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MINSURFO.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MINSURFO
* Problem :
* *********
* Find the surface with minimal area, given boundary conditions,
* and above an obstacle.
* This is problem 17 in the COPS (Version 2) collection of
* E. Dolan and J. More'
* see "Benchmarking Optimization Software with COPS"
* Argonne National Labs Technical Report ANL/MCS-246 (2000)
* SIF input: Nick Gould, December 2000
* classification OBR2-AN-V-V
* grid points in x direction (fixed at 50 in COPS)
*IE NX 25
IE NX 50
*IE NX 75
*IE NX 100
* grid points in y direction
*IE NY 25
*IE NY 50
*IE NY 75
IE NY 100
* Other useful values
IE 0 0
IE 1 1
RE ONE 1.0
IA NX+1 NX 1
IA NY+1 NY 1
RI NX+1 NX+1
RI NY+1 NY+1
* Grid spacing and area of triangle
RD HX NX+1 1.0
RD HY NY+1 1.0
R* AREA HX HY
RM AREA AREA 0.5
RD 1/AREA AREA 1.0
RD 1/HX HX 1.0
R* 1/HX2 1/HX 1/HX
RD 1/HY HY 1.0
R* 1/HY2 1/HY 1/HY
VARIABLES
* v defines the finite element approximation.
DO I 0 NX+1
DO J 0 NY+1
X V(I,J)
ND
GROUPS
* Define a group for each objective term {i in 0..nx,j in 0..ny}
* area*(1+((v[i+1,j]-v[i,j])/hx)^2+((v[i,j+1]-v[i,j])/hy)^2)^(1/2)
DO I 0 NX
DO J 0 NY
ZN A(I,J) 'SCALE' 1/AREA
ND
* Define a group for each objective term {i in 1..nx+1,j in 1..ny+1}
* area*(1+((v[i-1,j]-v[i,j])/hx)^2+((v[i,j-1]-v[i,j])/hy)^2)^(1/2))
DO I 1 NX+1
DO J 1 NY+1
ZN B(I,J) 'SCALE' 1/AREA
ND
CONSTANTS
* Constant terms for the above
DO I 0 NX
DO J 0 NY
X MINSURFO A(I,J) -1.0
ND
DO I 1 NX+1
DO J 1 NY+1
X MINSURFO B(I,J) -1.0
ND
BOUNDS
* bound {i in floor(0.25/hx)..ceil(0.75/hx),
* j in floor(0.25/hy)..ceil(0.75/hy)}: v[i,j] >= 1
RD 1/4HX HX 0.25
RD 3/4HX HX 0.75
RD 1/4HY HY 0.25
RD 3/4HY HY 0.75
RA 3/4HX 3/4HX 0.9999999999
RA 3/4HY 3/4HY 0.9999999999
IR 1/4HX 1/4HX
IR 1/4HY 1/4HY
IR 3/4HX 3/4HX
IR 3/4HY 3/4HY
DO I 1/4HX 3/4HX
DO J 1/4HY 3/4HY
XL MINSURFO V(I,J) 1.0
ND
DO J 0 NY+1
XX MINSURFO V(0,J) 0.0
XX MINSURFO V(NX+1,J) 0.0
ND
DO I 0 NX+1
RI I I
RM VIJ I 2.0
R* VIJ VIJ HX
RA VIJ VIJ -1.0
R* VIJ VIJ VIJ
R- VIJ ONE VIJ
ZX MINSURFO V(I,0) VIJ
ZX MINSURFO V(I,NY+1) VIJ
ND
START POINT
* let {i in 0..nx+1,j in 0..ny+1} v[i,j]:= 1 - (2*i*hx-1)^2
DO I 0 NX+1
RI I I
RM VIJ I 2.0
R* VIJ VIJ HX
RA VIJ VIJ -1.0
R* VIJ VIJ VIJ
R- VIJ ONE VIJ
DO J 0 NY+1
Z MINSURFO V(I,J) VIJ
ND
ELEMENT TYPE
EV ISQ V1 V2
IV ISQ U
ELEMENT USES
DO I 0 NX
IA I+1 I 1
DO J 0 NY
IA J+1 J 1
XT I(I,J) ISQ
ZV I(I,J) V1 V(I+1,J)
ZV I(I,J) V2 V(I,J)
XT J(I,J) ISQ
ZV J(I,J) V1 V(I,J+1)
ZV J(I,J) V2 V(I,J)
ND
DO J 0 NY+1
IA J1 J 1
XT J(NX+1,J) ISQ
ZV J(NX+1,J) V1 V(NX+1,J1)
ZV J(NX+1,J) V2 V(NX+1,J)
ND
DO I 0 NX+1
IA I1 I 1
XT I(I,NY+1) ISQ
ZV I(I,NY+1) V1 V(I1,NY+1)
ZV I(I,NY+1) V2 V(I,NY+1)
ND
GROUP TYPE
GV ROOT ALPHA
GROUP USES
* Define a group for each objective term {i in 0..nx,j in 0..ny}
* area*(1+((v[i+1,j]-v[i,j])/hx)^2+((v[i,j+1]-v[i,j])/hy)^2)^(1/2)
DO I 0 NX
DO J 0 NY
XT A(I,J) ROOT
ZE A(I,J) I(I,J) 1/HX2
ZE A(I,J) J(I,J) 1/HY2
ND
* Define a group for each objective term {i in 1..nx+1,j in 1..ny+1}
* area*(1+((v[i-1,j]-v[i,j])/hx)^2+((v[i,j-1]-v[i,j])/hy)^2)^(1/2))
DO I 1 NX+1
IA I-1 I -1
DO J 1 NY+1
IA J-1 J -1
XT B(I,J) ROOT
ZE B(I,J) I(I-1,J) 1/HX2
ZE B(I,J) J(I,J-1) 1/HY2
ND
OBJECT BOUND
* Solution
*LO SOLUTION 2.51948D+00 $ (NX=50,NY=25)
*LO SOLUTION 2.51488D+00 $ (NX=50,NY=50)
*LO SOLUTION 2.50568D+00 $ (NX=50,NY=75)
*LO SOLUTION 2.50694D+00 $ (NX=50,NY=100)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MINSURFO
INDIVIDUALS
* Difference squared
T ISQ
R U V1 1.0 V2 -1.0
F U * U
G U U + U
H U U 2.0
ENDATA
****************************
* SET UP THE GROUP ROUTINE *
****************************
GROUPS MINSURFO
TEMPORARIES
R ROOTAL
M SQRT
INDIVIDUALS
T ROOT
A ROOTAL SQRT( ALPHA )
F ROOTAL
G 0.5 / ROOTAL
H - 0.25 / ROOTAL ** 3
ENDATA