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 PROCESSING OPTION        (NIVO) :      3 PENALTY VALUE             (VTG) :    1.000000     INPUT D.S. NDL1            (NFNDL1 AND NINDL1) :      0     0 INPUT D.S. MUA             (NFMUAE AND NIMUAE) :    -14     0 INPUT D.S. B                   (NFBE AND NIBE) :    -15     1 INPUT D.S. BDCL            (NFBDCL AND NIBDCL) :     13     1 INPUT D.S. MUA             (NFMUAS AND NIMUAS) :    -14     0 OUTPUT D.S. B                  (NFBS AND NIBS) :    -15     1 &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; END OF MODULE CLIMPS  &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; MODULE CHOLPS :      PRECISION                    (EPS) :   0.1000000E-14 RETURN OPTION             (NENTRE) :     0 INPUT D.S. NDL1 (NFNDL1 ET NINDL1) :     0     0 INPUT D.S. MUA  (NFMUAE ET NIMUAE) :   -14     0 OUTPUT D.S. MUA (NFMUAS ET NIMUAS) :   -14     0 SP INITMP : NUMBER OF PAGES IN MAIN MEMORY :     35 ** FACTORISATION EXECUTION TIME               0.996348E+02 S ** END OF MODULE CHOLPC  &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; MODULE DRCHPS :      PROCESSING OPTION                     (NIVEAU) :      3 PRESENCE OF BOUNDARY CONDITIONS IN L.R. (NCLRL) :      0 INPUT D.S. NDL1            (NFNDL1 AND NINDL1) :      0     0 INPUT D.S. MUA             (NFMUAE AND NIMUAE) :    -14     0 INPUT D.S. B                   (NFBE AND NIBE) :    -15     1 INPUT D.S. BDCL            (NFBDCL AND NIBDCL) :     13     1 OUTPUT D.S. B                  (NFBS AND NIBS) :    -15     1 SP INITMP : NUMBER OF PAGES IN MAIN MEMORY :      2 ** SOLUTION EXECUTION TIME                    0.267583E+02 S ** &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;     PRINT OUT OF D.S. B    OF LEVEL  1 &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; TITLE                           :                                                                                  DATE AND USER'S NAME            : 09/07/93  pate                     DATA STRUCTURE TYPE             : B    LEVEL AND STATE NUMBER          :      1     2 NUMBER OF ASSOCIATED TABLES     :      0 TABLE  B 2 ---------- TYPE OF THE TABLE                           (NTYT) :      5 NUMBER OF INDICES AND THEIR MAX VALUES    (NIND..) :      2     1  2048 OPTION (1: PAGES OF SAME SIZE , 0: IF NOT)  (NCOD) :      1 NUMBER OF PAGES OF THE TABLE B4            (NBLOC) :      2 NUMBER OF NODES                              (NOE) :    937 NUMBER OF TABLES B4 IN THIS D.S.          (NBBLOC) :      1 CONSTANT NUMBER OF D.O.F. AT EACH NODE OR 0   (ND) :      3 NUMBER OF D.O.F. OR LENGHT OF A B4 PAGE     (NTDL) :   2811 STORAGE OPTION FOR B4                     (NCODSB) :     -1 TABLE  B 3  ----------  POINTER ON THE LAST ROW OF EACH PAGE OF B4     1           0     2        2048     3        2811 -- CREATE THE DATA  =-=  EXECUTE MODULE (DATA EXISTING)  =-=  END  =-=  ?    -                     -                                    ---F</PRE><P> <P><P> <H2><A NAME=SECTION05124000000000000000>1.2.4 Solution by frontal Cholesky</A></H2><P> <P><P> The optimization of memory space is accomplished by the frontal method, which manages this resource to the best, by storing only the indispensable rows of the linear system.<P> Main program <b> FRONXX</b> successively calls modules PREPAF and FRONT. The listing of the data of <b> FRONXX</b> is shown below:<P><PRE>                          mail                               $ FILE NAME                            1                              $     AND LEVEL OF THE D.S.      1     5     3                  $ NDSM  NTYP  ND tae                                $ FILE NAME                            1                              $     AND LEVEL OF THE D.S.      1                              $ 1 IF BOUNDARY CONDITIONS I.T.O.                                    $  LINEAR RELATIONS EXIST  bdcl                               $ FILE NAME                            1                              $     AND LEVEL OF THE D.S.  crochet.bfron                                  $ FILE NAME                            1                              $     AND LEVEL OF THE D.S.      3                              $ IMPREB      2                             $ INCREASE OF THE NUMBER OF FRONTS</PRE><P> The corresponding results are given below. Files <b> fron</b> and <b> gaus</b> are temporary files used by modules PREPAF and FRONT.<P><PRE>      M   M    OOO    DDDD    U   U   L       EEEEE   FFFFF MM MM   O   O   D   D   U   U   L       E       F M M M   O   O   D   D   U   U   L       EEEE    FFFF M   M   O   O   D   D   U   U   L       E       F M   M    OOO    DDDD     UUU    LLLLL   EEEEE   F    VERSION 93 DATE   : 15/06/93 AUTEUR : dutoit ***************************************************************** EXECUTION OF THE FRONTAL SOLUTION METHOD WITH SEQUENTIAL FILES ***************************************************************** -- CREATE THE DATA  =-=  EXECUTE MODULE (DATA EXISTING)  =-=  END  =-=  ?    -                     -                                    ---E -- NAME OF DATA FILE ? dfron.data_gb -- PRINT PARAMETER FOR THE EXECUTION ? 3 ++ OPEN(11,FILE='mail',SPEC='OLD,UNFORMATTED',RECL=0) ++ OPEN(12,FILE='tae',SPEC='OLD,UNFORMATTED',RECL=0) ++ OPEN(13,FILE='bdcl',SPEC='OLD,UNFORMATTED',RECL=0) ++ OPEN(14,FILE='crochet.bfron',SPEC='UNFORMATTED',RECL=0) ++ OPEN(15,FILE='',SPEC='SCRATCH,UNFORMATTED',RECL=0) ++ OPEN(16,FILE='',SPEC='SCRATCH,UNFORMATTED',RECL=0) &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; MODULE PREPAF :      MAXIMUM NUMBER OF NODES IN AN ELEMENT (NNOMAX)  :      8 CONSTANT NUMBER OF D.O.F. PER NODES (OR 0) (ND) :      3 MAXIMUM NUMBER OF D.O.F. AT A NODE     (NDLMAX) :      3 TOTAL NUMBER OF FRONTS                 (NTYPFR) :      1 NUMBER OF D.O.F. PER FRONT  :             FRONT NUMBER      1 :      3 NUMBER OF ELEMENTS :   1006 NUMBER OF NODES    :    937 NUMBER OF FRONTS   :      1 LENGTH OF FRONT EXPECTED ( FOR ANY TYPE OF FRONT ) :    937 FRONT NUMBER :      1  (NODES SUPPORTING   3 D.O.F.)  LENGTH OF FRONT :    242 NUMBER OF DEGREES OF FREEDOM OF SYSTEM         :   2811 NUMBER OF DEGREES OF FREEDOM OF FRONTAL SYSTEM :    726 SIZE OF NON-SYMMETRIC FRONTAL MATRIX           : 527076 SIZE OF SYMMETRIC FRONTAL MATRIX               : 263901 SIZE OF FRONTAL R.H.S.                         :    726 ** PREPARATION EXECUTION TIME                 0.166020E+01 S ** &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; END OF MODULE PREPAF  &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; MODULE FRONT  :      SOLUTION OF A SYMMETRIC SYSTEM  TOTAL NO OF ELEMENTSB    1006 TOTAL NUMBER OF NODES      937 RANK OF SYSTEM           726 NUMBER OF R.H.S.     1 ** RESOLUTION EXECUTION TIME                  0.780065E+03 S ** &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; END OF MODULE FRONT   &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;     PRINT OUT OF D.S. B    OF LEVEL  1 &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; TITLE                           :                                                                                  DATE AND USER'S NAME            : 06/05/93  pate                     DATA STRUCTURE TYPE             : B    LEVEL AND STATE NUMBER          :      1     0 NUMBER OF ASSOCIATED TABLES     :      0 TABLE  B 2 ---------- TYPE OF THE TABLE                           (NTYT) :      5 NUMBER OF INDICES AND THEIR MAX VALUES    (NIND..) :      2     1  2811 OPTION (1: PAGES OF SAME SIZE , 0: IF NOT)  (NCOD) :      1 NUMBER OF PAGES OF THE TABLE B4            (NBLOC) :      1 NUMBER OF NODES                              (NOE) :    937 NUMBER OF TABLES B4 IN THIS D.S.          (NBBLOC) :      1 CONSTANT NUMBER OF D.O.F. AT EACH NODE OR 0   (ND) :      3 NUMBER OF D.O.F. OR LENGHT OF A B4 PAGE     (NTDL) :   2811

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