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AUG2D.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME AUG2D
* Problem :
* *********
* An expanded system formulation of a 2-D PDE system.
* A five-point discretization of Laplace's equation in a
* rectangular domain may be expressed in the form
* - M v = b,
* where M = sum a_i a_i^T. Letting A = (a_1 .... a_m),
* this system may be expanded as
* ( I A^T ) (x) = (0),
* ( A 0 ) (v) (b)
* which is then equivalent to solving the EQP
* minimize 1/2 || x ||_2^2 s.t. A x = b
* In this variant, we replace the leading I block in the
* above formulation with a zero-one diagonal matrix D.
* This corresponds to certain boundary conditions.
* The resulting QP is thus convex but not strictly convex.
* SIF input: Nick Gould, February 1994
* classification QLR2-AN-V-V
* Number of nodes in x direction
*IE NX 3 $-PARAMETER
*IE NX 10 $-PARAMETER
*IE NX 40 $-PARAMETER
IE NX 100 $-PARAMETER
*IE NX 200 $-PARAMETER
* Number of nodes in y direction
*IE NY 3 $-PARAMETER
*IE NY 10 $-PARAMETER
*IE NY 40 $-PARAMETER
IE NY 100 $-PARAMETER
*IE NY 200 $-PARAMETER
* Other useful parameters
IA X+ NX 1
IA X- NX -1
IA Y+ NY 1
IA Y- NY -1
IE 1 1
IE 0 0
* It is easier to describe this problem by columns.
GROUPS
* objective function
DO J 1 Y-
DO I 1 X-
XN OX(I,J)
XN OY(I,J)
ND
DO I 1 X-
XN OX(I,NY)
ND
DO J 1 Y-
XN OY(NX,J)
ND
* constraints
DO J 1 NY
DO I 1 NX
XE V(I,J)
ND
VARIABLES
* objective function terms
DO J 1 Y-
DO I 1 X-
X X(I,J) OX(I,J) 1.0
X Y(I,J) OY(I,J) 1.0
ND
DO I 1 X-
X X(I,NY) OX(I,NY) 1.0
ND
DO J 1 Y-
X Y(NX,J) OY(NX,J) 1.0
ND
* constraints : central constraints
DO J 1 Y-
IA J+ J 1
DO I 1 X-
IA I+ I 1
X X(I,J) V(I,J) 1.0 V(I+,J) -1.0
X Y(I,J) V(I,J) 1.0 V(I,J+) -1.0
ND
DO I 1 X-
IA I+ I 1
X X(I,NY) V(I,NY) 1.0 V(I+,NY) -1.0
ND
DO J 1 Y-
IA J+ J 1
X Y(NX,J) V(NX,J) 1.0 V(NX,J+) -1.0
ND
* edge constraints
DO I 1 NX
X X(I,0) V(I,1) 1.0
X X(I,Y+) V(I,NY) 1.0
ND
DO J 1 NY
X Y(0,J) V(1,J) 1.0
X Y(X+,J) V(NX,J) 1.0
ND
CONSTANTS
X AUG2D 'DEFAULT' 1.0
BOUNDS
FR AUG2D 'DEFAULT'
GROUP TYPE
GV SQUARE ALPHA
GROUP USES
DO J 1 Y-
DO I 1 X-
XT OX(I,J) SQUARE
XT OY(I,J) SQUARE
ND
DO I 1 X-
XT OX(I,NY) SQUARE
ND
DO J 1 Y-
XT OY(NX,J) SQUARE
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
GROUPS AUG2D
INDIVIDUALS
T SQUARE
F 5.0D-1 * ALPHA * ALPHA
G ALPHA
H 1.0D+0
ENDATA