
             NTRIP1 = 1
             NUMER  = 0
             DO 339 J=1,NNO
                SOLP1(J) = SOLU(NONO(J))
                INDIC(J) = J
  339        CONTINUE
             CALL RANGP1(NUMER,COORP,INDIC,SOLP1,XX,YY,SOL)
         ELSE .....
              .....
              .....               elements unknown
         ELSE
             WRITE (IMPRIM,200) NOM1,NOM2
             CALL TILT                           elements unknown
         END IF
C     -------------------------------------------------------
C     ------------         THE QUADRILATERALS    ------------
C     -------------------------------------------------------
      ELSE IF ( NOM1 .EQ. 'QUAD' ) THEN
         IF ( NOM2 .EQ. '2Q1D' ) THEN
C        ------   QUAD 2Q1D   ------
             NTRIP1 = 4
             DO 406 J=1,NNO
               SOLQ1(J) = SOLU(NONO(J))
               INDIC(J) = J
  406        CONTINUE
             NUMER = 0
             CALL RANGQ1(NUMER,COORP,INDIC,SOLQ1,XX,YY,SOL)
         ELSE .....
              .....
              .....               elements unknown
         ELSE
             WRITE (IMPRIM,200) NOM1,NOM2
             CALL TILT
         END IF                               elements unknown
      ELSE
         WRITE (IMPRIM,200) NOM1,NOM2
         CALL TILT                      elements unknown
      END IF
      END
</PRE>
<P>
Subroutine RANGPQ uses a certain number of element subroutines
(RANGP1, RANGP2, RANGQ1, RANGQ2 ...). To add a finite element corresponds to adding the
appropriate  branch and using the appropriate element subroutine or writing
a new one (each one very simple). To govern  the computation, we have at our disposal,
 NOM1 and NOM2, the two parts of the
element name, its geometric code, its number of points and nodes and the
arrays containing its points and nodes (it seems that with this information we are able
to recognize all the elements without ambiguity).
<P>
<DL COMPACT><DT>Remark:
<DD> The label used for an element recalls its geometry and number.
For example, a 2P1D triangle has a geometric code NCGE = 3 and number 1 (100001 or 200001). The label of this
element is thus set to 301.
<P>
 </DL>
<P>
Decomposition example using the subroutine names:
<P>
<TABLE COLS=3>
<COL ALIGN=RIGHT><COL ALIGN=CENTER><COL ALIGN=JUSTIFY WIDTH="6cm">
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP>
    RANGPQ </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
        if </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> TRIA 2P1D  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> RANGP1        1 P1 <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img71.gif"> 1 P1   </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> TRIA AP1D  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> the same                                </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
        if </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> TRIA 2P2D  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> RANGP2        1 P2 <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img71.gif"> 4 P1   </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - calculate the middle coordinates       </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - and store RANGP1 the solution          </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
        if </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> TRIA 2P2C  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> RANGP2        1 P  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img71.gif">2 4 P1  </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - store RANGP1 the solution             </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> TRIA AP2C  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> the same                                </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
        if </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> QUAD 2Q1D  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> RANGQ1        1 Q1  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img71.gif"> 4 P1  </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - calculate the barycentre and the solution  </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - and store RANGP1 this solution             </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> QUAD AQ1C  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> the same                                      </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
        if </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> QUAD 2Q2D  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> RANGQ2        1 Q2  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img71.gif"> 16 P1 </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - calculate the middle coordinates      </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - calculate the barycentre and the solution </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> and store RANGQ1 (RANGP1) this solution   </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
        if </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> QUAD 2Q2C  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> RANGQ2        1 Q2  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img71.gif">  16 P1  </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - calculate the barycentre and the solution </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>                 </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> - and store RANGQ1 (RANGP1) this solution   </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> QUAD AQ2C  :    </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170"> the same                                  </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 
           </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> ...... etc      </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170">
</TD></TR>
</TABLE>
<P>
<P>
<P>
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