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1.11 DS MUA

1.11.1 Contents

This DS stores, for each line, the coefficients lying between the first column with a a priori non-zero coefficient and the diagonal of a sparse finite element matrix. This type of storage is called profile or skyline storage.

DS MUA consists of 6 arrays of predefined order.

Array MUA0:

General information.

This integer array contains 32 variables, consisting of a general description of the job (title, date, name), of DS MUA (type, level, ...), and indicates the presence or absence of array MUA1.

1:20 TITRE

the job title in 20 words of 4 characters,

21:22 DATE

the data of creation in 2 words of 4 characters,

23:28 NOMCRE

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

29 'MUA'

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 MUA1).

Array MUA1:

Description of any supplementary arrays.

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

Array MUA2:

General description of the matrix.

This integer array contains 12 values.

1 NTYP

the type of matrix coefficients,

2 NBLOC

the number of blocks or pages in the matrix,

3 NTCOL

the number of columns of the largest block,

4 NMOPB

the number of words required in m.m. to store the largest block,

5 NMATA

the number of matrices on file,

6 NCODSA

the type of matrix storage:

• 1: symmetric matrix, only the lower triangle is stored, line by line,
• 0: diagonal matrix, or
• -1: non-symmetric matrix, ordered line after line, with the diagonal coefficient placed at the end.
  

7 LBDP

the largest difference + 1 between the 2 node numbers in the same element if NCODSA is non-zero, and the half band-width in terms of nodes if NCODSA=0,

8 LBDPDL

the largest difference + 1 between the degree of freedom numbers of 2 nodes belonging to the same element if NCODSA is non-zero, and the half band-width in terms of degrees of freedom if NCODSA=0,

9 ND

the number of degrees of freedom per node if it is constant, 0 otherwise,

10 NOE

the number of nodes,

11 NTDL

the matrix order,

12 MUA5AR

the assembly is already performed if 1,
the assembly is not yet performed if 0.

Array MUA3:

Pointer to the last degree of freedom of each block.

This integer array , of length NBLOC+1, contains:

• MUA3(1) = 0,
• MUA3(i+1) = the number of the last degree of freedom of block i in the matrix.

Array MUA4:

Pointer to the diagonal coefficient of each line.

This integer array, of length NTDL+1 or 2 depending on NCODSA, contains:

• NCODSA = 0
  • MUA4(1) = 0
  • MUA4(2) = NTDL,
• NCODSA 0
  • MUA4(1) = 0
  • MUA4(i+1) = the address of diagonal coefficient i.

Array MUA5:

The matrix coefficients.

This NTYP type array contains the matrix coefficients:

• MUA5(k) = value of the k-th matrix coefficient (if it is not paginated),
• or MUA5(k-MUA3(i)) the k-th coefficient of block i (if it is paginated).

1.11.2 Corresponding tools

Reading and writing a DS MUA

This DS is a category 2 DS. A DS residing in main memory is written partially (only its 5 generic arrays and any associated arrays described in array MUA1) on sequential or direct access file via module SDECRI.

Similarly, a DS residing on file is read and transferred partially (only its 5 generic arrays and any associated arrays described in array MUA1) to main memory via module SDLECT; only array MUA5 is addressed:

• When reading, array MUA5 is only addressed and the read is performed by the program via a WRITE type command:

  READ(NFMUA) LE,(M(IAMUA5-1+I),I=1,LE)

  or if it is a direct access file:

  READ(NFMUA,NEMUA) LE,(M(IAMUA5-1+I),I=1,LE)

• When writing, array MUA5 is transferred via a WRITE type command.

Printing a DS MUA and plotting its profile

The contents (total or partial) of a DS MUA can be printed by module IMMUA. Preprocessor IMAGXX is used when a conversational call of IMMUA is desired.

The matrix profile contained in a file can be plotted via preprocessor TRPRXX (see [96]).

Creation and modification module for DS MUA

DS MUA is created using a DS TAE by assembly of the element matrices, for example via module ASSMUA and ASMAPS.

1.11.3 Storage structure

Consider the following 2 matrix examples:

Example 1:

Symmetric matrix.

Consider the 12-th order matrix given below (the values correspond to the the rows in the storage and not to the matrix coefficients) constituting 3 pages:

Array MUA5, of length MUA4(13), is subdivided into 3 pages, line 1 to 5, 6 to 10 and 11 to 12. Each page contains a maximum of 22 words. Thus, we have:

• NCODSA = 1
• array MUA3:
  

• array MUA4:
  

Example 2:

Non-symmetric matrix.

Consider the 12-th order matrix given below (the values correspond to the the rows in the storage and not to the matrix coefficients) constituting 3 pages:

Here, each page contains a maximum of 32 words. Thus, we have:

• NCODSA = -1
• array MUA3:
  

• array MUA4: