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NOBNDTOR.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME NOBNDTOR
* Problem :
* *********
* The quadratic elastic torsion problem
* The problem comes from the obstacle problem on a square.
* The square is discretized into (px-1)(py-1) little squares. The
* heights of the considered surface above the corners of these little
* squares are the problem variables, There are px**2 of them.
* The dimension of the problem is specified by Q, which is half the
* number discretization points along one of the coordinate
* direction.
* Since the number of variables is P**2, it is given by 4Q**2
* Source: problem 1 (c=5, starting point U = upper bound) in
* J.J. More',
* "A collection of nonlinear model problems"
* Proceedings of the AMS-SIAM Summer seminar on the Computational
* Solution of Nonlinear Systems of Equations, Colorado, 1988.
* Argonne National Laboratory MCS-P60-0289, 1989.
* SIF input: Ph. Toint, Dec 1989.
* A variant of TORSION1 in which some of the variables are
* unconstrained.
* classification QBR2-AY-V-0
* Q is half the number of discretized points along the X axis
*IE Q 2 $-PARAMETER n= 16
*IE Q 5 $-PARAMETER n= 100 original value
*IE Q 11 $-PARAMETER n= 484
*IE Q 16 $-PARAMETER n= 1024
IE Q 37 $-PARAMETER n= 5476
*IE Q 50 $-PARAMETER n= 10000
*IE Q 61 $-PARAMETER n= 14884
* The force constant
RE C 5.0
* Define a few helpful parameters
IA Q+1 Q 1
I+ P Q Q
IA P-1 P -1
RI 1/H P-1
RD H 1/H 1.0
R* H2 H H
R* C0 H2 C
RM LC C0 -1.0
IE 1 1
IE 2 2
VARIABLES
* Define one variable per discretized point in the unit square
DO J 1 P
DO I 1 P
X X(I,J)
ND
GROUPS
* Define a group per interior node
DO I 2 P-1
DO J 2 P-1
ZN G(I,J) X(I,J) LC
ND
BOUNDS
* Fix the variables on the lower and upper edges of the unit square
DO J 1 P
XX NOBNDTOR X(1,J) 0.0
XX NOBNDTOR X(P,J) 0.0
ND
* Fix the variables on the left and right edges of the unit square
DO I 2 P-1
XX NOBNDTOR X(I,P) 0.0
XX NOBNDTOR X(I,1) 0.0
ND
* Define the upper and lower bounds from the distance to the
* boundary
* Lower half of the square
DO I 2 Q
DO J 2 I
IA J-1 J -1
RI RJ-1 J-1
R* UPPL RJ-1 H
RE UPPL 1.0D+21
RM LOWL UPPL -1.0
ZL NOBNDTOR X(I,J) LOWL
ZU NOBNDTOR X(I,J) UPPL
OD J
IM MI I -1
I+ P-I P MI
IA I-1 I -1
RI RI-1 I-1
R* UPPM RI-1 H
RE UPPM 1.0D+21
RM LOWM UPPM -1.0
IA P-I+1 P-I 1
DO J I P-I+1
ZL NOBNDTOR X(I,J) LOWM
ZU NOBNDTOR X(I,J) UPPM
OD J
DO J P-I+1 P-1
IM MJ J -1
I+ P-J P MJ
RI RP-J P-J
R* UPPR RP-J H
RE UPPR 1.0D+21
RM LOWR UPPR -1.0
ZL NOBNDTOR X(I,J) LOWR
ZU NOBNDTOR X(I,J) UPPR
ND
* Upper half of the square
DO I Q+1 P-1
IM MI I -1
I+ P-I P MI
IA P-I+1 P-I 1
DO J 2 P-I+1
IA J-1 J -1
RI RJ-1 J-1
R* UPPL RJ-1 H
RM LOWL UPPL -1.0
ZL NOBNDTOR X(I,J) LOWL
ZU NOBNDTOR X(I,J) UPPL
OD J
RI RP-I P-I
R* UPPM RP-I H
RM LOWM UPPM -1.0
DO J P-I+1 I
ZL NOBNDTOR X(I,J) LOWM
ZU NOBNDTOR X(I,J) UPPM
OD J
DO J I P-1
IM MJ J -1
I+ P-J P MJ
RI RP-J P-J
R* UPPR RP-J H
RM LOWR UPPR -1.0
ZL NOBNDTOR X(I,J) LOWR
ZU NOBNDTOR X(I,J) UPPR
ND
START POINT
* Start from the boundary values on the lower and upper edges
DO J 1 P
X NOBNDTOR X(1,J) 0.0
X NOBNDTOR X(P,J) 0.0
ND
* Start from the boundary values on the left and right edges
DO I 2 P-1
X NOBNDTOR X(I,P) 0.0
X NOBNDTOR X(I,1) 0.0
ND
* Start from the upper bounds (starting point U)
* Lower half of the square
DO I 2 Q
DO J 2 I
IA J-1 J -1
RI RJ-1 J-1
R* UPPL RJ-1 H
Z NOBNDTOR X(I,J) UPPL
OD J
IM MI I -1
I+ P-I P MI
IA I-1 I -1
RI RI-1 I-1
R* UPPM RI-1 H
IA P-I+1 P-I 1
DO J I P-I+1
Z NOBNDTOR X(I,J) UPPM
OD J
DO J P-I+1 P-1
IM MJ J -1
I+ P-J P MJ
RI RP-J P-J
R* UPPR RP-J H
Z NOBNDTOR X(I,J) UPPR
ND
* Upper half of the square
DO I Q+1 P-1
IM MI I -1
I+ P-I P MI
IA P-I+1 P-I 1
DO J 2 P-I+1
IA J-1 J -1
RI RJ-1 J-1
R* UPPL RJ-1 H
Z NOBNDTOR X(I,J) UPPL
OD J
RI RP-I P-I
R* UPPM RP-I H
DO J P-I+1 I
Z NOBNDTOR X(I,J) UPPM
OD J
DO J I P-1
IM MJ J -1
I+ P-J P MJ
RI RP-J P-J
R* UPPR RP-J H
Z NOBNDTOR X(I,J) UPPR
ND
ELEMENT TYPE
EV ISQ V1 V2
IV ISQ U
ELEMENT USES
* Each node has four elements
DO I 2 P-1
IA I-1 I -1
IA I+1 I 1
DO J 2 P-1
IA J-1 J -1
IA J+1 J 1
XT A(I,J) ISQ
ZV A(I,J) V1 X(I+1,J)
ZV A(I,J) V2 X(I,J)
XT B(I,J) ISQ
ZV B(I,J) V1 X(I,J+1)
ZV B(I,J) V2 X(I,J)
XT C(I,J) ISQ
ZV C(I,J) V1 X(I-1,J)
ZV C(I,J) V2 X(I,J)
XT D(I,J) ISQ
ZV D(I,J) V1 X(I,J-1)
ZV D(I,J) V2 X(I,J)
ND
GROUP USES
DO I 2 P-1
DO J 2 P-1
XE G(I,J) A(I,J) 0.25 B(I,J) 0.25
XE G(I,J) C(I,J) 0.25 D(I,J) 0.25
ND
OBJECT BOUND
* Solution
*LO SOLTN(2) -5.1851852D-1
*LO SOLTN(5) -4.9234185D-1
*LO SOLTN(11) -4.5608771D-1
*LO SOLTN(16) ???
*LO SOLTN(37) ???
*LO SOLTN(50) ???
*LO SOLTN(61) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS NOBNDTOR
INDIVIDUALS
T ISQ
R U V1 1.0 V2 -1.0
F U * U
G U U + U
H U U 2.0
ENDATA