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CLPLATEB.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CLPLATEB
* Problem :
* *********
* The clamped plate problem (Strang, Nocedal, Dax)
* The problem comes from the discretization the following problem
* in mechanics: a plate is clamped on one edge and loaded on the
* opposite side. The plate is the unit square.
* The plate is clamped on its lower edge, by fixing the
* corresponding variables to zero.
* In this version of the problem, the weight WGHT is distributed
* equally along the upper edge, introducing a symmetry with respect
* to the vertical axis.
* Source:
* J. Nocedal,
* "Solving large nonlinear systems of equations arising in mechanics",
* Proceedings of the Cocoyoc Numerical Analysis Conference, Mexico,
* pp. 132-141, 1981.
* SIF input: Ph. Toint, Dec 1989.
* classification OXR2-MN-V-0
* P is the number of points in one side of the unit square
* The number of variables is P*P, of which (P-1)*(P-1) are free.
*IE P 4 $-PARAMETER n = 16
*IE P 7 $-PARAMETER n = 49 original value
*IE P 10 $-PARAMETER n = 100
*IE P 23 $-PARAMETER n = 529
*IE P 32 $-PARAMETER n = 1024
IE P 71 $-PARAMETER n = 5041
* Total weight on the upper edge
RE WGHT -0.1
* Constants
IE 1 1
IE 2 2
* Some useful parameters
IA P-1 P -1
RI RP-1 P-1
RD 1/P-1 RP-1 1.0
R* DISW WGHT 1/P-1
I* P2 P P
RI RP2 P2
RM HP2 RP2 0.5
RD 1/HP2 HP2 1.0
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 four groups per node of the discretized grid
DO I 2 P
IA I-1 I -1
DO J 2 P
IA J-1 J -1
XN A(I,J) 'SCALE' 2.0
XN A(I,J) X(I,J) 1.0 X(I,J-1) -1.0
XN B(I,J) 'SCALE' 2.0
XN B(I,J) X(I,J) 1.0 X(I-1,J) -1.0
ZN C(I,J) 'SCALE' 1/HP2
XN C(I,J) X(I,J) 1.0 X(I,J-1) -1.0
ZN D(I,J) 'SCALE' 1/HP2
XN D(I,J) X(I,J) 1.0 X(I-1,J) -1.0
ND
* Define a linear group that will represent the weight
DO J 1 P
ZN W X(P,J) DISW
ND
BOUNDS
FR CLPLATEB 'DEFAULT'
* Fix the variables on the lower edge of the unit square
DO J 1 P
XX CLPLATEB X(1,J) 0.0
ND
START POINT
XV CLPLATEB 'DEFAULT' 0.0
GROUP TYPE
* Least squares and least fourth power groups
GV L2 GVAR
GV L4 GVAR
GROUP USES
DO I 2 P
DO J 2 P
XT A(I,J) L2
XT B(I,J) L2
XT C(I,J) L4
XT D(I,J) L4
ND
OBJECT BOUND
LO CLPLATEB 0.0
* Solution
*LO SOLTN(4) -9.3705D-03
*LO SOLTN(7) -6.9193D-03
*LO SOLTN(10) -6.2008D-03
*LO SOLTN(23) -5.4274D-03
*LO SOLTN(32) -5.2835D-03
*LO SOLTN(71) -5.0948D-03
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS CLPLATEB
INDIVIDUALS
* Least squares groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
* Least fourth power
T L4
F GVAR**4
G 4.0 * GVAR**3
H 12.0 * GVAR**2
ENDATA