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1.4 DS BDCL

1.4.1 Contents

This DS is used to store information regarding the boundary conditions, which can be of two types:

• Value prescribed to a degree of freedom (Dirichlet):
• Linear relation constraining some degrees of freedom:
  

There are four description types possible to define the constraints. Each consists of a description of the nodes and degrees of freedom which must be constrained.

DS BDCL is composed of seven arrays of predefined order.

Array BDC0:

General information.

This integer array contains 32 variables, consisting of a general description of the job (title, date, name), of DS BDCL (type, level, ...), and indicates the presence or absence of array BDC1.

1:20 TITRE

the job title in 20 words of 4 characters,

21:22 DATE

the date of creation in 2 words of 4 characters,

23:28 NOMCRE

the creator's name in 6 words of 4 characters,

29 'BDCL'

the DS type,

30 NIVEAU

the DS level,

31 ETAT

a reserved parameter,

32 NTACM

the number of supplementary arrays associated with the DS
(they are described in array BDC1).

Array BDC1:

Description of any supplementary arrays.

This array is analogous to array B1 of DS B (see this DS).

Array BDC2:

General description of the constraints.

This integer array contains 8 values.

1 NTYP

the constraint coefficient type,

2 NCART

the number of data items describing prescribed constraints such as value,

3 NCLRL

the number of linear relations to describe,

4 NOPTFI

storage option:

• NOPTFI = 0: the 4 arrays, BDC3, BDC4, BDC5 and BDC6, are in M.M.
• NOPTFI = 1: a file will be used.
  

5 NMOT3

the number of words necessary to store array BDC3,

6 NMOT4

the number of words necessary to store array BDC4,

7 NMOT5

the number of words necessary to store array BDC5,

8 NMOT6

the number of words necessary to store array BDC6.

Array BDC3:

Description of the data type for the constraints per degree of freedom.

This integer array, NMOT3 long, contains:

• if NOPTFI = 0: Loop from 1 to NCART

  NTYCAR

  the data type number (1, 2, 3 or 4),

  • 1: constraint at node i of degree of freedom l
  • 2: constraint from node i to node j with step of degree of freedom l
  • 3: constraint at node i of degrees of freedom l to m with step
  • 4: constraint from node i to node j with step of degrees of freedom l to m with step

  DCART

  the data description (i.e. 2, 4, 4 or 6 integers),

  • if NTYCAR = 1: node number i and degree of freedom number l
  • if NTYCAR = 2: node numbers i and j, the step and the degree of freedom number l.
  • if NTYCAR = 3: node number i followed by the degree of freedom numbers l and m and the step
  • if NTYCAR = 4: node numbers i and j and the step followed by the degree of freedom numbers l and m and the step

  End of loop

• if NOPTFI = 1, the array contains one description:

  NTYCAR

  the data type number (1, 2, 3 or 4),

  DCART

  the data description (i.e., 2, 4, 4 or 6 integers),

Array BDC4:

Prescribed values at degrees of freedom.

This NTYP type array is NMOT4 long and contains:

• if NOPTFI = 0:

  the NCART prescribed values

• if NOPTFI = 1:

  The prescribed value of the data card under consideration. In this case BDC3 and BDC4 are read sequentially on file, the first array indicating the data type and the type of data description, followed by the second array giving the corresponding prescribed value.

If NCLRL = 0, arrays BDC5 and BDC6 do not exist. If not, they function, depending on the value of NOPTFI, as described below.

Array BDC5:

Description of constraints in linear relations.

This integer array contains NMOT5 words:

• if NOPTFI = 0: Loop from 1 to NCLRL

  N(i)

  the number of terms in linear relation i, and for each term, therefore for j=1,N(i) :

  NOEUD(j)

  the node number

  NDLI(j)

  the local degree of freedom number

  End of loop

• if NOPTFI = 1, the array contains one definition:

  N

  the number of terms in the linear relation, and for each term (j=1,N):

  NOEUD(j)

  the node number

  NDLI(j)

  the local degree of freedom number

Array BDC6:

Coefficient values in the linear relations.

This NTYP type array contains the coefficient values of the linear combinations:

• if NOPTFI = 0: Loop from 1 to NCLRL

  ALPHA(i)

  the RHS of linear relation i, and for each term, therefore for j=1,N(i):

  V(j)

  the value of coefficient j in the relation

  End of loop

• if NOPTFI = 1, the array contains one definition:

  ALPHA

  the RHS of the linear relation, and for each term, therefore for j=1,N:

  V(j)

  the value of coefficient j of the relation. In this case, BDC5 and BDC6 are read sequentially on file and function in a synchronized manner.

1.4.2 Corresponding tools

Reading and writing a DS BDCL

A DS, residing in main memory, is written in secondary memory on a sequential access file.

This is a category 1 DS if NOPTFI = 0, and a category 2 DS if NOPTFI = 1. In the first case, all the arrays are generated automatically, and in the second case, only the 3 first arrays as well as any associated arrays (described in array BDC1) are read (module SDLECT) or written (module SDECRI):

• when reading, arrays 4 to 6 are only addressed and the read is performed by the program via a READ command.
• when writing, they are transfered via a WRITE command.

Remark:

When NOPTFI=1 and NCART or NCLRL are non-zero, the arrays are stored in the following form:

• arrays 3 and 4:
  • NTYCAR = 1: LE, 3, NTYCAR, NOEUD1, DL1, L4, V
  • NTYCAR = 2: LE, 5, NTYCAR, NOEUD1, NOEUD2, NOEUD3, DL1, L4, V
  • NTYCAR = 3: LE, 5, NTYCAR, NOEUD1, DL1, DL2, DL3, L4, V
  • NTYCAR = 4: LE, 7, NTYCAR, NOEUD1, NOEUD2, NOEUD3, DL1, DL2, DL3, L4, V

where LE is the number of words which follow, and L4 is the number of words of value V.

• arrays 5 and 6:
  • LE, L5, N, ((NOEUD(J),NDL(J)),J=1,N), L6, ALPHA, (V(J),J=1,N)

where LE is the number of words which follow, L5 = 2N+1 and L6 is the number of words of prescribed values.

Printing a DS BDCL

The contents (total or partial) of a DS BDCL can be printed by module IMBDCL. Preprocessor IMAGXX is used if a conversational call of IMBDCL is desired.

Creation and manipulation modules of a DS BDCL

DS BDCL is created using a DS MAIL, and sometimes a DS COOR, for example via modules COBDCL, etc.

1.4.3 Remark regarding the linear relation conditions

This type of condition, written in the simplified form as:

leads to the change of variables:

and thus the prescription of this value to .

The system, which is written as follows:

where A is the system matrix and b the right-hand-side vector, now becomes:

after the change of variables of matrix P.

Whether or not the solution of is possible, depends on the solution method chosen. Note that the skyline of the matrix is significantly modified by this type of relation, which may consequently cause problems when using a frontal solution method.