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READING3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME READING3
* Problem :
* *********
* A nonlinear optimal control problem from Nancy Nichols
* with a periodic boundary condition.
* This problem arises in tide modelling.
* Source:
* S. Lyle and N.K. Nichols,
* "Numerical Methods for Optimal Control Problems with State Constraints",
* Numerical Analysis Report 8/91, Dept of Mathematics,
* University of Reading, UK.
* SIF input: Nick Gould, July 1991.
* classification OOR2-MN-V-V
* Number of discretized points in [0,1]
*IE N 2 $-PARAMETER n=6, m=3
*IE N 5 $-PARAMETER n=12, m=6
*IE N 50 $-PARAMETER n=102, m=51
*IE N 100 $-PARAMETER n=202, m=101 original value
*IE N 500 $-PARAMETER n=1002, m=501
*IE N 1000 $-PARAMETER n=2002, m=1001
IE N 2000 $-PARAMETER n=4002, m=2001
*IE N 5000 $-PARAMETER n=10002, m=5001
* Other useful constants
RE PI 3.141592653589
RM 2PI PI 2.0
*RE 1/A 12.96
RE A 0.07716
RD 1/A A 1.0
RM 1/2A 1/A 0.5
RM 2A A 2.0
RM -2A 2A -1.0
RD -1/2A -2A 1.0
* Mesh
IA N-1 N -1
RI RN N
RD H RN 1.0
RM 2/H RN 2.0
RM H/2 H 0.5
RM 1/H RN 1.0
RM -1/H RN -1.0
* Constants
IE 0 0
IE 1 1
VARIABLES
DO I 0 N
X X(I)
X U(I)
ND
GROUPS
DO I 1 N
XN I(I)
ND
DO I 1 N
RI RI I
R* TI RI H
R* 2PITI 2PI TI
R( CTI COS 2PITI
R* CCTI CTI -1/2A
IA I-1 I -1
RI RI-1 I-1
R* TI-1 RI-1 H
R* 2PITI-1 2PI TI-1
R( CTI-1 COS 2PITI-1
R* CCTI-1 CTI-1 -1/2A
ZE C(I) X(I) 1/H
ZE C(I) X(I-1) -1/H
ZE C(I) U(I) CCTI
ZE C(I) U(I-1) CCTI-1
ND
XE PERIOD X(0) 1.0 X(N) -1.0
BOUNDS
DO I 0 N
XL READING3 X(I) -0.5
XU READING3 X(I) 0.5
ND
DO I 0 N
XL READING3 U(I) 0.0
XU READING3 U(I) 1.0
ND
ELEMENT TYPE
EV PROD U
EV PROD X
EP PROD P
EV ENERGY U
EV ENERGY X
EP ENERGY T
EP ENERGY HOVER2
ELEMENT USES
DO I 0 N
RI RI I
R* TI RI H
XT I(I) ENERGY
ZV I(I) X X(I)
ZV I(I) U U(I)
ZP I(I) T TI
ZP I(I) HOVER2 H/2
ND
DO I 0 N
XT NC(I) PROD
ZV NC(I) X X(I)
ZV NC(I) U U(I)
ZP NC(I) P 1/2A
ND
GROUP USES
DO I 1 N
IA I-1 I -1
XE I(I) I(I) -1.0
XE I(I) I(I-1) -1.0
ND
DO I 1 N
IA I-1 I -1
XE C(I) NC(I) NC(I-1)
ND
OBJECT BOUND
LO READING3 0.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
ELEMENTS READING3
* Least-square groups
TEMPORARIES
R C2PIT
M COS
INDIVIDUALS
T PROD
F P * U * X
G U P * X
G X P * U
H X U P
T ENERGY
A C2PIT COS(2.0*3.141592653589*T)
F HOVER2 * U * ( X - C2PIT ) ** 2
G U HOVER2 * ( X - C2PIT ) ** 2
G X HOVER2 * 2.0 * U * ( X - C2PIT )
H X U HOVER2 * 2.0 * ( X - C2PIT )
H X X HOVER2 * 2.0 * U
ENDATA