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<DL COMPACT><DT>Aim:
<DD> Perform the incomplete Cholesky or Crout factorization<A NAME=1827>&#160;</A>
<A NAME=1828>&#160;</A>, in main memory, of a symmetric matrix <b>A</b>, already 
assembled in structure MUA.
Depending on the option chosen by the user, the module performs an incomplete Cholesky or Crout factorization.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures AMAT and B (and eventually BDCL and NDL1),
</UL>
<P>
Call the module:
<P>
<PRE> 
            CALL FANIGC(M,NIVEAU,NFACTO,
     +                  NFAMAT,NIAMAT,NFAMAP,NIAMAP,NBPIVO)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array,
<LI> NIVEAU: the level of incomplete factorization (always <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img64.gif">) (the higher the level, 
the more the matrix is filled), if NIVEAU is sufficiently large an exact factorization is obtained.
<LI> NFACTO: factorization option of the  matrix of I.D.S. AMAT,
<UL><LI>  if NFACTO = 1, incomplete Cholesky factorization,
<LI>  if NFACTO = 2, incomplete Crout factorization,
</UL>
<LI> NFAMAT: the number of the support file of I.D.S.  AMAT (the system matrix),
<LI> NIAMAT: its level number,
<LI> NFAMAC: the number of the support file of O.D.S. AMAT (the preconditioned matrix),
<LI> NIAMAC: its level number,
<LI> NBPIVO: the number of incorrect pivots (replaced by their predecessors)
</UL>
<P>
<DT>Remark:
<DD> This module replaces FAINGC. Note that there are additional parameters. The old version, 
FANIGC, corresponds to  <b> NIVEAU=0 </b>.
<P>
 </DL>
<P>
<H2><A NAME=SECTION04219000000000000000>2.1.9 GCDIAG: preconditioned conjugate gradient</A></H2>
<P>
<DL COMPACT><DT>Aim:
<DD>  Solve a linear system by conjugate gradient iterations with diagonal preconditioning
<A NAME=1838>&#160;</A>, when matrix <b>A</b> is symmetric positive definite.
Only the matrix of the linear system must be stored  in a AMAT structure, while the 
preconditioning matrix is determined by the program.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures AMAT and B (and eventually BDCL and NDL1),
</UL>
<P>
Call the module:
<P>
<PRE> 
      CALL GCDIAG(M,EPS,NOMTA0,NFNDL1,NINDL1,
     +            NFBE,NIBE,NFAMAT,NIAMAT,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array, 
<LI> EPS:  the convergence threshold  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img46.gif">, according to the criterion:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img68.gif">
<LI> NOMTA0: the name of the array containing vector X0, to initialize the preconditioned conjugate gradient 
algorithm,  if this array does not exist <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img69.gif"> is initialized to 0,
<LI> NFNDL1: the number of the support file of I.D.S.  NDL1,
<LI> NINDL1: its level number,
<LI> NFBE: the number of the support file of I.D.S.  B (the RHS),
<LI> NIBE: its level number,
<LI> NFAMAT: the number of the support file of I.D.S.  AMAT (the system matrix),
<LI> NIAMAT: its level number,
<LI> NFBS: the number of the support file of O.D.S.  B (the solution),
<LI> NIBS: its level number.
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION042110000000000000000>2.1.10 ICHRGC: preconditioned conjugate gradient</A></H2>
<P>
<DL COMPACT><DT>Aim:
<DD>  Solve a linear system by conjugate gradient iterations with  preconditioning,
 when matrix <b>A</b> is symmetric positive definite.
The matrix of the linear system and the preconditioning matrix  are already stored in a AMAT structure.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structure AMAT of the matrix of the linear system
(using module ASSAMA), and that of the preconditioner (using module FANIGC),
and then data structure B (and eventually BDCL and NDL1).
</UL>
<P>
Call the module:
<P>
<PRE> 
      CALL ICHRGC(M,EPS,NOMTA0,NCLRL,
     +            NFBDCL,NIBDCL,NFNDL1,NINDL1,
     +            NFBE,NIBE,NFAMAC,NIAMAC,
     +            NFAMAT,NIAMAT,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array, 
<LI> EPS:  the convergence threshold  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img46.gif">, according to the criterion:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img70.gif">
<LI> NOMTA0: the name of the array containing vector X0, to initialize the preconditioned conjugate gradient 
algorithm,   if this array does not exist <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img69.gif"> is initialized to 0,
<P>
<LI> NCLRL: number of boundary conditions i.t.o. linear relations,
<LI> NFBDCL: the number of the support file of I.D.S. BDCL,
<LI> NIBDCL: its level number,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFBE:  the number of the support file of I.D.S. B (the RHS),
<LI> NIBE: its level number,
<LI> NFAMAC: the number of the support file of I.D.S. AMAC (the preconditioning matrix),
<LI> NIAMAC: its level number,
<LI> NFAMAT: the number of the support file of I.D.S. AMAT (the system matrix),
<LI> NIAMAT: its level number,
<LI> NFBS: the number of the support file of O.D.S. B (the solution),
<LI> NIBS: its level number.
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION042111000000000000000>2.1.11 PREPGC: computation of pointers for AMAT</A></H2>
<P>
<A NAME=1853>&#160;</A>
<P>
<DL COMPACT><DT>Aim:
<DD> Determine pointers AMAT3 and AMAT4, and AMAT5, of the data structure AMAT, 
 and compute the memory space required to store matrix <b>A</b>.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structure NOPO and, eventually,  NDL1 and BDCL.
<P>
</UL>
<P>
Call the module:
<P>
<PRE>  
      CALL PREPGC(M,ND,NCODSA,NTY,NCLRL,NFBDCL,NIBDCL,
     +            NFNDL1,NINDL1,NFNOPO,NINOPO,
     +            NFAMAT,NIAMAT,NTAMAT,MCAMAT)
</PRE>
<P>
where:
<P>
<UL><LI> M:  the super array,
<LI> ND: the number of degrees of freedom at each node, if constant (0 if not)
<LI> NCODSA: the matrix storage code,
<LI>NCODSA  <b>&gt;</b> 0: symmetric storage of the lower triangular part,
<LI>NCODSA  = 0:  diagonal storage of the matrix assumed diagonal,
<LI>NCODSA  <b>&lt;</b> 0: non-symmetric storage of the entire matrix,
<LI> NTY: the type of arrays AMAT6 and  B4 to assemble,
<LI> NCLRL : the number of boundary conditions i.t.o. linear relations,
<LI> NFBDCL: the number of the support file of I.D.S. BDCL,
<LI> NIBDCL: its level number,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFNOPO: the number of the support file of I.D.S. NOPO,
<LI> NINOPO: its level number,
<LI> NFAMAT: the number of the support file of O.D.S.  AMAT,
<LI> NIAMAT: its level number,
<LI> NTAMAT: the number of associated arrays,
<LI> MCAMAT: the number of words in structure AMAT.
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION042112000000000000000>2.1.12 SIMPGC: non-preconditioned conjugate gradient</A></H2>
<P>
<DL COMPACT><DT>Aim:
<DD>  Solve a linear system by conjugate gradient iterations <b> without</b>  preconditioning,
 when matrix <b>A</b> is symmetric positive definite.
The matrix of the linear system must be stored in a symmetric AMAT structure.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures  AMAT and B (and eventually BDCL and NDL1).
</UL>
<P>
Call the module:
<P>
<PRE>     
      CALL SIMPGC(M,EPS,NOMTA0,NCLRL,
     +            NFBDCL,NIBDCL,NFNDL1,NINDL1,
     +            NFBE,NIBE,NFAMAT,NIAMAT,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array, 
<LI> EPS:  the convergence threshold  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img46.gif">, according to the criterion:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img68.gif">
<LI> NOMTA0: the name of the array containing vector X0, to initialize the conjugate gradient 
algorithm,  if this array does not exist <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img69.gif"> is initialized to 0,
<P>
<LI> NCLRL: number of boundary conditions i.t.o. linear relations,
<LI> NFBDCL: the number of the support file of I.D.S. BDCL,
<LI> NIBDCL: its level number,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFBE:  the number of the support file of I.D.S. B (the RHS),
<LI> NIBE: its level number,
<LI> NFAMAT: the number of the support file of I.D.S. AMAT (the system matrix),
<LI> NIAMAT: its level number,
<LI> NFBS: the number of the support file of O.D.S. B (the solution),
<LI> NIBS: its level number.
</UL> 
 </DL>
<P>
<H2><A NAME=SECTION042113000000000000000>2.1.13 SSORGC: preconditioned conjugate gradient</A></H2>
<P>
<DL COMPACT><DT>Aim:
<DD>  Solve a linear system by conjugate gradient iterations with SSOR preconditioning,
 when matrix <b>A</b> is symmetric positive definite.
Only the  matrix of the linear system must be stored in a AMAT structure, while the preconditioning
matrix is determined by the program, without an increase in memory space.
<P>
<DT>Utilization:
<DD>  
<UL><LI> dimension array M (in the blank common),
<LI> call INITI,
<LI> create the input data structures AMAT and B
 (and eventually BDCL and NDL1).
</UL>
<P>
Call the module:
<P>
<PRE> 
      CALL SSORGC(M,OMEGA,EPS,NOMTA0,NCLRL,
     +            NFBDCL,NIBDCL,NFNDL1,NINDL1,
     +            NFBE,NIBE,NFAMAT,NIAMAT,NFBS,NIBS)
</PRE>
<P>
where:
<P>
<UL><LI> M: the super array, 
<LI> OMEGA: the relaxation parameter:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img71.gif">
<LI> EPS:  the convergence threshold  <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img46.gif">, according to the criterion:
<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img68.gif">
<LI> NOMTA0: the name of the array containing vector X0, to initialize the preconditioned conjugate gradient 
algorithm,   if this array does not exist <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img69.gif"> is initialized to 0,
<P>
<LI> NCLRL: number of boundary conditions i.t.o. linear relations,
<LI> NFBDCL: the number of the support file of I.D.S. BDCL,
<LI> NIBDCL: its level number,
<LI> NFNDL1: the number of the support file of I.D.S. NDL1,
<LI> NINDL1: its level number,
<LI> NFBE:  the number of the support file of I.D.S. B (the RHS),
<LI> NIBE: its level number,
<LI> NFAMAT: the number of the support file of I.D.S. AMAT (the system matrix),
<LI> NIAMAT: its level number,
<LI> NFBS: the number of the support file of O.D.S. B (the solution),
<LI> NIBS: its level number.
</UL> 
 </DL>
<P>
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