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<P>
<DL COMPACT><DT>Aim:
<DD> Impose the boundary conditions<A NAME=1550>&#160;</A> of prescribed value or linear 
relation  type.
<P>
<DT>Utilization:
<DD>  
<P>
<UL><LI> dimension array M (in the blank common),
<LI> call  INITI,
<LI> create the input data structures MUA and B (and eventually NDL1).
</UL>
(e.g execute module PREPAC, then modules ASSMUA and ASEMBV, to create 
structures MUA and B)
<P>
Call the module:
<P>
<PRE>  
      CALL CLIMPC(M,NIVO,VTG,NFNDL1,NINDL1,
     +            NFMUAE,NIMUAE,NFBE,NIBE,NFBDCL,NIBDCL,
     +            NFMUAS,NIMUAS,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array,
<LI> NIVO: the type of boundary conditions imposed:
      <UL><LI>  if NIVO = 0, the boundary conditions 
        affect matrix <b>A</b> only, and have the form <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img37.gif">,
       <LI> if NIVO = 1, the boundary conditions affect the RHS only, and have the form
        <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img38.gif">,
       <LI>  if NIVO = 2, the boundary conditions affect <b>A</b> and <b>B</b>, 
     and have the form <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img39.gif"> 
    and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img40.gif">,
    <LI> if NIVO = 3, the boundary conditions affect
    <b>A</b> and <b>B</b>, and are applied as follows:
    <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img37.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img38.gif"> for all prescribed degrees of freedom <b>i</b>, then for all  
     <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img41.gif"> for <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img42.gif">, 
     <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img43.gif">, and finally, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img44.gif">,
    <LI> if NIVO = 4, the boundary conditions affect
    only <b>A</b>, and have the form <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img45.gif">.
    </UL>
<LI> VTG: multiplication value for the diagonal coefficients with prescribed degrees of freedom,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFMUAE:  the number of the support file of I.D.S.  MUA,
<LI> NIMUAE: its level number,
<LI> NFBDCL: the number of the support file of I.D.S. BDCL,
<LI> NIBDCL: its level number,
<LI> NFBE: the number of the support file of I.D.S. B,
<LI> NIBE: its level number,
<LI> NFMUAS: the number of the support file of O.D.S. MUA,
<LI> NIMUAS: its level number (the O.D.S. can be distinct from the I.D.S.).
<P>
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION04128000000000000000>1.2.8 CLIMPS: boundary conditions</A></H2>
<P>
<DL COMPACT><DT>Aim:
<DD> Impose the boundary conditions<A NAME=1570>&#160;</A> of prescribed value or linear relation type.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures MUA and B (and eventually NDL1).
</UL>
(eg execute module PREPAC, then modules ASMAPS and ASMBMS, to create 
structures MUA and B.)
<P>
Call the module:
<P>
<PRE>  
      CALL CLIMPS(M,NIVO,VTG,NFNDL1,NINDL1,
     +            NFMUAE,NIMUAE,NFBE,NIBE,NFBDCL,NIBDCL,
     +            NFMUAS,NIMUAS,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M:  the super array,
<LI> NIVO: the type of boundary conditions imposed:
<UL><LI>  if NIVO = 0, the boundary conditions 
        only affect matrix <b>A</b>, and have the form <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img37.gif">,
       <LI> if NIVO = 1, the boundary conditions only affect the RHS, and have the form
        <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img38.gif">,
       <LI>  if NIVO = 2, the boundary conditions affect <b>A</b> and <b>B</b>, 
     and have the form <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img39.gif"> 
    and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img40.gif">,
    <LI> if NIVO = 3, the boundary conditions affect
    <b>A</b> and <b>B</b>, and are applied as follows:
    <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img37.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img38.gif"> for all prescribed degrees of freedom <b>i</b>, then for all  
     <b>k</b> such that <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img42.gif">, 
     <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img43.gif">, and finally, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img44.gif">,
    <LI> if NIVO = 4, the boundary conditions affect
    only <b>A</b>, and have the form <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img45.gif">.
</UL>
<LI> VTG: multiplication value for the diagonal coefficients with prescribed degrees of freedom,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFMUAE:  the number of the support file of I.D.S.  MUA (always <b>&lt;</b> 0), 
<LI> NIMUAE: its level number,
<LI> NFBDCL: the number of the support file of I.D.S. BDCL,
<LI> NIBDCL: its level number,
<LI> NFBE: the number of the support file of I.D.S. B (always <b>&lt;</b> 0),
<LI> NIBE: its level number,
<LI> NFMUAS: the number of the support file of O.D.S. MUA (always <b>&lt;</b> 0),
<LI> NIMUAS: its level number (the O.D.S. can be distinct from the I.D.S.).
<DL COMPACT><DT>Note:
<DD> If  NFMUAE and NFMUAS (resp. NFBE and NFBS) are  distinct, 
the number of words in their pages must be equal!
<P>
 </DL></UL> 
 </DL>
<P>
<H2><A NAME=SECTION04129000000000000000>1.2.9 CONDL1: construction of NDL1</A></H2>
<P>
<A NAME=condl1>&#160;</A>
<P>
<DL COMPACT><DT>Aim:
<DD> Construct D.S. NDL1 using D.S. MAIL. The algorithms described in this guide perform a call
to function NDL<A NAME=1593>&#160;</A>, to assign the number of the last degree of freedom
associated with node I to NDL(I+1) (with NDL(1)=0). 
To initialize this function, the module performs a call to  function LRNDL1, and then
<UL><LI> if the number of degrees of freedom at each node ND is constant,
    NDL(I+1) = I * ND
   <LI> if not NDL(I+1), the number of the last degree of freedom associated with node I, is stored in
    D.S.  NDL1
</UL>
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
</UL>
<P>
Call the module:
<P>
<PRE>  
      CALL CONDL1(M,NNSEG,NFMAIL,NIMAIL,NFNDL1,NINDL1,LNOET,
     +            NNOMAX,ND,NDLMAX)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array,
<LI> NNSEG: the number of nodes per segment of NDL1 (if it is initialized to a very large number, it contains the
number of nodes + 1 on exit),
<LI> NFMAIL:  the number of the support file of I.D.S. MAIL,
<LI> NIMAIL: its level number,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1:  its level number,
</UL>
<P>
On exit the module returns:
<UL><LI> LNOET: the total number of nodes of element types,
<LI> NNOMAX: the maximum number of nodes among all the element types,
<LI> ND: the number of degrees of freedom at each node, if constant (0 if not),
<LI> NDLMAX: the maximum number of degrees of freedom at any node
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION041210000000000000000>1.2.10 CROUPC: Crout factorization</A></H2>
<P>
<DL COMPACT><DT>Aim:
<DD> Performs the Crout factorization<A NAME=1605>&#160;</A>, in main memory,
of a symmetric matrix <b>A</b><A NAME=1606>&#160;</A>, already assembled in a MUA structure.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structure MUA  (and eventually NDL1).
</UL>
(eg  execute module PREPAC, then module ASSMUA to create 
the input data structure MUA)
<P>
Call the module:
<P>
<PRE>  
      CALL CROUPC(M,EPS,NENTRE,NFNDL1,NINDL1,NFMUAE,
     +            NIMUAE,NFMUAS,NIMUAS,NRETOU)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array,
<LI> EPS: <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img46.gif">, the minimum value accepted for a pivot <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img47.gif"> according to the criterion
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img48.gif">,
<LI> NENTRE: if NENTRE = 0 the module returns to the calling program as soon as a pivot is smaller that
 the absolute value of EPS, or continue the computations if  NENTRE = 1,
<LI> NFNDL1:  the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFMUAE:  the number of the support file of I.D.S.  MUA,
<LI> NIMUAE: its level number,
<LI> NFMUAS:  the number of the support file of O.D.S. MUA,
<LI> NIMUAS: its level number (the O.D.S. can be identical to the I.D.S. (NIMUAS = NIMUAE), 
or distinct (NIMUAS <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img3.gif"> NIMUAE)),
<LI> NRETOU: output parameter: NRETOU = 1 if at least one pivot was judged too small,
 NRETOU = 0 if not.
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION041211000000000000000>1.2.11 DRCHPC: Cholesky forward- and backsubstitution</A></H2>
<P>
<A NAME=1616>&#160;</A>
<P>
<DL COMPACT><DT>Aim:
<DD> Performs  the solution of a linear system in main memory, using Cholesky factorization.
The lower triangular matrix  <b>L</b>  is already stored in 
structure MUA.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures MUA and B (and eventually NDL1),
<LI> execute module CHOLPC, to perform the Cholesky factorization of matrix <b>A</b>:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img49.gif"></UL>
<P>
Call the module:
<P>
<PRE>  
      CALL DRCHPC(M,NIVEAU,NCLRL,NFNDL1,NINDL1,
     +            NFMUA,NIMUA,NFBE,NIBE,
     +            NFBDCL,NIBDCL,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array,
<LI> NIVEAU: the type of solution chosen:
<UL><LI>  if NIVEAU = 0, only the backward substitution  <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img50.gif"> is performed,
    <LI>  if NIVEAU = 1, only the forward substitution <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img51.gif"> is performed,
    <LI>  if NIVEAU <b>&gt;</b> 1, the complete solution <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img52.gif"> is performed,
</UL>
<LI> NCLRL: the number of boundary conditions in linear relations,
<LI> NFNDL1:  the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFMUA: the number of the support file of I.D.S.  MUA,
<LI> NIMUA: its level number,
<LI> NFBDCL: the number of the support file of I.D.S.   BDCL,
<LI> NIBDCL:  its level number,
<LI> NFBE: the number of the support file of I.D.S. B (containing the RHS),
<LI> NIBE:  its level number,
<LI> NFBS:  the number of the support file of O.D.S. B (containing the solution),
<LI> NIBS:  its level number,
<DL COMPACT><DT>Note:
<DD> If NIBS = NIBE, the solution overwrites the RHS !
<P>
 </DL></UL> 
 </DL>
<P>
<H2><A NAME=SECTION041212000000000000000>1.2.12 DRCRPC: Crout forward- and backsubstitution</A></H2>
<P>
<A NAME=1628>&#160;</A>
<P>
 <DL COMPACT><DT>Aim:
<DD> Performs  the solution of a linear system in main memory, using Crout factorization.
The lower triangular matrix  <b>L</b> and the diagonal <b>D</b> are already stored in 
structure MUA.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures MUA and B (and eventually NDL1),
<LI> execute module CROUPC, to perform the Crout factorization of matrix <b>A</b>:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img53.gif"></UL>
<P>
Call the module:
<P>
<PRE>  
      CALL DRCRPC(M,NIVEAU,NCLRL,NFNDL1,NINDL1,
     +            NFMUA,NIMUA,NFBE,NIBE,
     +            NFBDCL,NIBDCL,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array,
<LI> NIVEAU: the type of solution chosen:
<UL><LI>  if NIVEAU = 0, only the backward substitution  <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img50.gif"> is performed,
    <LI>  if NIVEAU = 1, only the forward substitution <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img51.gif"> is performed,
    <LI>  if NIVEAU = 2, the forward substitution <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img54.gif"> is performed,