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AUG3D.SIF
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AUG3D.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME AUG3D
* Problem :
* *********
* An expanded system formulation of a 3-D PDE system.
* A nine-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 equivalentto 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 20 $-PARAMETER
* Number of nodes in y direction
*IE NY 3 $-PARAMETER
*IE NY 10 $-PARAMETER
IE NY 20 $-PARAMETER
* Number of nodes in z direction
*IE NZ 3 $-PARAMETER
*IE NZ 10 $-PARAMETER
IE NZ 20 $-PARAMETER
* Other useful parameters
IA X+ NX 1
IA X- NX -1
IA Y+ NY 1
IA Y- NY -1
IA Z+ NZ 1
IA Z- NZ -1
I= M NX
I= N NY
I= P NZ
IE 1 1
IE 0 0
* It is easier to describe this problem by columns.
GROUPS
* objective function
DO K 1 Z-
DO J 1 Y-
DO I 1 X-
XN OX(I,J,K)
XN OY(I,J,K)
XN OZ(I,J,K)
ND
DO K 1 Z-
DO J 1 Y-
XN OY(NX,J,K)
XN OZ(NX,J,K)
ND
DO K 1 Z-
DO I 1 X-
XN OX(I,NY,K)
XN OZ(I,NY,K)
ND
DO J 1 Y-
DO I 1 X-
XN OX(I,J,NZ)
XN OY(I,J,NZ)
ND
* constraints
DO K 1 NZ
DO J 1 NY
DO I 1 NX
XE V(I,J,K)
ND
VARIABLES
* objective function terms
DO K 1 Z-
DO J 1 Y-
DO I 1 X-
X X(I,J,K) OX(I,J,K) 1.0
X Y(I,J,K) OY(I,J,K) 1.0
X Z(I,J,K) OZ(I,J,K) 1.0
ND
DO K 1 Z-
DO J 1 Y-
X Y(NX,J,K) OY(NX,J,K) 1.0
X Z(NX,J,K) OZ(NX,J,K) 1.0
ND
DO K 1 Z-
DO I 1 X-
X X(I,NY,K) OX(I,NY,K) 1.0
X Z(I,NY,K) OZ(I,NY,K) 1.0
ND
DO J 1 Y-
DO I 1 X-
X X(I,J,NZ) OX(I,J,NZ) 1.0
X Y(I,J,NZ) OY(I,J,NZ) 1.0
ND
* constraints : central constraints
DO K 1 Z-
IA K+ K 1
DO J 1 Y-
IA J+ J 1
DO I 1 X-
IA I+ I 1
X X(I,J,K) V(I,J,K) 1.0 V(I+,J,K) -1.0
X Y(I,J,K) V(I,J,K) 1.0 V(I,J+,K) -1.0
X Z(I,J,K) V(I,J,K) 1.0 V(I,J,K+) -1.0
ND
DO K 1 Z-
IA K+ K 1
DO J 1 Y-
IA J+ J 1
X Y(NX,J,K) V(NX,J,K) 1.0 V(NX,J+,K) -1.0
X Z(NX,J,K) V(NX,J,K) 1.0 V(NX,J,K+) -1.0
ND
DO K 1 Z-
IA K+ K 1
DO I 1 X-
IA I+ I 1
X X(I,NY,K) V(I,NY,K) 1.0 V(I+,NY,K) -1.0
X Z(I,NY,K) V(I,NY,K) 1.0 V(I,NY,K+) -1.0
ND
DO J 1 Y-
IA J+ J 1
DO I 1 X-
IA I+ I 1
X X(I,J,NZ) V(I,J,NZ) 1.0 V(I+,J,NZ) -1.0
X Y(I,J,NZ) V(I,J,NZ) 1.0 V(I,J+,NZ) -1.0
ND
* edge constraints
DO K 1 NZ
DO J 1 NY
X Y(0,J,K) V(1,J,K) 1.0
X Z(0,J,K) V(1,J,K) 1.0
X Y(X+,J,K) V(NX,J,K) 1.0
X Z(X+,J,K) V(NX,J,K) 1.0
ND
DO K 1 NZ
DO I 1 NX
X X(I,0,K) V(I,1,K) 1.0
X Z(I,0,K) V(I,1,K) 1.0
X X(I,Y+,K) V(I,NY,K) 1.0
X Z(I,Y+,K) V(I,NY,K) 1.0
ND
DO J 1 NY
DO I 1 NX
X X(I,J,0) V(I,J,1) 1.0
X Y(I,J,0) V(I,J,1) 1.0
X X(I,J,Z+) V(I,J,NZ) 1.0
X Y(I,J,Z+) V(I,J,NZ) 1.0
ND
CONSTANTS
X AUG3D 'DEFAULT' 1.0
BOUNDS
FR AUG3D 'DEFAULT'
GROUP TYPE
GV SQUARE ALPHA
GROUP USES
DO K 1 Z-
DO J 1 Y-
DO I 1 X-
XT OX(I,J,K) SQUARE
XT OY(I,J,K) SQUARE
XT OZ(I,J,K) SQUARE
ND
DO K 1 Z-
DO J 1 Y-
XT OY(M,J,K) SQUARE
XT OZ(M,J,K) SQUARE
ND
DO K 1 Z-
DO I 1 X-
XT OX(I,N,K) SQUARE
XT OZ(I,N,K) SQUARE
ND
DO J 1 Y-
DO I 1 X-
XT OX(I,J,P) SQUARE
XT OY(I,J,P) SQUARE
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
GROUPS AUG3D
INDIVIDUALS
T SQUARE
F 5.0D-1 * ALPHA * ALPHA
G ALPHA
H 1.0D+0
ENDATA