Code_Aster ®
Version
7.4
Titrate:
Operator FACT_GRAD


Date:
31/01/05
Author (S):
X. DESROCHES Key
:
U4.55.03-G Page
: 1/4

Organization (S): EDF-R & D/AMA

Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.55.03

Operator FACT_GRAD

1 Goal

To build a matrix of prepacking for a resolution by combined gradient. This
matrix makes it possible to accelerate the convergence of the algorithm of the gradient combined (operator
RESO_GRAD [U4.55.04]). This operator applies only to real and symmetrical matrices.

Product a structure of data of the matr_asse_ type *.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator FACT_GRAD


Date:
31/01/05
Author (S):
X. DESROCHES Key
:
U4.55.03-G Page
: 2/4

2 Syntax

matfac [matr_asse_ *] = FACT_GRAD




(MATR_ASSE
= chechmate
,
/
[matr_asse_DEPL_R]
/
[matr_asse_TEMP_R]
/
[matr_asse_PRES_R]





PRE_COND
= “LDLT_INC”
,
[DEFAUT]





NIVE_REMPLISSAGE
=
/
0,
[DEFAUT]
/
N,
[I]





INFO
=
/
1,
[DEFAUT]










/2,




);

if MATR_ASSE: [matr_asse_DEPL_R]
then [*]
- > DEPL_R
[matr_asse_TEMP_R]
[*]
- > TEMP_R
[matr_asse_PRES_R]
[*]
- > PRES_R

Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator FACT_GRAD


Date:
31/01/05
Author (S):
X. DESROCHES Key
:
U4.55.03-G Page
: 3/4

3 Operands

3.1 Operand
MATR_ASSE

MATR_ASSE
=

Name of the real and symmetrical matrix which one wants préconditionner.

3.2 Operand
PRE_COND


PRE_COND =

Method of prepacking:

“LDLT_INC”:
the matrix of prepacking is obtained by a decomposition LDLT
incomplete of the assembled matrix.
This decomposition is more or less complete, according to the level of
filling. The matrix matfac result is of type matr_asse.

3.3 Operand
NIVE_REMPLISSAGE

NIVE_REMPLISSAGE
=/0







/N

The matrix of prepacking (P) used to accelerate the convergence of the gradient
combined by factorizing in a more or less complete way the initial matrix (A) is obtained.

If niv = 0 (defect)

P has same storage that A. factorization is incomplete because one does not use for calculations
that the terms which one can store in P.

P thus represents an approximation (poor) of A1; its storage is weak.

If niv = 1

One stores in P in addition to the terms which had their place in initial storage, them
“downward” of first generation of the initial terms. Indeed during factorization, one
null term in A can become nonnull in P. One obtains thus the filling of level 1.

If niv = 2,…

The same process is taken again: the matrix P filled on the level niv-1 creates the terms of
stamp P on the level niv.

The larger niv is, the closer the matrix P is to A1 and thus more the combined gradient
converge quickly (in iteration count).

On the other hand, more niv is the great more storage of P becomes bulky (in memory and on
disc) and more the iterations are expensive in CPU.

The first tests showed (roughly) that the size of P was worth:

·
3,5 * size (A) for niv = 1
·
7,5 * size (A) for niv = 2

Our experiment of this key word is still limited and we advise to use the value by
defect (niv = 0).

If niv = 0 does not allow the gradient combined to converge, one will test successively them
values niv = 1, 2, 3.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator FACT_GRAD


Date:
31/01/05
Author (S):
X. DESROCHES Key
:
U4.55.03-G Page
: 4/4

3.4 Operand
INFO

INFO
=

1: no impression,
2: this option is reserved for the developers. Intermediate impressions on the file
message.

4 Example
of use

naked
= NUME_DDL (MATR_RIGI= mel, METHODE= “GCPC”);
subdued = ASSE_MATRICE (MATR_ELEM= mel, naked NUME_DDL=
);
kmatas = FACT_GRAD
(MATR_ASSE= subdued);
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Outline document