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1.8 DS MAIL

1.8.1 Contents

This DS stores two- or three-dimensional meshes, as well as information regarding the finite element interpolation chosen. It corresponds to an element by element mesh description and an interpolation description for the unknown type.

DS MAIL is composed of 22 arrays or predefined order.

Array MAI0:

General information.

This integer array contains 32 variables, consisting of a general description of the job (title, date, name), of DS MAIL (type, level, ...), and indicates the presence or absence of array MAI1.

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 'MAIL'

the DS type,

30 NIVEAU

the DS level,

31 ETAT

a reserved parameter,

32 NTACM

the number of supplementary arrays
(they are described in array MAIL).

Array MAI1:

Description of any supplementary arrays.

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

Array MAI2:

General description.

This integer array contains 12 values.

1 NDIM

the space dimension (2 or 3),

2 NINCFV

the number of unknowns of the variational formulation,

3 NTYELM

the number of finite element types,

4 NDSR

the maximum of the reference numbers,

5 NTYNOE

the number of node types,

6 NTYPOI

the number of point types,

7 NCACAR

1 if the points have other characteristics than their coordinates,
0 if not,

8 NCOPNP

1 if the nodes coincide everywhere with the points, 0 if not,

9 MAXT

the maximum number of geometric element types (see below); used to dimension array MAI3

10 NMMAM

the maximum number of words necessary to store all the information pertaining to an element,

11 LMAIL

the size of array MAIL,

12 NOPFI

file write option.

Array MAI3:

The list of finite element types.

This integer and character array contains 4 + 4.MAXT.NDSD values.

1 NE

the number of elements,

2 NOE

the number of nodes,

3 NP

the number of points,

4 NDSD

the maximum of the sub-domain numbers.

• Loop i from 1 to NDSD
  • ICODEL(1:2,1:2*MAXT,i) the element name (in 2 words) of geometric type J (see below) for sub-domain i
  End of loop i

There are 16 types possible for the usual geometries, corresponding to:

• 1 and 2: node - node
• 3 and 4: straight segment - curved segment
• 5 and 6: straight triangle - curved triangle
• 7 and 8: straight quadrilateral - curved quadrilateral
• 9 and 10: straight tetrahedron - curved tetrahedron
• 11 and 12: straight pentahedron - curved pentahedron
• 13 and 14: straight hexahedron - curved hexahedron
• 15 and 16: straight super element - curved super element

The other types (17 to ...) correspond to particular elements:

• ... (particular elements).

Array MAI4:

The physical significance of the variational unknowns.

This integer array contains NINCFV times 4 words (of 4 characters) representing this signification.

Array MAI5:

Number of unknowns per type of nodes.

This integer array contains NTYNOE words:

• MAI5(i), the number of unknowns of node type i

Array MAI6:

Unknown numbers.

This integer array contains MAI5(i) words:

• MAI6(j), the number of unknowns j

Array MAI7:

Number of degrees of freedom per unknown.

This integer array contains MAI5(i) words:

• MAI7(j), the number of degrees of freedom of unknown j

Array MAI8:

The mnemonic code corresponding to the degree of freedom.

This integer array contains MAI7(i) words:

• MAI8(j), the mnemonic code corresponding to degree of freedom j

The codes are the following;

• 1: VN: nodal value
• 2: DX: X derivative at a node
• 3: DY: Y derivative at a node
• 4: DZ: Z derivative at a node
• 5: DTG: derivative tangential to an edge or face at a node
• 6: DDXX: second derivative with respect to X at a node
• 7: DDYY: second derivative with respect to Y at a node
• ... (see subroutine MNEMO below)

Array MAI9:

Number of mnemonics per point type.

This integer array contains NTYPOI words:

• MAI9(i), the number of mnemonics of point type i

Array MAIA:

The mnemonic number per point type.

This integer array contains MAI9(i) words:

• MAIA(i), the mnemonic code of point type i (see MAI8 or MNEMO),

Array MAIB:

Libraries and finite elements.

This integer and character array contains 4 NTYELM words:

• MAIB(1,i), the library name of a type i finite element
• MAIB(2,i), the first word of the name of a type i finite element
• MAIB(3,i), the second words of the name of a type i finite element
• MAIB(4,i), the code number of a type i finite element.

Array MAIC:

Geometry of the finite element types.

This integer array contains NTYELM words:

• MAIC(i), the geometric code of a type i finite element

This code is described in DS NOPO (3: triangle, 4: quadrangle, etc.).

Array MAID:

Number of nodes per finite element type.

This integer array contains NTYELM words:

• MAID(i), the number of nodes of a finite element of type i

Array MAIE:

Number of points per finite element type.

This integer array contains NTYELM words:

• MAID(i), the number of points of type i finite element

Array MAIF:

The number of associated arrays per finite element type.

This integer array contains NTYELM words:

• MAIF(i), the number of arrays for finite element type i

Array MAIG:

Pointer in MAIJ.

This integer array contains NTYELM words:

• MAIG(i), address in MAIJ of the words preceding the nodal type numbers of a type i finite element

Array MAIH:

Pointer in MAIJ.

this integer array contains NTYELM words:

• MAIG(i), address in MAIJ of the word preceding the point type numbers of a type i finite element

Array MAII:

Pointer in MAIJ.

this integer array contains NTYELM words:

• MAII(i), address in MAIJ of the first word describing the arrays associated with a type i finite element

remark:

These addresses are relative to the beginning of array MAIJ.

Array MAIJ:

Pointer in MAIK and description of the associated arrays.

This integer array contains:

• Loop i from 1 to NTYELM
  • address in array MAIK of the first coordinate of the first node of the i-th type element
  • Loop j from 1 to MAID(i)
    • node j type
    End of loop j

  • address in array MAIK of the first coordinate of the first point of the i-th type element
  • loop j from 1 to MAIE(i)
    • point j type
    End of loop j
  • if MAIF(i) = 0, go to the end of element type loop
  • Loop j from 1 to MAIF(i)
    • array type
    • number of indices
    • maximum value of each index
    End of loop j
  End of loop i

LMAIJ, the length of array MAIJ, equals the number of words required to store all this information. In the file, this value can be recuperated as each record starts with the number of words which follow.

Array MAIK:

Point and node coordinates of the reference element.

This array, of type given in MAIJ, contains:

• Loop i from 1 to NTYELM
  • Loop j from 1 MAID(i)
    • the NDIM coordinates of node j in the reference element
    End of loop j
  • Loop j from 1 to MAIE(i)
    • the NDIM coordinates of point j in the reference element
    End of loop j
  End of loop i

Nodes and points are arranged in the order defined by DS NOPO (see this DS). If the reference element is typically two-dimensional, but is considered as three-dimensional, it suffices to set the z components to 0.

Array MAIL:

Element description.

This double precision complex array contains:

• Loop i from 1 to NE
  • NEL, the element number
  • NTYE, the element type (between 1 and NTYELM)
  • NMAE, 0 if the element is internal, or the number of words necessary to store the reference numbers (see below)
  • NDSDE, the sub-domain number
  • NTALIR, the number of arrays associated with the element (see below)
  • if NCACAR (of MAI2 is non-zero: NCCAR, 0 if all the element points do not have characteristics other than the coordinates, or the address in DS COOR of the first characteristic other than the coordinates
  • NNO, the number of nodes in the element
  • Loop j from 1 to NNO
    • NONO(j), the number of node j in the element
    End of loop j
  • if NCOPNP (see array MAI2) is zero:
    • NPO, the number of points in the element
    • Loop j from 1 to NPO

      NOPO(j), the number of point j in the element

      End of loop j
  • if NTALIR > 1: loop over the associated arrays to read and for each one its coefficients.
  • if NMAE is non-zero, NTALIR is at least 1 and we have:
    • INING, indicator of the level of information on the reference numbers (see array NOP5 of DS NOPO).

      Loop from 2 to NMAE

      1. if INING = 3, vertex references,
      2. if INING = 2, edge and vertex references,
      3. if INING = 1, face, edge and vertex references.

      End of loop

  End of loop i

1.8.2 Corresponding tools

Reading and writing a DS MAIL

If NOPTFI=0, the DS is category 1; consequently, in this case, a DS residing in main memory is written wholly on sequential file via module SDECRI. Similarly, it is read from file and transferred wholly into main memory via module SDLECT.

If NOPTFI=1, the DS is category 2; array MAIL is read and written outside of these modules. Each element constitutes a record:

WRITE(NFMAIL) LE,(M(IAMAIL-1+I),I=1,LE)

Printing a DS MAIL and plotting a mesh

The contents (total or partial) of a DS MAIL can be printed by the following modules:

IMMAIL:

the whole DS (according to the print parameter IMPRE)

      SUBROUTINE  IMMAIL(M,NFMAIL,NIMAIL,IMPRE)
C AIM : PRINT THE ARRAYS OF DS MAIL, INCREASING WITH IMPRE
C ---  FILE NFMAIL (OR MC IF 0), LEVEL NIMAIL

INFOMA:

print a particular value contained in the DS

      SUBROUTINE INFOMA(M,IOPT,TYPESD,NIVEAU,TAB2,TAB3,TABC,TABI,TABJ,
     +                  IAMAIL,NUMREC)
C AIM : GIVE INFORMATION ON A DS MAIL

Preprocessors IMAGXX and INFOXX are used if a conversational call of IMMAIL and INFOMA, respectively, is desired.

The mesh contained in a file can be plotted via preprocessor TRMCXX (see [96]) in two dimensions, or TRC3XX in three dimensions which also uses DS COOR.

Creation and modification modules of DS MAIL

DS MAIL is constructed via modules COMACO, COMAC2 or COMAC3.

Manipulation utilities of DS MAIL

Numerous utilities exist for manipulating the contents of a DS MAIL, amongst which the utilities facilitating the exploration of array MAIL.

 

      SUBROUTINE CLMAI5(MAI2,MAIC,MAIL,COO4,IA,NTYE,NDSDE,NNO,NONO,NPO
     +                  ,NOPOI,COORP,NREF,NCGE,IFLAG)
C AIM :  READ ARRAY MAILAND EXPLAIN IT (!)

 

      SUBROUTINE AELESU(M,LONREE,NCOPNP,NTYE,NTALIR,IAMAII,IAMAIJ,IA,
     +                  NMA)
C AIM : CALCULATE THE ADDRESS OF THE WORD PRECEDING THAT OF THE NEXT ELEMENT

 

       FUNCTION MNEMO(NUMERO,MNEMON,CODE)
C AIM : ENTER THE CORRESPONDENCE BETWEEN A NUMBER AND ITS MNEMONIC
C ---   MNEMO ALWAYS RETURNS THE MNEMONIC CODE IN AN INTEGER
      .
      .
      PARAMETER (NBRE = 24)
      INTEGER CODE
      CHARACTER*4 MNEM(NBRE),MNEMON
      DATA MNEM/'VN  ','DX  ','DY  ','DZ  ','DTG ','DN  ',
     +          'DDXX','DDYY','DDZZ','DDXY','DDYZ','DDZX','DDTG',
     +          'DDNN','DDTN','DLSP','IADN','TRAN','ITI1','ITI2',
     +          'ITI3','ITI4','ROTX','ROTY'/
C     
     .
     .

 

      SUBROUTINE TYPGEL(N,NM1,NM2,NM3)
C AIM :  WRITE CLEARLY IN 3 WORDS NM1, NM2, NM3 THE
C ---    GEOMETRIC TYPE OF THE ELEMENT OF CODE N