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Code_Aster
®
Version
8.1
Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
1/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
Organization (S):
EDF-R & D/SINETICS















Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
D4.06.21 document


Structures of Data
SD_FETI




Summary:

Description of the data-processing objects allowing to represent the decomposition in under-fields of one
mesh (cf operator of decomposition DEFI_PART_FETI [U4.23.05]). This partitioning is intended for
to nourish a linear solvor multidomaine of the type FETI (cf solvor FETI [U4.50.01] [R6.01.03]).
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Code_Aster
®
Version
8.1
Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
2/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
1 General information
An object of the type SD_FETI is created by operator DEFI_PART_FETI [U4.23.05] on the total basis
in order to represent the decomposition in under-fields of a mesh. It must be provided to the solvor
linear multi-fields FETI (key word SOLVEUR/PARTITION).
The size of this object is about nb_ma_tot +2 X nb_no_tot + 12 X nb_no_int + nb_sd
(cf object .DIME for the notations).
This concept of partitioning FETI requires some explanations on the described entities. In
summary:
· The meshs of the ligrel of the model are divided into several under-fields. The latter
thus consist of a whole of only one holding (connexity 1) of meshs listed in
object .FETA. A mesh can thus belong only to one under-field: no the mesh
divided of pieces or commune with several under-fields.
· The new borders generated by this cutting constitute the interface. Nodes
of interface describing it are shared with at least two under-fields (multiplicity
geometrical of .FETI and list .FETJ).
· The resolution of problem FETI is carried out on a vector of unknown factors, Lagranges
interfaces (not to be confused with other Lagranges intervening in Code_Aster:
conditions of Dirichlet, contacts…) (object .FETI), coinciding with these nodes of interface. With
a node of interface corresponds as much of Lagranges than it is necessary to control
continuity enters the under-fields. Lagrange east required for each binomial of under
fields.











Appear 1-a: Illustration of Lagranges of interfaces in 2D with 2 and 3 under-fields

Important remark on the interfaces:
For the moment, one highly disadvises the use of an interface of size
N
- 2 compared to
dimension
N
problem. For example, in a 3D problem (
N
=3), an interface of the type
segment enters a hexahedral under-field and a under-field made up of hulls.
In addition, it is to better avoid “polluting” these interfaces by loadings, conditions
limits of generalized the Dirichlet type, the fissures, the areas of contact… Developments
FETI currently industrialized in the code, do not ensure us of the good unfolding of
things that when these interfaces are relatively virgin of any particular processing.
12
13
23
12
Nodes
of interface
1 Lagrange
3 Lagranges
Sd 2
Under-field 1
Sd 3
Sd 1
Sd 2
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Code_Aster
®
Version
8.1
Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
3/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
2 Tree structures
SD_FETI (K19)::=record
“.FDIM”
:
OJB
S V I
“.FETA”
:
OJB
XD V I
“.FETB”
:
OJB
XD V I
“.FETG”
:
OJB
XD V I
“.FETH”
:
OJB
S V I
“.FETI”
:
OJB
S V I
“.FETJ”
:
OJB
S V I
“.FREF”
:
OJB
S V K8
“.FLIN”
:
OJB
XD V K24
“.FLIM”
:
OJB
XD V I
“.FLII”
:
OJB
XD V I

%
temporary objects of work total to all process FETI (cf remarks [§4])
“&&”//SDFETI (1:17)//“.FINF”:
OJB
S V K24
“&FETI.INFO.STOCKAGE.FID”
:
OJB
S V I
“&FETI.INFO.STOCKAGE.FVAF”
:
OJB
S V I
“&FETI.INFO.STOCKAGE.FVAL”
:
OJB
S V I
“&FETI.INFO.STOCKAGE.FNBN”
:
OJB
S V I
“&FETI.INFO.CPU.FACN”
:
OJB
S V R
“&FETI.INFO.CPU.FACS”
:
OJB
S V R
“&FETI.INFO.CPU.ASSE”
:
OJB
S V R
SDFETI (1:8)//“.MAILLE.NUMSD”:
OJB
S V I
LIGREL_DE_CHARGE (K19).“FEL1”:
OJB
S V K24
LIGREL_DE_CHARGE (K19).“FEL2”:
OJB
S V I
LIGREL_DE_CHARGE (K19).“FEL3”:
OJB
S V I
LIGREL_DE_CHARGE (K19).“FEL4”:
OJB
S V I
LIGREL_DE_CHARGE (K19).“FEL5”:
OJB
S V I
“&FETI.LISTE.SD.MPI”
:
OJB
S V I
“&FETI.LISTE.SD.MPIB”
:
OJB
S V I
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Code_Aster
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Version
8.1
Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
4/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
3
Contents of the objects
JEVEUX
.FDIM:
S V I DIM=5

Listing vector of the sizes characteristic of the cut out model.
FDIM (1)
= a number of nb_sd under-fields.
FDIM (2)
= a number of Lagranges of interface nb_no_int.
FDIM (3)
= a total number of meshs of the model nb_ma_tot.
FDIM (4)
= a number of DDLs of interface nb_ddl_int.
FDIM (5)
= a total number of nodes of the model nb_no_tot.
.FETA:
XD V I LONG=nb_sd

Dispersed collection enumerating the list of the meshs by under-fields (meshs
voluminal and associated meshs of skin to which apply a loading)
That is to say
V
I
=
.FETA (
I
)
V
I
(J)
= number of
J
ème
net
I
ème
under-field.
The LONMAX of
V
I
is equal to the number of meshs of the selected under-field.
.FETB:
XD V I LONG=nb_sd

Dispersed collection describing the nodes of the under-fields.
That is to say
V
I
=
.FETB (
I
)
V
I
(2 (j-1) +1)
= the number of
J
ème
node of
I
ème
under-field. This number is
preceded by a sign ­ if it is about a node of interface (
V
I
(2 (j-1) +1) <0
), of a sign +
if not.
V
I
(2 (j-1) +2)
= the number of DDLs until this node included. Thus a number of DDLs
J
ème
node is written:
If
j=1
nb_ddl_j =
V
I
(2)
,
If not nb_ddl_j =
V
I
(2 (j-1) +2) - V
I
(2 (j-2) +2).
The LONMAX of
V
I
is equal to twice the number of nodes of the selected under-field:
nb_no_j = LONMAX/2.
.FETG:
XD V I LONG=nb_sd

Dispersed collection simulating the action of the operators of restriction/prediction.
That is to say
W
I
=
.FETG (
I
)
W
I
(2 (j-1) +1)
= index of
J
ème
Lagrange of interface of
I
ème
under-field in the object
.FETI. This number must be signed to check the continuity of the unknown field with
the interface.
Can imports the convention of sign provided that its logic is respected
everywhere. One can for example make precede this index by a sign ­ if this Lagrange
is shared with another under-field of number
K > J
(
W
I
(2 (j-1) +1) <0
), of one
sign + if not. This convention is that retained by operator DEFI_PART_OPS
[U4.23.05].
W
I
(2 (j-1) +2)
= index of same Lagrange in the whole of the nodes (it is
supposed coinciding with one of the nodes of interface of the mesh) of the under-field
chosen
V
I
= '
.FETB (
I
)
'(thus
V
I
(W
I
(2 (j-1) +2)) < 0).

The LONMAX of
W
I
is equal to twice the number of Lagrange of interface of under
selected field: nb_no_int_j = LONMAX/2.
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Code_Aster
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Version
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Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
5/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
.FETH:
S V I dim=nb_sd
Vector listing the numbers of DDLs per under-field (of the physical nodes and of
late nodes).
That is to say
X
=
.FETG
X (I)
= a number of DDLs of
I
ème
under-field.
.FETI:
S V I dim= 4 * nb_no_int
Vector describing Lagranges of interface.
That is to say
Y
=
.FETI
Y (4 (j-1) +1)
= number of
J
ème
Lagrange of interface. It must thus be present in
two '
.FETB
'negative (they exist
K
,
L
,
m
and
N
such as
Y (4 (j-1) +1) =
- FETB (K) (2 (l-1) +1) = - FETB (m) (2 (n-1) +1)
)
Y (4 (j-1) +2)
= its geometrical multiplicity mult_j.
Y (4 (j-1) +3)
= the number of DDLs until this node included. Thus a number of DDLs
is written:
If
J
=1 nb_ddl_j =
Y (3)
,
If not nb_ddl_j =
Y (4 (J-1) +3) - Y (4 (J-2) +3).
Y (4 (j-1) +4)
= index, in the object
.FETJ
, of the first of the mult_j under-fields
comprising this Lagrange on one their interfaces. The other under-fields are with
the continuation.
.FETJ:
S V I dim= somme_mult =
=
nb_no_int
mult_j
1
J
Vector describing the list of the under-fields containing the nodes of interface.
The access to this vector of storage indirect and is carried out via the pointer.
FETI (4 (J
1) +4)
.
.FREF:
S V K8 dim=
1 +
nb_char
(a number of loadings)
Listing vector of the general features of partitioning for the possible ones
checks (key word SOLVEUR/VERIF_SDFETI).
FREF (1)
= name of the model,
FREF (1+i)
= name of
I
ème
loading.
.FLIN:
XD V K24 LONG=nb_sd
For a given under-field, names of
LIGREL
S of load comprising of the meshs
late with late nodes (condition of Dirichlet…) or not (nodal force). See also them
objects
.FEL1/3
with the §4.
.FLII:
XD V I LONG=nb_sd
For
I
ème
under-field, is
X
I
=
.FLII (
I
)
and
J
varying from 1 with
LONMAX
(
.FLIN (
I
)
)
X
I
(
2 (j-1) +1
)
= a number of late meshs of
J
ème
LIGREL
of
.FLIN (
I
)
,
X
I
(
2 (j-1) +2
)
= a number of these late meshs concerning this under-field (because one
LIGREL
of load can be with horse between several under-fields),
.FLIM:
XD V I LONG=nb_sd
List absolute values of the late meshs concerning the under-field
I
, in
the command preceded by the two preceding objects
.FLIN
and
.FLIM
. This object of
collection is thus length
(
)
=
+
-
IN (I))
LONMAX (.FL
I
X
1
2
)
1
(
2
J
J
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Code_Aster
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Version
8.1
Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
6/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
4 Objects
related
These temporary objects of the volatile base exist during a good share of a resolution FETI.
For the needs for monitoring
“&&”//SDFETI (1:17)//“.FINF”
S V K24
dim=
1
Character string to refine it
monitoring of FETI [U4.50.01].
“&FETI.INFO.STOCKAGE.FIDD”
S V I
dim=
2
Auxiliary vector for
filling of .FVAF and .FVAL.
V (1) = under-field running,
V (2) = a number of under-fields
'
&FETI.INFO.STOCKAGE.FVAF'
S V I
dim=
nb_sd+1
Component counts of
factorized local
“&FETI.INFO.STOCKAGE.FVAL”
S V I
dim=
nb_sd+1
Component counts of
local matrices
“&FETI.INFO.STOCKAGE.FNBN”
S V I
dim=
nb_sd+1
Numbers of nodes of under
fields
“&FETI.INFO.CPU.FACN”
S V R
dim=
nb_sd+1
Time (obtained via the routine
UTTCPU, which is thus lower than
true spent time
(elapsed)) CPU + SYS of
local numerical factorizations.
“&FETI.INFO.CPU.FACS”
S V R
dim=
nb_sd+1
Time CPU + SYS of
factorizations local symbolic systems.
“&FETI.INFO.CPU.ASSE”
S V R
dim=
nb_sd+1
Time CPU + SYS of
local assemblies.
For the routines of assembly
SDFETI (1:8)//“.MAILLE.NUMSD”
S V I
dim=
nb_ma_tot
Indicate the number of under-field
which a mesh belongs of
model. Initialized value with ­ 999,
that makes it possible to test the membership
of all the meshs of the model to one
only under-field (only in
sequential mode. In parallel,
each processor reaches only
partial information and thus these
checks are invalid) and
to assemble the matrices and vectors
buildings.
For the routines of assembly in
presence of ligrel with meshs and/or
with late nodes
LIGREL_DE_CHARGE (K19).“FEL1”
S V K24
dim=
nb_sd
Names of projections of the ligrel
on the under-fields concerned.
LIGREL_DE_CHARGE (K19).“FEL2” S V I
dim=
2 * a number of
late meshs of
ligrel
For
I
ème
late mesh:
V
(
2 (i-1) +1
) = new number in
the projected ligrel,
If
V
(
2 (i-1) +2
) >0 then number of
under-field concerned, if not
- V
(
2 (i-1) +2
) = multiplicity of
late mesh (DDL_IMPO on
the interface e.g.) and associated one
.FEL4.
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Code_Aster
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Version
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Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
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O. BOITEAU
Key
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D4.06.21-B
Page
:
7/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
LIGREL_DE_CHARGE (K19).“FEL3”
Only if late meshs with
late nodes
S V I
dim=
2 * a number of
late nodes of
ligrel
For
I
ème
late node
V
(
2 (i-1) +1
) = new number in
the projected ligrel,
If
V
(
2 (i-1) +2
) >0 then number of
under-field concerned, if not
- V
(
2 (i-1) +2
) = multiplicity of the node
late (DDL_IMPO on the interface by
e.g.) and associated a .FEL5.
LIGREL_DE_CHARGE (K19).“FEL4”
S V I
dim=
3 * a number of
late meshs
of interface
potential
V
(
1
) = last index used of
vector
For
I
ème
multiple late mesh
V
(
3 (i-1) +2
) = new number in
the projected ligrel,
V
(
3 (i-1) +3
) = number of under
field concerned,
- V
(
3 (i-1) +4
) = old number.
LIGREL_DE_CHARGE (K19).“FEL5”
Only if late meshs with
late nodes
S V I
dim=
3 * a number of
late nodes
of interface potentials
V
(
1
) = last index used of
vector
For
I
ème
multiple late node
V
(
3 (i-1) +2
) = new number in
the projected ligrel,
V
(
3 (i-1) +3
) = number of under
field concerned,
- V
(
3 (i-1) +4
) = old number.
For parallelism MPI
“&FETI.LISTE.SD.MPI”
S V I
dim=
nb_sd+1
Indicate in the loops on
under-fields, if the processor
current is concerned with
I
ème
under-field:
V
(
i+1
) = 1
the loop on it under
field is carried out,
V
(
i+1
) = 0
it is jumped.
By convention of the loops,
V
(
1
)
relate to the total field and is worth
always 1.
Into sequential,
V
(
I
) = 1 for all
I.
“&FETI.LISTE.SD.MPIB”
S V I
dim=
nb_sd
Object reverses precedent
V
(
I
) =
J
the under-field
I
is
concerned with the processor
J
.
Into sequential,
V
(
I
) = 0 for all
I.
Notice on parallelism:
During a parallel execution, these temporary objects are declined by processor. However, according to
distribution of load, each processor is concerned only by certain under-fields
(cf objects “&FETI.LISTE…”). Therefore, put besides these the last two objects JEVEUX, others
related objects contain only information relating to the under-fields which them
interest.
For example, object SDFETI (1:8)//“.MAILLE.NUMSD” will comprise values initialized with
­ 999 for the meshs of the under-fields concerning the other processors.
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Code_Aster
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Version
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Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
8/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
5 Examples
In the case test FETI002A, partionnement in four under-fields leads to SD SD_FETI
following:
built named SD_FETI “SDFETI” following
====> IMPR_CO OF THE STRUCTURE OF DATA: SDFETI????????????????
ATTRIBUTE: F CONTENTS: T BASE: >G<
A NUMBER Of OBJECTS (OR COLLECTIONS) FIND: 8
================================================================================
IMPRESSION OF THE CONTENTS OF THE OBJECTS FIND:
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >SDFETI .FDIM <
1 - 4 10 36 20 19
--------------------------------------------------------------------------------
IMPRESSION OF THE COLLECTION: SDFETI .FETA
SEGMENT IMPRESSION OF VALUES >SDFETI .FETA$$NOM <
>>>>> INDEX OF NAMES OF THE COLLECTION:SDFETI
1 - >SD1 <>SD2 <>SD3 <>SD4 <
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 1
1 - 1 2 3 4 5
6 - 6 25 27
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 2
1 - 19 20 21 22 23
6 - 24 29 31
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 3
1 - 13 14 15 16 17
6 - 18 30 32 33 34
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 4
1 - 7 8 9 10 11
6 - 12 26 28 35 36
--------------------------------------------------------------------------------
IMPRESSION OF THE COLLECTION: SDFETI .FETB
SEGMENT IMPRESSION OF VALUES >SDFETI .FETB$$NOM <
>>>>> INDEX OF NAMES OF THE COLLECTION:SDFETI
1 - >SD1 <>SD2 <>SD3 <>SD4 <
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETB< OC: 1
1 - - 1 2 2 4 - 3
6 - 6 - 4 8 10 10
11 - 14 12 - 17 14
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETB< OC: 2
1 - - 1 2 - 3 4 - 8
6 - 6 9 8 11 10
11 - 15 12 - 16 14
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETB< OC: 3
1 - - 3 2 - 5 4 7
6 - 6 - 8 8 12 10
11 - - 16 12 18 14
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETB< OC: 4
1 - - 3 2 - 4 4 - 5
6 - 6.6 8 13 10
11 - - 17 12 19 14
--------------------------------------------------------------------------------
IMPRESSION OF THE COLLECTION: SDFETI .FETG
SEGMENT IMPRESSION OF VALUES >SDFETI .FETG$$NOM <
>>>>> INDEX OF NAMES OF THE COLLECTION:SDFETI
1 - >SD1 <>SD2 <>SD3 <>SD4 <
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETG< OC: 1
1 - - 1 1 - 2 3 - 3
6 - 3 - 6 4 - 10 7
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETG< OC: 2
1 - 1 1 2 2 - 4
6 - 2 - 8 3 - 9 7
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETG< OC: 3
1 - 4 1 - 5 1 - 7
6 - 2 8 4 9 6
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETG< OC: 4
1 - 3 1 5 1 6
6 - 2 7 3 10 6
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >SDFETI .FETH <
1 - 14 14 14 14
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >SDFETI .FETI <
1 - 1 2 2 1 3
6 - 4 4 3 3 4
11 - 6 5 3 4 8
16 - 7 3 4 10 9
21 - 4 2 12 11 5
26 - 2 14 13 8 2
31 - 16 15 16 2 18
36 - 17 17 2 20 19
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >SDFETI .FETJ <
1 - 1 2 1 2 1
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Code_Aster
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Version
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Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
Author (S):
O. BOITEAU
Key
:
D4.06.21-B
Page
:
9/10
Data-processing manual of Description
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
6 - 4 2 3 3 4
11 - 1 4 3 4 2
16 - 3 2 3 1 4
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >SDFETI .FREF <
1 - >MODM <>CH1 <
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Titrate:
Structure of Data
SD_FETI
Date:
29/09/05
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O. BOITEAU
Key
:
D4.06.21-B
Page
:
10/10
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D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A
























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