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Titrate:
Structure of Données SD_FETI


Date:
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O. BOITEAU Key
:
D4.06.21-B Page
: 1/10

Organization (S): EDF-R & D/SINETICS
Handbook of Descriptif Informatique
D4.06 booklet: Structures related to the finite elements
D4.06.21 document

Structures of Données SD_FETI

Summary:

Description of the data-processing objects allowing to represent the decomposition in under-fields of one
grid (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]).
Handbook of Descriptif Informatique
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A

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Titrate:
Structure of Données SD_FETI


Date:
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:
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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 grid. 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.

Nodes
Sd 2

of interface
Under-field 1
12


23


Sd 3

12
Sd 1
13

Sd 2

1 Lagrange
3 Lagranges

Appear 1-a: Illustration de 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 N2 compared to
dimension N of the 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 zones 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.

Handbook of Descriptif Informatique
D4.06 booklet: Structures related to the finite elements
HT-66/05/003/A

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Structure of Données SD_FETI


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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

% total objects temporary of work 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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Structure of Données SD_FETI


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3
Contents of 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 Vi=.FETA (I)
VI (J) = number of the jème mesh of the ième under-field.
The LONMAX of VI 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 Vi=.FETB (I)
VI (2 (j-1) +1) = the number of the jème node of the ième under-field. This number is
preceded by a sign ­ if it is about a node of interface (VI (2 (j-1) +1) <0), of a sign +
if not.
VI (2 (j-1) +2) = the number of DDLs until this node included. Thus a number of DDLs
jème node is written:
If j=1 nb_ddl_j = VI (2),
If not nb_ddl_j = VI (2 (j-1) +2) - VI (2 (j-2) +2).
The LONMAX of VI 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 Wi=.FETG (I)
Wi (2 (j-1) +1) = index of the jème Lagrange of interface of the ième 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
with another under-field of number K > J (Wi (2 (j-1) is shared +1) <0), of one
sign + if not. This convention is that retained by operator DEFI_PART_OPS
[U4.23.05].

Wi (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 grid) of the under-field
chosen Vi='.FETB (I) '(thus VI (Wi (2 (j-1) +2)) < 0).

The LONMAX of Wi is equal to twice the number of Lagrange of interface of under
selected field: nb_no_int_j = LONMAX/2.
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.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 the ième 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 the jème Lagrange of interface. It must thus be present in
two negative “.FETB” (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 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:
nb_no_int
S V I dim= somme_mult =
mult_j
J =1

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 pointer .FETI (4 (J
1) +4).

.FREF:
S V K8 dim= 1 + nb_char (a number of loadings)

Listing vector of the general characteristics of partitioning for the possible ones
checks (key word SOLVEUR/VERIF_SDFETI).
FREF (1) = name of the model,

FREF (1+i) = name of the ième loading.

.FLIN:
XD V K24 LONG=nb_sd

For a given under-field, names of comprising LIGRELs of load of the meshs
late with late nodes (condition of Dirichlet…) or not (nodal force). See also them
.FEL1 objects/3 with the §4.

.FLII:
XD V I LONG=nb_sd

For the ième under-field, that is to say Xi=.FLII (I) and J varying of 1 to LONMAX (.FLIN (I))
Xi (2 (j-1) +1) = a number of late meshs of jème LIGREL of .FLIN (I),
Xi (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 under-field I, in
the command preceded by two objects preceding .FLIN and .FLIM. This object of
IN (I))
LONMAX (.FL
collection is thus length
X ((2 J -) 1 + 2)
I

J =1
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Structure of Données SD_FETI


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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
Character string to refine it
dim= 1
monitoring of FETI [U4.50.01].
“&FETI.INFO.STOCKAGE.FIDD”
S V I
Auxiliary vector for
dim= 2
filling of .FVAF and .FVAL.
V (1) = under-field running,
V (2) = a number of under-fields
“&FETI.INFO.STOCKAGE.FVAF”
S V I
Component counts of
dim= nb_sd+1
factorized local
“&FETI.INFO.STOCKAGE.FVAL”
S V I
Component counts of
dim= nb_sd+1
local matrices
“&FETI.INFO.STOCKAGE.FNBN”
S V I
Numbers of nodes of under
dim= nb_sd+1
fields
“&FETI.INFO.CPU.FACN”
S V R
Time (obtained via the routine
dim= nb_sd+1
UTTCPU, which is thus lower than
true spent time
(elapsed)) CPU + SYS of
local numerical factorizations.
“&FETI.INFO.CPU.FACS”
S V R
Time CPU + SYS of
dim= nb_sd+1
factorizations local symbolic systems.
“&FETI.INFO.CPU.ASSE”
S V R
Time CPU + SYS of
dim= nb_sd+1
local assemblies.
For the routines of assembly


SDFETI (1:8)//“.MAILLE.NUMSD”
S V I
Indicate the number of under-field
dim= nb_ma_tot
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
Names of projections of the ligrel
dim= nb_sd
on the under-fields concerned.
LIGREL_DE_CHARGE (K19).“FEL2” S V I
For the ième late mesh:
dim= 2 * a number of V (2 (i-1) +1) = new number in
late meshs of
ligrel
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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LIGREL_DE_CHARGE (K19).“FEL3” S V I
For the ième late node
Only if late meshs with
dim= 2 * a number of V (2 (i-1) +1) = new number in
late nodes
late nodes of
ligrel
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
V (1) = last index used of

dim= 3 * a number of vector
late meshs
For the ième multiple late mesh
of interface
potential
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” S V I
V (1) = last index used of
Only if late meshs with
dim= 3 * a number of vector
late nodes
late nodes
For the ième multiple late node
of interface potentials 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
Indicate in the loops on
dim= nb_sd+1
under-fields, if the processor
current is concerned with ième
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 any I.
“&FETI.LISTE.SD.MPIB”
S V I
Object reverses precedent
dim= nb_sd
V (I) = J under-field I is
concerned with the processor J.
Into sequential, V (I) = 0 for any 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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D4.06 booklet: Structures related to the finite elements
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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????????????????
ATTRIBUT: 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$$NOM <
>>>>> REPERTORY OF NAMES OF THE COLLECTION:SDFETI
1 - >SD1 <>SD2 <>SD3 <>SD4 <
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 1
1 - 1 2 3 4 5
6 - 6 25 27
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 2
1 - 19 20 21 22 23
6 - 24 29 31
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 3
1 - 13 14 15 16 17
6 - 18 30 32 33 34
OBJECT IMPRESSION OF COLLECTION >SDFETI .FETA< OC: 4
1 - 7 8 9 10 11
6 - 12 26 28 35 36
--------------------------------------------------------------------------------
IMPRESSION OF THE COLLECTION: SDFETI .FETB
SEGMENT IMPRESSION OF VALUES >SDFETI .FETB$$NOM <
>>>>> REPERTORY 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 <
>>>>> REPERTORY 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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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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