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MINSURF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MINSURF
* Problem :
* *********
* Variable dimension full rank linear problem
* A version of the minimum surface problem
* on the unit square with simple boundary conditions.
* SIF input: Ph. Toint, Jan 1991.
* classification OXR2-MY-64-0
* Discretization parameter
IE P 7
* Other parameters
IE 1 1
IA P+1 P 1
RI RP P
R* RPSQ RP RP
VARIABLES
DO i 1 P+1
DO j 1 P+1
X X(i,j)
OD j
OD i
GROUPS
DO i 1 P
DO j 1 P
XN S(i,j)
ZN S(i,j) 'SCALE' RPSQ
OD j
OD i
CONSTANTS
DO i 1 P
DO j 1 P
X MINSURF S(i,j) -1.0
OD j
OD i
BOUNDS
* Free variables inside the unit square
IE 2 2
DO i 2 P
DO j 2 P
XR MINSURF X(i,j)
OD j
OD i
* Boundaries
DO i 1 P+1
XX MINSURF X(1,i) 1.0
XX MINSURF X(P+1,i) 1.0
XX MINSURF X(i,1) 1.0
XX MINSURF X(i,P+1) 1.0
OD i
ELEMENT TYPE
EV ISQ V W
IV ISQ U
ELEMENT USES
DO i 1 P
IA i+1 i 1
DO j 1 P
IA j+1 j 1
* Diagonal
XT A(i,j) ISQ
ZV A(i,j) V X(i,j)
ZV A(i,j) W X(i+1,j+1)
* Antidiagonal
XT B(i,j) ISQ
ZV B(i,j) V X(i,j+1)
ZV B(i,j) W X(i+1,j)
OD j
OD i
GROUP TYPE
GV SQROOT ALPHA
GROUP USES
RM WEIGHT RPSQ 0.5
DO i 1 P
DO j 1 P
XT S(i,j) SQROOT
ZE S(i,j) A(i,j) WEIGHT
ZE S(i,j) B(i,j) WEIGHT
OD j
OD i
ENDATA
ELEMENTS MINSURF
INDIVIDUALS
T ISQ
R U V 1.0 W -1.0
F U * U
G U U + U
H U U 2.0
ENDATA
GROUPS MINSURF
TEMPORARIES
R SQRAL
M SQRT
INDIVIDUALS
T SQROOT
A SQRAL SQRT( ALPHA )
F SQRAL
G 0.5 / SQRAL
H -0.25 / ( ALPHA * SQRAL )
ENDATA