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JNLBRNG1.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME JNLBRNG1
* Problem :
* *********
* The quadratic journal bearing problem (with excentricity = 0.1)
* This is a variant of the problem stated in the report quoted below.
* It corresponds to the problem as distributed in MINPACK-2.
* Source:
* J. More' and G. Toraldo,
* "On the Solution of Large Quadratic-Programming Problems with Bound
* Constraints",
* SIAM J. on Optimization, vol 1(1), pp. 93-113, 1991.
* SIF input: Ph. Toint, Dec 1989.
* modified by Peihuang Chen, according to MINPACK-2, Apr 1992
* classification QBR2-AY-V-0
* The rectangle is discretized into (pt-1)(py-1) little rectangles. The
* heights of the considered surface above the corners of these little
* rectangles are the problem variables, There are px*py of them.
* PT is the number of points along the T (\theta) side of the rectangle
* PY is the number of points along the Y side of the rectangle
*IE PT 4 $-PARAMETER n=16
*IE PY 4 $-PARAMETER
*IE PT 10 $-PARAMETER n=100
*IE PY 10 $-PARAMETER
*IE PT 23 $-PARAMETER n=529
*IE PY 23 $-PARAMETER
*IE PT 32 $-PARAMETER n=1024
*IE PY 32 $-PARAMETER
*IE PT 34 $-PARAMETER n=1156
*IE PY 34 $-PARAMETER
*IE PT 75 $-PARAMETER n=5625 original value
*IE PY 75 $-PARAMETER original value
IE PT 100 $-PARAMETER n=10000
IE PY 100 $-PARAMETER
*IE PT 125 $-PARAMETER n=15625
*IE PY 125 $-PARAMETER
* The excentricity
RE EX 0.1 $-PARAMETER the excentricity
* The domain is the rectangle [0,LT]x[0,LY]
RF PI/4 ARCTAN 1.
RM LT PI/4 8.
RE LY 20.0
*
RE SIX 6.0
* Compute the step in the \theta direction and its inverse
IA PT-1 PT -1
RI RPT-1 PT-1
RD HT1 RPT-1 1.0
R* HT HT1 LT
RD 1/HT HT 1.0
* Compute the step in the y direction and its inverse
IA PY-1 PY -1
RI RPY-1 PY-1
RD HY1 RPY-1 1.0
R* HY HY1 LY
RD 1/HY HY 1.0
* Compute their ratio and product
R* HTHY HT HY
R* HT/HY HT 1/HY
R* HY/HT HY 1/HT
* Compute the common coefficient for the linear term
R* EXHTHY HTHY EX
RM CLINC EXHTHY -1.0
* Useful constants
IE 1 1
IE 2 2
VARIABLES
* Define one variable per discretized point in the unit square
DO I 1 PT
DO J 1 PY
X X(I,J)
ND
GROUPS
* Group of the linear terms
DO I 2 PT-1
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HT
R( SXI1 SIN XI1
R* COEFF SXI1 CLINC
DO J 2 PY-1
ZN G X(I,J) COEFF
ND
* TRIANGLES at the right upper side of node(i,j)
DO I 1 PT-1
DO J 1 PY-1
ZN GR(I,J)
XN GR(I,J) 'SCALE' 2.0
ND
* TRIANGLES at the left lower side of node(i,j)
DO I 2 PT
DO J 2 PY
ZN GL(I,J)
XN GL(I,J) 'SCALE' 2.0
ND
BOUNDS
* Fix the variables on the lower and upper edges of the domain
DO J 1 PY
XX JNLBRNG1 X(1,J) 0.0
XX JNLBRNG1 X(PT,J) 0.0
ND
* Fix the variables on the left and right edges of the domain
DO I 2 PT-1
XX JNLBRNG1 X(I,PY) 0.0
XX JNLBRNG1 X(I,1) 0.0
ND
* Other variables are positive
START POINT
DO I 2 PT-1
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HT
R( SXI1 SIN XI1
DO J 2 PY-1
ZV JNLBRNG1 X(I,J) SXI1
ND
ELEMENT TYPE
* The only element type.
* The parameter will care for the factors involving HX and HY, MU
* and LA(mbda).
EV ISQ V1 V2
IV ISQ U
ELEMENT USES
* Each node has four elements
DO I 1 PT-1
IA I+1 I 1
DO J 1 PY-1
IA J+1 J 1
XT A(I,J) ISQ
ZV A(I,J) V1 X(I+1,J)
ZV A(I,J) V2 X(I,J)
XT B(I,J) ISQ
ZV B(I,J) V1 X(I,J+1)
ZV B(I,J) V2 X(I,J)
ND
DO I 2 PT
IA I-1 I -1
DO J 2 PY
IA J-1 J -1
XT C(I,J) ISQ
ZV C(I,J) V1 X(I-1,J)
ZV C(I,J) V2 X(I,J)
XT D(I,J) ISQ
ZV D(I,J) V1 X(I,J-1)
ZV D(I,J) V2 X(I,J)
ND
GROUP USES
* All groups are TRIVIAL
* GROUPS OF ALL THE TRIANGLES AT THE RIGHT OF A NODE
DO I 1 PT-1
* Compute w_q(z_{i,j}) = w_q(z_{i+1,j}) = w_q(z_{i-1,j})
* (independent of J, that is of \xi_2)
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HT
R( CXI1 COS XI1
R* ECX CXI1 EX
RA ECX1 ECX 1.0
R* E12 ECX1 ECX1
R* WI ECX1 E12
R+ 2WI WI WI
* Compute w_q(z_{i+1,j}) (independent of J, that is of \xi_2)
R+ XI+1 XI1 HT
R( CXI+1 COS XI+1
R* E+CX0 CXI+1 EX
RA E+CX1 E+CX0 1.0
R* E22 E+CX1 E+CX1
R* WI+1 E+CX1 E22
* Compute \LAMBDA_{i,j}/ h_t^2 and \LAMBDA_{i,j} / h_y^2
* (independent of J, that is of \xi_2)
R+ PM0 2WI WI+1
R/ PM1 PM0 SIX
R* LA/HY2 PM1 HT/HY
R* LA/HT2 PM1 HY/HT
DO J 1 PY-1
ZE GR(I,J) A(I,J) LA/HT2
ZE GR(I,J) B(I,J) LA/HY2
ND
* GROUPS OF ALL THE TRIANGLES AT THE LEFT OF A NODE
DO I 2 PT
* Compute w_q(z_{i,j}) = w_q(z_{i+1,j}) = w_q(z_{i-1,j})
* (independent of J, that is of \xi_2)
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HT
R( CXI1 COS XI1
R* ECX CXI1 EX
RA ECX1 ECX 1.0
R* E12 ECX1 ECX1
R* WI ECX1 E12
R+ 2WI WI WI
* Compute w_q(z_{i-1,j}) (independent of J, that is of \xi_2)
R- XI-1 XI1 HT
R( CXI-1 COS XI-1
R* E-CX0 CXI-1 EX
RA E-CX1 E-CX0 1.0
R* E32 E-CX1 E-CX1
R* WI-1 E-CX1 E32
* Compute \MU_{i,j} / h_y^2 and \MU_{i,j} / h_t^2
* (independent of J, that is of \xi_2)
R+ PL0 2WI WI-1
R/ PL1 PL0 SIX
R* MU/HY2 PL1 HT/HY
R* MU/HT2 PL1 HY/HT
DO J 2 PY
ZE GL(I,J) C(I,J) MU/HT2
ZE GL(I,J) D(I,J) MU/HY2
ND
OBJECT BOUND
LO JNLBRNG1 0.0
* Solution
*LO SOLTN(4) -0.2247400
*LO SOLTN(10) -0.1789600
*LO SOLTN(23) -0.1800500
*LO SOLTN(32) -0.1803000
*LO SOLTN(75) -0.1805500
*LO SOLTN(100) -0.1805700
*LO SOLTN(125) -0.1805800
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS JNLBRNG1
INDIVIDUALS
T ISQ
R U V1 1.0 V2 -1.0
F U * U
G U U + U
H U U 2.0
ENDATA