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2.3 Manipulation of a D.S. B resulting from a transient problem

The solution of a parabolic problem by a variable time-step method leads to computation of the solutions at times a priori unknown. The aim of module INTERQ is therefore to interpolate these solutions to obtain a B structure containing the solutions at those times selected.

      SUBROUTINE INTERQ(M,XM,NQ,NFB,NIB,PAS,NPAS,T0,TSAV,NFBS,NIBS)
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C   SUBROUTINE INTERQ  . SINGLE PRECISION
C   AIM  : INTERPOLATE TO THE ORDER NQ THE SOLUTIONS RESULTING FROM
C          EVO*GE(RK)
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

where

• M and XM represent the super array,
• NQ is the order of interpolation, it also encodes the manner in which the solutions is saved:
  • 1 NQ 10: interpolation of the order NQ and saves the solution at a specific time TSAV,
  • 11 NQ 20: interpolation of the order NQ - 10 and saves the solution at all time steps,
• NFB, NIB are the file numbers and the level of structure B resulting from the transient module,
• PAS is the time step,
• NPAS is the number of time steps (initial solution included),
• T0 is the initial time,
• TSAV is not used if NQ > 10, otherwise it is the time at which we want to save the solution. The value of time, obtained after T0, PAS and NPAS, is defined by:
  

• NFBS, NIBS are the file number and level of structure B on exit.

The solution of a parabolic problem by an arbitrary method can, in certain cases, lead to computing the solutions in two overlapping time intervals and . The aim of module UNIONB is therefore to form a solution in the interval by removing the intersection.

Several options are available. To describe them, let us consider the following example:

• the first structure B contains the solutions at times
  
  while an associated array contains the values of
• the second structure contains the solutions at times
  
  while an associated array contains the values of

• the concatenated structure contains the solutions at times:
  
  if we choose the truncation option in increasing order. Its associated array contains the values of all these times.
• the concatenated structure contains the solutions at times:
  
  if we choose the truncation option in decreasing order. Its associated array contains the values of all these times.
• the concatenated structure contains the solutions placed end-to-end, if this option is chosen

Preprocessor UNIOXX calls module UNIONB which performs the concatenation.

     

      SUBROUTINE UNIONB(M,XM,NFB1,NIB1,NFB2,NIB2,JOPTIO,NFBS,NIBS)
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C   SUBROUTINE UNIONB  . SINGLE PRECISION
C   AIM  : GLUE TOGETHER 2  I.D.S. B INTO A SINGLE O.D.S. B
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

where

• M and XM represent the super array,
• NFB1, NIB1 are the file number and level of the first B structure,
• NFB2, NIB2 are the file number and level of the second B structure,
• JOPTIO is the truncation option:

  0

  : place end-to-end

  1

  : increasing order according to the last associated array,

  2

  : decreasing order according to the last associated array,

• NFBS, NIBS are the file number and level of the output structure B.