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RDW2D51U.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME RDW2D51U
* 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.
* The problem is stated as a quadratic program
* Source: example 5.1 in
* T. Rees, H. S. Dollar and A. J. Wathen
* "Optimal solvers for PDE-constrained optimization"
* SIAM J. Sci. Comp. (to appear) 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 0.01 $-PARAMETER
* Other useful parameters
RE ZERO 0.0
RE ONE 1.0
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/2
RI RI I
RM 2RI RI 2.0
R* 2RIH 2RI H
R- 2RIH-1 2RIH ONE
R* 2RIH-1S 2RIH-1 2RIH-1
DO J 0 N/2
RI RJ J
RM 2RJ RJ 2.0
R* 2RJH 2RJ H
R- 2RJH-1 2RJH ONE
R* 2RJH-1S 2RJH-1 2RJH-1
R* V 2RIH-1S 2RJH-1S
A= V(I,J) V
ND
DO I N/2+1 N
DO J N/2+1 N
AE V(I,J) ZERO
ND
DO I 0 N/2
DO J N/2+1 N
AE V(I,J) ZERO
ND
DO I N/2+1 N
DO J 0 N/2
AE V(I,J) ZERO
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
*X B(0,0)
*X B(N,0)
*X B(0,N)
*X B(N,N)
*DO I 1 N-1
*X B(0,I)
*X B(N,I)
*X B(I,0)
*X B(I,N)
*ND
GROUPS
* objective function
N OBJ
* constraints
DO I 1 N-1
DO J 1 N-1
XE L(I,J)
ND
BOUNDS
XR RDW2D51U 'DEFAULT'
ZX RDW2D51U U(0,0) V(0,0)
ZX RDW2D51U U(N,0) V(N,0)
ZX RDW2D51U U(0,N) V(0,N)
ZX RDW2D51U U(N,N) V(N,N)
DO I 1 N-1
ZX RDW2D51U U(0,I) V(0,I)
ZX RDW2D51U U(N,I) V(N,I)
ZX RDW2D51U U(I,0) V(I,0)
ZX RDW2D51U U(I,N) V(I,N)
ND
XX RDW2D51U F(0,0) 0.0
XX RDW2D51U F(N,0) 0.0
XX RDW2D51U F(0,N) 0.0
XX RDW2D51U F(N,N) 0.0
DO I 1 N-1
XX RDW2D51U F(0,I) 0.0
XX RDW2D51U F(N,I) 0.0
XX RDW2D51U F(I,0) 0.0
XX RDW2D51U F(I,N) 0.0
ND
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 RDW2D51U 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 RDW2D51U
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