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RDW2D52B.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME RDW2D52B
* Problem :
* *********
* A finite-element approximation to the distributed optimal control problem
* min 1/2||u-v||_L2^2 + beta ||f||_L2^2
* subject to - nabla^2 u = f
* where v is given on and within the boundary of a unit [0,1] box in
* 2 dimensions, and u = v on its boundary. The discretization uses
* quadrilateral elememts. There are simple bounds on both the controls
* f and states u
* The problem is stated as a quadratic program
* Source: example 5.2 in
* T. Rees, H. S. Dollar and A. J. Wathen
* "Optimal solvers for PDE-constrained optimization"
* SIAM J. Sci. Comp. (to appear) 2009
* with the control bounds as specified in
* M. Stoll and A. J. Wathen
* "Preconditioning for PDE constrained optimization with
* control constraints"
* OUCL Technical Report 2009
* SIF input: Nick Gould, May 2009
* classification QLR2-AN-V-V
* Number of nodes in each direction (a power of 2)
*IE N 2 $-PARAMETER
*IE N 4 $-PARAMETER
*IE N 8 $-PARAMETER
*IE N 16 $-PARAMETER
*IE N 32 $-PARAMETER
*IE N 64 $-PARAMETER
*IE N 128 $-PARAMETER
IE N 256 $-PARAMETER
*IE N 512 $-PARAMETER
*IE N 1024 $-PARAMETER
*IE N 2048 $-PARAMETER
*IE N 4096 $-PARAMETER
*IE N 8192 $-PARAMETER
*IE N 16384 $-PARAMETER
* Regularisation
RE BETA 0.005 $-PARAMETER
* Other useful parameters
RE ZERO 0.0
RE ONE 1.0
RE TWO 2.0
RE SIX 6.0
RE THIRTYSIX 36.0
IE 0 0
IE 1 1
IE 2 2
IA N- N -1
IA N-1 N -1
IA N-2 N -2
I/ N/2 N 2
I+ N/2+1 N/2 1
RI RN N
R/ H ONE RN
R* H**2 H H
R/ H**2/36 H**2 THIRTYSIX
RM -H**2/36 H**2/36 -1.0
RM 2BETA BETA 2.0
R* 2BH**2/36 2BETA H**2/36
R/ 1/6 ONE SIX
* target data
DO I 0 N
RI RI I
R* X RI H
RA X- X -0.5
R* X-**2 X- X-
DO J 0 N
RI RJ J
R* Y RJ H
RA Y- Y -0.5
R* Y-**2 Y- Y-
R+ SS X-**2 Y-**2
RM -64SS SS -64.0
R( V EXP -64SS
A= V(I,J) V
ND
VARIABLES
DO I 0 N
DO J 0 N
X F(I,J)
ND
DO I 0 N
DO J 0 N
X U(I,J)
ND
GROUPS
* objective function
N OBJ
* constraints
DO I 1 N-1
DO J 1 N-1
XE L(I,J)
ND
BOUNDS
XR RDW2D52B 'DEFAULT'
ZX RDW2D52B U(0,0) V(0,0)
ZX RDW2D52B U(N,0) V(N,0)
ZX RDW2D52B U(0,N) V(0,N)
ZX RDW2D52B U(N,N) V(N,N)
DO I 1 N-1
ZX RDW2D52B U(0,I) V(0,I)
ZX RDW2D52B U(N,I) V(N,I)
ZX RDW2D52B U(I,0) V(I,0)
ZX RDW2D52B U(I,N) V(I,N)
ND
XX RDW2D52B F(0,0) 0.0
XX RDW2D52B F(N,0) 0.0
XX RDW2D52B F(0,N) 0.0
XX RDW2D52B F(N,N) 0.0
DO I 1 N-1
XX RDW2D52B F(0,I) 0.0
XX RDW2D52B F(N,I) 0.0
XX RDW2D52B F(I,0) 0.0
XX RDW2D52B F(I,N) 0.0
ND
DO I 1 N-1
DO J 1 N-1
XU RDW2D52B U(I,J) 0.01
ND
DO I 1 N-1
RI RI I
R* X1 RI H
R* X1**2 X1 X1
RM -X1**2 X1**2 -1.0
R- 2-X1 TWO X1
RM 0.1(2-X1) 2-X1 0.1
DO J 1 N-1
RI RJ J
R* X2 RJ H
R* X2**2 X2 X2
R- ARG -X1**2 X2**2
R( EARG EXP ARG
R* UA 0.1(2-X1) EARG
ZL RDW2D52B F(I,J) UA
OD J
DO J 1 N/2
XU RDW2D52B F(I,J) 0.6
OD J
DO J N/2+1 N-1
XU RDW2D52B F(I,J) 0.9
OD J
OD I
START POINT
DO I 0 N
DO J 0 N
I+ I+J I J
RI RI+J I+J
R/ RI+J/N RI+J RN
*Z RDW2D52B U(I,J) RI+J/N
ND
ELEMENT TYPE
* 1/2 (u-v)^T M (u-v) term
EV M U1 U2
EV M U3 U4
EP M V1 V2
EP M V3 V4
* 1/2 f^T M f term
EV M0 F1 F2
EV M0 F3 F4
* linear terms
EV A U1 U2
EV A U3 U4
EV B U1 U2
EV B U3 U4
EV C U1 U2
EV C U3 U4
EV D U1 U2
EV D U3 U4
EV P F1 F2
EV P F3 F4
EV Q F1 F2
EV Q F3 F4
EV R F1 F2
EV R F3 F4
EV S F1 F2
EV S F3 F4
ELEMENT USES
DO I 0 N-1
I+ I+ I 1
DO J 0 N-1
I+ J+ J 1
XT E(I,J) M
ZV E(I,J) U1 U(I,J)
ZV E(I,J) U2 U(I,J+)
ZV E(I,J) U3 U(I+,J)
ZV E(I,J) U4 U(I+,J+)
ZP E(I,J) V1 V(I,J)
ZP E(I,J) V2 V(I,J+)
ZP E(I,J) V3 V(I+,J)
ZP E(I,J) V4 V(I+,J+)
ND
DO I 0 N-1
I+ I+ I 1
DO J 0 N-1
I+ J+ J 1
XT F(I,J) M0
ZV F(I,J) F1 F(I,J)
ZV F(I,J) F2 F(I,J+)
ZV F(I,J) F3 F(I+,J)
ZV F(I,J) F4 F(I+,J+)
ND
DO I 0 N-1
I+ I+ I 1
DO J 0 N-1
I+ J+ J 1
XT A(I,J) A
ZV A(I,J) U1 U(I,J)
ZV A(I,J) U2 U(I,J+)
ZV A(I,J) U3 U(I+,J)
ZV A(I,J) U4 U(I+,J+)
XT B(I,J) B
ZV B(I,J) U1 U(I,J)
ZV B(I,J) U2 U(I,J+)
ZV B(I,J) U3 U(I+,J)
ZV B(I,J) U4 U(I+,J+)
XT C(I,J) C
ZV C(I,J) U1 U(I,J)
ZV C(I,J) U2 U(I,J+)
ZV C(I,J) U3 U(I+,J)
ZV C(I,J) U4 U(I+,J+)
XT D(I,J) D
ZV D(I,J) U1 U(I,J)
ZV D(I,J) U2 U(I,J+)
ZV D(I,J) U3 U(I+,J)
ZV D(I,J) U4 U(I+,J+)
ND
DO I 0 N-1
I+ I+ I 1
DO J 0 N-1
I+ J+ J 1
XT P(I,J) P
ZV P(I,J) F1 F(I,J)
ZV P(I,J) F2 F(I,J+)
ZV P(I,J) F3 F(I+,J)
ZV P(I,J) F4 F(I+,J+)
XT Q(I,J) Q
ZV Q(I,J) F1 F(I,J)
ZV Q(I,J) F2 F(I,J+)
ZV Q(I,J) F3 F(I+,J)
ZV Q(I,J) F4 F(I+,J+)
XT R(I,J) R
ZV R(I,J) F1 F(I,J)
ZV R(I,J) F2 F(I,J+)
ZV R(I,J) F3 F(I+,J)
ZV R(I,J) F4 F(I+,J+)
XT S(I,J) S
ZV S(I,J) F1 F(I,J)
ZV S(I,J) F2 F(I,J+)
ZV S(I,J) F3 F(I+,J)
ZV S(I,J) F4 F(I+,J+)
ND
GROUP USES
DO I 0 N-1
DO J 0 N-1
ZE OBJ E(I,J) H**2/36
ZE OBJ F(I,J) 2BH**2/36
ND
DO I 1 N-2
I+ I+ I 1
DO J 1 N-2
I+ J+ J 1
ZE L(I,J) A(I,J) 1/6
ZE L(I,J+) B(I,J) 1/6
ZE L(I+,J) C(I,J) 1/6
ZE L(I+,J+) D(I,J) 1/6
ZE L(I,J) P(I,J) -H**2/36
ZE L(I,J+) Q(I,J) -H**2/36
ZE L(I+,J) R(I,J) -H**2/36
ZE L(I+,J+) S(I,J) -H**2/36
ND
DO I 1 N-2
I+ I+ I 1
ZE L(I,N-) A(I,N-) 1/6
ZE L(I,1) B(I,0) 1/6
ZE L(I+,N-) C(I,N-) 1/6
ZE L(I+,1) D(I,0) 1/6
ZE L(I,N-) P(I,N-) -H**2/36
ZE L(I,1) Q(I,0) -H**2/36
ZE L(I+,N-) R(I,N-) -H**2/36
ZE L(I+,1) S(I,0) -H**2/36
ND
DO J 1 N-2
I+ J+ J 1
ZE L(N-,J) A(N-,J) 1/6
ZE L(N-,J+) B(N-,J) 1/6
ZE L(1,J) C(0,J) 1/6
ZE L(1,J+) D(0,J) 1/6
ZE L(N-,J) P(N-,J) -H**2/36
ZE L(N-,J+) Q(N-,J) -H**2/36
ZE L(1,J) R(0,J) -H**2/36
ZE L(1,J+) S(0,J) -H**2/36
ND
ZE L(N-,N-) A(N-,N-) 1/6
ZE L(N-,1) B(N-,0) 1/6
ZE L(1,N-) C(0,N-) 1/6
ZE L(1,1) D(0,0) 1/6
ZE L(N-,N-) P(N-,N-) -H**2/36
ZE L(N-,1) Q(N-,0) -H**2/36
ZE L(1,N-) R(0,N-) -H**2/36
ZE L(1,1) S(0,0) -H**2/36
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS RDW2D52B
TEMPORARIES
R UV1
R UV2
R UV3
R UV4
R C1
R C2
R C3
R C4
INDIVIDUALS
T M
A UV1 U1 - V1
A UV2 U2 - V2
A UV3 U3 - V3
A UV4 U4 - V4
F 2.0 * UV1 ** 2 + 2.0 * UV2 ** 2 +
F+ 2.0 * UV3 ** 2 + 2.0 * UV4 ** 2 +
F+ 2.0 * UV1*UV2 + 2.0 * UV1*UV3 +
F+ UV1*UV4 + UV2*UV3 +
F+ 2.0 * UV2*UV4 + 2.0 * UV3*UV4
G U1 4.0 * UV1 + 2.0 * UV2 + 2.0 * UV3 + UV4
G U2 2.0 * UV1 + 4.0 * UV2 + UV3 + 2.0 * UV4
G U3 2.0 * UV1 + UV2 + 4.0 * UV3 + 2.0 * UV4
G U4 UV1 + 2.0 * UV2 + 2.0 * UV3 + 4.0 * UV4
H U1 U1 4.0
H U1 U2 2.0
H U1 U3 2.0
H U1 U4 1.0
H U2 U2 4.0
H U2 U3 1.0
H U2 U4 2.0
H U3 U3 4.0
H U3 U4 2.0
H U4 U4 4.0
T M0
F 2.0 * F1 ** 2 + 2.0 * F2 ** 2 +
F+ 2.0 * F3 ** 2 + 2.0 * F4 ** 2 +
F+ 2.0 * F1*F2 + 2.0 * F1*F3 +
F+ F1*F4 + F2*F3 +
F+ 2.0 * F2*F4 + 2.0 * F3*F4
G F1 4.0 * F1 + 2.0 * F2 + 2.0 * F3 + F4
G F2 2.0 * F1 + 4.0 * F2 + F3 + 2.0 * F4
G F3 2.0 * F1 + F2 + 4.0 * F3 + 2.0 * F4
G F4 F1 + 2.0 * F2 + 2.0 * F3 + 4.0 * F4
H F1 F1 4.0
H F1 F2 2.0
H F1 F3 2.0
H F1 F4 1.0
H F2 F2 4.0
H F2 F3 1.0
H F2 F4 2.0
H F3 F3 4.0
H F3 F4 2.0
H F4 F4 4.0
T A
A C1 4.0
A C2 -1.0
A C3 -1.0
A C4 -2.0
F C1 * U1 + C2 * U2 + C3 * U3 + C4 * U4
G U1 C1
G U2 C2
G U3 C3
G U4 C4
T B
A C1 -1.0
A C2 4.0
A C3 -2.0
A C4 -1.0
F C1 * U1 + C2 * U2 + C3 * U3 + C4 * U4
G U1 C1
G U2 C2
G U3 C3
G U4 C4
T C
A C1 -1.0
A C2 -2.0
A C3 4.0
A C4 -1.0
F C1 * U1 + C2 * U2 + C3 * U3 + C4 * U4
G U1 C1
G U2 C2
G U3 C3
G U4 C4
T D
A C1 -2.0
A C2 -1.0
A C3 -1.0
A C4 4.0
F C1 * U1 + C2 * U2 + C3 * U3 + C4 * U4
G U1 C1
G U2 C2
G U3 C3
G U4 C4
T P
A C1 4.0
A C2 2.0
A C3 2.0
A C4 1.0
F C1 * F1 + C2 * F2 + C3 * F3 + C4 * F4
G F1 C1
G F2 C2
G F3 C3
G F4 C4
T Q
A C1 2.0
A C2 4.0
A C3 1.0
A C4 2.0
F C1 * F1 + C2 * F2 + C3 * F3 + C4 * F4
G F1 C1
G F2 C2
G F3 C3
G F4 C4
T R
A C1 2.0
A C2 1.0
A C3 4.0
A C4 2.0
F C1 * F1 + C2 * F2 + C3 * F3 + C4 * F4
G F1 C1
G F2 C2
G F3 C3
G F4 C4
T S
A C1 1.0
A C2 2.0
A C3 2.0
A C4 4.0
F C1 * F1 + C2 * F2 + C3 * F3 + C4 * F4
G F1 C1
G F2 C2
G F3 C3
G F4 C4
ENDATA