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<P>
<UL><LI> B3(1) = 0 
<LI> B3(i+1) =  number of the last node in block i if NCODSB = -2 <BR> 
      B3(i+1) =  number of the last degree of freedom in block i if NCODSB = -1
</UL>
<P>
<DT>Array B4:
<DD> the array coefficients. <BR>
<P>
This NTYP type array contains the NDSM*M2 values of each page.
<P>
<DL COMPACT><DT>
<DD> B4(1,l+1) to B4(NDSM,l+1) then
<DT>
<DD> B4(1,l+2) to B4(NDSM,l+2)  then 
<DT>
<DD> ....
<DT>
<DD> B4(1,l') to B4(NDSM,l')
<P>
 </DL> 
where  <BR> 
 l = NDL(B3(i)+1),  l' = NDL(B3(i+1)+1) and NDL is the number of
degrees of freedom per node.
<P>
 </DL>
<P>
<P>
<H2><A NAME=SECTION05142000000000000000>1.3.2 Corresponding tools</A></H2>
<P>
<P>
<P>
<H3><A NAME=SECTION05142100000000000000> Reading and writing a DS B</A></H3>
<P>
<P>
<P>
A DS residing in M.M. is written to S.M. on a sequential or direct access file.
<P>
This is a category 2 DS where only the first 4 arrays and any 
associated arrays 
 (described in array <b> B1</b>)are read (module <b> SDLECT</b>) or
written  (module <b> SDECRI</b>):
<P>
<UL><LI> When reading, array <b> B4</b> is only addressed and the read is performed by the program
via a READ type command:
<blockquote> READ(NFB) LE,(M(IAB4-1+I),I=1,LE)
<P>
or
<P>
DOUBLE PRECISION B4(LE)
<P>
READ(NFB) NBREMO*LE,(B4(I),I=1,LE) 
</blockquote>
<P>
<LI> When writing, array <b> B4</b> is transferred via a WRITE type command.
</UL>
<P>
<P>
<P>
<H3><A NAME=SECTION05142200000000000000> Printing a DS B</A></H3>
<P>
<P>
<P>
The contents (total or partial)  of a DS <b> B</b>  can be printed by using the following modules;
<P>
<DL COMPACT><DT>IMB:
<DD> The entire DS when the number of degrees of freedom per node is constant
(as a function of the  print parameter IMPRE, all or part of array <b> B4</b> will be printed).
<P>
<PRE>      SUBROUTINE IMB(M,NFB,NIB,IMPRE)
C AIM : PRINT THE ARRAYS OF DS B, INCREASING WITH IMPRE
C ---   FILE NFB (OR MC IF 0), LEVEL NIB
</PRE>
<P>
<DT>IMBND0:
<DD> The entire DS when the number of degrees of freedom per node is not constant; in this case
DS <b> MAIL</b> is necessary.
<P>
<PRE>      SUBROUTINE IMBND0(M,XM,DM,NFMAIL,NIMAIL,NFB,NIB,IMPR)
C AIM : PRINT THE CONTENTS OF A DS B (CASE ND = 0)
C ---   (SEE IMB IF ND NOT 0) (NDSM = 1 !!!)
</PRE>
<P>
<DT>INFOBB:
<DD> Print a particular value contained in the DS.
<P>
<PRE>      SUBROUTINE INFOBB(M,IOPT,TYPESD,NIVEAU,TAB2,TAB3,TAB4,DTAB4,
     +                  NUMREC)
C AIM : OUTPUT INFORMATION ON A DS B
</PRE>
<P>
Processors  <b> IMAGXX</b> and <b> INFOXX</b>  calls  <b> IMB</b>, <b> IMBND0</b> 
 and <b> INFOBB</b>, respectively, in a conversational manner.
<P>
<DT>PRINTB
<DD> is the module used to obtain the type of each value:
<P>
<PRE> 
      SUBROUTINE PRINTB(M,NFB,NIB,NFTYNO,NITYNO,TSIFO,IND1,ITAB,IND2,
     +              NFNDL1,NINDL1,IMPR)
C AIM : PRINTS DS B WITH A DESCRIPTION OF THE NODE TYPES
</PRE>
<P>
This module uses DS <b> TYNO</b>, which can be created using module <b> COTYNO</b>  (see DS 
<b> TYNO</b>).
<P>
 </DL>
<P>
<P>
<P>
<H3><A NAME=SECTION05142300000000000000> Creation and manipulation modules for DS B</A></H3>
<P>
<P>
<P>
DS  <b> B</b> is generally the result of computation performed by a specific module (assembly of the RHS,
solution of the system, ...); it can also, in certain cases, be constructed manually
(for example, to input the initial  solution of a time-dependent problem).
<P>
<DL COMPACT><DT>Manual creation:
<DD>    <BR>
<P>
<DL COMPACT><DT>COSDB:
<DD> Creation by inputing one (or two) vector(s) explicitly.
<P>
<PRE>      SUBROUTINE COSDB(M,NVEC,U,V,LUV,ND,NFB,NIB,NTAB)
C AIM : CREATE A DS B FROM ONE OR TWO VECTORS
</PRE>
<P>
<DT>COSNOB:
<DD> Creation in terms of the nodal coordinates of the mesh; DS  
<b> NOPO</b> is therefore used.
<P>
<PRE>      SUBROUTINE COSNOB(M,XM,NFNOPO,NINOPO,NVEC,U0,U1,DU0,DU1,ND,
     +                  NFB,NIB,NTAB,FONINT,VALCLR,VALCLD)
C AIM : CREATE A DS B FROM  A DS NOPO AND A FUNCTION
C ---   (SAME AIM AS COSDB)
C U(I) ( V(I) ) = FUNCTION(X(I),Y(I),Z(I)) AT POINT I OF DS NOPO
</PRE>
<P>
<DT>COSMCB:
<DD> Creation in terms of  the nodal coordinates  for the case when the number of
degrees of freedom per node is arbitrary; DS  <b> MAIL</b> and DS <b> COOR</b> are used.
<P>
<PRE>      SUBROUTINE COSMCB (M,XM,DM,NFMAIL,NIMAIL,NFCOOR,NICOOR,NVEC,
     +   NFBS,NIBS,NTAB,FONINT,VALCLR,VALCLD,U0,U1,DU0,DU1)
C AIM : SEE COSNOB, HERE ND = 0 IS POSSIBLE
</PRE>
<P>
 </DL>
<P>
Preprocessor <b> COSDXX</b> is employed to perform a conversational call of these modules.
<P>
<DT>Assembly of the element arrays:
<DD>      <BR>
<P>
<DL COMPACT><DT>ASEMBV:
<DD> Assembly, in main memory or on sequential file, by using  DS
 <b> TAE</b> containing the element RHS vectors of a system.
<P>
<PRE>      SUBROUTINE ASEMBV(M,NOT,NDSM,NCODSB,NFTAE,NITAE,NFNDL1,NINDL1,
     +                  NFB,NIB,NTB)
C AIM : ASSEMBLY OF THE RHS
C ---   REAL  SINGLE OR DOUBLE PRECISION COMPLEX SINGLE PRECISION
C       ALL THE ARRAYS RESIDE SIMULTANEOUSLY IN M.M.
</PRE>
<P>
<DT>ASMBMS:
<DD> Assembly, in main memory or on direct access file, by using 
DS <b> TAE</b> containing the element  RHS of a system.
<P>
<PRE>      SUBROUTINE ASMBMS(M,NOT,NDSM,NCODBB,NFTAE,NITAE,NFNDL1,
     +                  NINDL1,NFB,NIB,NTB)
C AIM : ASSEMBLY OF THE RHS
C ---               REAL  SINGLE OR  DOUBLE PRECISION
C                   COMPLEX SINGLE PRECISION
C       THE ODS B RESIDES IN S.M. WITH DIRECT ACCESS
</PRE>
<P>
 </DL>
<P>
Preprocessor <b> ASSEXX</b> is employed to call these modules in a conversational manner.
Furthermore, the solution preprocessors (for example <b> CHOLXX</b>) includes the assembly phase,
consequently, the user only performs this operation him- or herself in some special 
cases (for example, to plot the matrix structure, or to compute the eigenvalues and eigenvectors of
a problem).
<P>
 </DL>
<P>
<P>
<P>
<H3><A NAME=SECTION05142400000000000000> Manipulation utilities for a DS B</A></H3>
<P>
<P>
<P>
There are numerous utilities to manipulate the contents of a DS <b> B</b>.
<P>
<DL COMPACT><DT>BDISEQ:
<DD> Change the type of the file storing a DS <b> B</b>, i.e. pass from
a sequential support to a direct access support, or the inverse.
<P>
<PRE>      SUBROUTINE  BDISEQ(M,INOUT,NFBDI,NIBDI,NFBSEQ,NIBSEQ)
C AIM : TRANSFORM A FILE DS B DIRECT INTO SEQUENTIAL OR INVERSE
</PRE>
<P>
<DT>MAXDLB:
<DD> Print the extremal values (maxima, minima, ...) contained in a DS.
<P>
<PRE>      SUBROUTINE MAXDLB(M,XM,DM,NFB,NIB,MAXI,NIMPR)
C AIM : PRINT THE NIMPR NODES OF OPTIMUM RESULT PER LOCAL D.O.F. 
C ---   ACCORDING TO MAXI
</PRE>
<P>
<DT>NORME:
<DD> Calculate the error norms between the calculated and  exact solution calculated via a function
 (SOLEX or DSOLEX depending on the type).
<P>
<PRE>      SUBROUTINE NORME (M,XM,DM,NFMAIL,NIMAIL,NFCOOR,NICOOR,NFB,NIB,
     +   NFBS,NIBS,INDICB,NSM,FONINT,SOLEX,DSOLEX)
C AIM : IPRINT THE EXACT SOLUTION, CALCULATED SOLUTION,
C ---   THE ABSOLUTE AND RELATVE DIFFERENCES BETWEEN THEM,
C       THE L1, L2 AND MAX ERRORS
</PRE>
<P>
<DT>ERREUR:
<DD>  Calculate the error between the calculated solution and the residuals.
<P>
<PRE>      SUBROUTINE ERREUR(M,NFTAE,NITAE,NFB,NIB,NFNDL1,NINDL1,NFBER,
     +                  NIBER,NTBER,NOT1,NOT2)
C AIM : CALCULATE THE ERROR VECTOR
</PRE>
<P>
<DT>SYMBEL:
<DD> Calculate the DS  <b> B</b> symmetric to a given DS <b> B</b> with respect to 
a line or a plane of known equation. This operation is useful in post-processing.
<P>
<PRE>      SUBROUTINE SYMBEL(M,DM,NF1,NI1,NF2,NI2,NDIM,AA,BB,CC,DD)
C AIM :  SYMMETRY TRIDIM W.R.T. A PLANE OF A DS B
C ---    SYMMETRY BIDIM W.R.T. A LINE OF A DS B
C LIMITS :   ELASTIC PROBLEM
C -------    THE D.O.F. ARE DISPLACED
</PRE>
<P>
<DT>INTERQ:
<DD> Interpolation between the solutions obtained when solving 
a parabolic problem by a Gear or Runga-Kutta method 
(with time-step <em> a priori</em> unknown).
<P>
<PRE>      SUBROUTINE INTERQ(M,XM,NQ,NFB,NIB,PAS,NPAS,T0,TSAV,NFBS,NIBS)
C AIM  : INTERPOLATE THE SOLUTIONS OBTAINED FROM EVO*GE(RK) USING AN ORDER NQ
</PRE>
<P>
<DT>UNIONB:
<DD>  Post-processing of a DS resulting from the solution of a parabolic problem.
<P>
<PRE>      SUBROUTINE UNIONB(M,XM,NFB1,NIB1,NFB2,NIB2,JOPTIO,NFBS,NIBS)
C AIM  : GLUE TOGETHER 2 IDS B TO FORM A SINGLE ODS B
</PRE>
<P>
<DT>SDB2MC:
<DD> Combining two DS <b> B</b>, residing in main memory or on on sequential files, linearly.
<P>
<PRE>       SUBROUTINE SDB2MC(M,ALFA1D,NDSM1,NFB1,NIB1,
     +                     ALFA2D,NDSM2,NFB2,NIB2,NDSMS,NFBS,NIBS)
C AIM : CREATE ODS BS BY LINEARLY COMBINING THE TWO IDS, B1 AND B2
C ---   BS(J) &lt;= SUM ALFA1D(I,J) * B1(I) + SUM ALFA2D(I,J) * B2(I)
C                I=1,...,NDSM1              I=1,...,NDSM2
C       FOR J=1,...,NDSMS
</PRE>
<P>
<DT>SDB2MS:
<DD> Combine the two DS <b> B</b>, residing on direct access files, linearly.
<P>
<PRE>       SUBROUTINE SDB2MS(M,ALFA1D,NDSM1,NFB1,NIB1,
     +                     ALFA2D,NDSM2,NFB2,NIB2,NDSMS,NFBS,NIBS)
C AIM : CREATE ODS BS BY LINEARLY COMBINING THE TWO  IDS, B1 AND B2
C ---   BS(J) &lt;= SUM ALFA1D(I,J) * B1(I) + SUM ALFA2D(I,J) * B2(I)
C                I=1,...,NDSM1              I=1,...,NDSM2
C       FOR J=1,...,NDSMS
C       B1 AND B2 RESIDE ON DIRECT ACCESS FILES =&gt; BS ALSO
</PRE>
<P>
 </DL>
<P>

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