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GRIDGENA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GRIDGENA
* Problem:
* ********
* A grid generation problem on an irregular grid,
* using Ivanienko functional.
* The problem is to generate a smooth 2D grid on domains with irregular
* boundaries. The domain considered in this example has the shape
*
* 10 +----+ +---------+
* | | | |
* 8 | +----+ |
* | +----+
* 6 +----+ |
* | |
* 4 | |
* | +----+
* 2 +----+ |
* | |
* 0 +-------------------+
*
* 0 2 4 6 8
*
* It is decomposed in 4 successive "vertical" slices, whose limits are
*
* [0, 2] [6, 8] (2 parts)
* [0, 8]
* [0, 10]
* [0, 3] [7, 10] (2 parts)
*
* Each of these slices has a "width" of 2 units. For the variables
* definition and initialisation, one must also consider the special case
* of the vertical line at x=2, along which all variables are defined.
* Source:
* P. Barrera, A. Perez and L. Castellanos,
* "Generacion de Sistemas Coordenados curvilineos Sobre Regiones
* Irregulares",
* Technical Report, Facultad de Ciencias, UNAM, Mexico, 1991.
* SIF input: Ph. Toint, April 1992.
* correction by Ph. Shott, Jan 1995.
* classification OBI2-MY-V-0
* Number of intervals per unit length
*IE NDELTA 1 $-PARAMETER n = 170
IE NDELTA 2 $-PARAMETER n = 578 original value
*IE NDELTA 3 $-PARAMETER n = 1226
*IE NDELTA 4 $-PARAMETER n = 2114
*IE NDELTA 5 $-PARAMETER n = 3242
*IE NDELTA 6 $-PARAMETER n = 4610
IE NDELTA 7 $-PARAMETER n = 6218
*IE NDELTA 10 $-PARAMETER n = 12482
* Mesh size
RI RND NDELTA
RD H RND 1.0
* Perturbation to the starting point defined by the regular square grid
RM PERT H 0.1
* Useful parameters
IE 0 0
IE 1 1
* Limits of slices: En stands for the End of slice n
IM E2 NDELTA 2
IA E2-1 E2 -1
IA E2+1 E2 1
IM E3 NDELTA 3
IA E3-1 E3 -1
IA E3+1 E3 1
IM E4 NDELTA 4
IA E4-1 E4 -1
IA E4+1 E4 1
IM E6 NDELTA 6
IA E6-1 E6 -1
IA E6+1 E6 1
IM E7 NDELTA 7
IA E7-1 E7 -1
IA E7+1 E7 1
IM E8 NDELTA 8
IA E8-1 E8 -1
IA E8+1 E8 1
IM E10 NDELTA 10
IA E10-1 E10 -1
VARIABLES
* First vertical slice (2 parts)
DO J 0 E2-1
DO I 0 E2
X X(I,J)
X Y(I,J)
OD I
DO I E6 E10
X X(I,J)
X Y(I,J)
OD I
OD J
* The vertical line at x=2
DO I 0 E10
X X(I,E2)
X Y(I,E2)
OD I
* Second vertical slice
DO J E2+1 E4-1
DO I 0 E8
X X(I,J)
X Y(I,J)
OD I
OD J
* Third vertical slice
DO J E4 E6
DO I 0 E10
X X(I,J)
X Y(I,J)
OD I
OD J
* Fourth vertical slice (2 parts)
DO J E6+1 E8
DO I 0 E3
X X(I,J)
X Y(I,J)
OD I
DO I E7 E10
X X(I,J)
X Y(I,J)
OD I
OD J
GROUPS
XN OBJ
BOUNDS
UP GRIDGENA 'DEFAULT' 10.0
* The variables corresponding to the nodes on the domain's boundary
* are fixed to the position given by the regular square grid.
* This is achieved by fixing the variables on each boundary segment
* in turn, proceeding counter-clockwise.
* Bottom part of the boundary
DO J 0 E8
RI RJ J
R* X RJ H
ZX GRIDGENA X(0,J) X
XX GRIDGENA Y(0,J) 0.0
OD J
* Right side of the boundary
DO I 1 E3
RI RI I
R* Y RI H
XX GRIDGENA X(I,E8) 8.0
ZX GRIDGENA Y(I,E8) Y
OD I
DO J E6 E8-1
RI RJ J
R* X RJ H
ZX GRIDGENA X(E3,J) X
XX GRIDGENA Y(E3,J) 3.0
OD J
DO I E3+1 E7
RI RI I
R* Y RI H
XX GRIDGENA X(I,E6) 6.0
ZX GRIDGENA Y(I,E6) Y
OD I
DO J E6+1 E8
RI RJ J
R* X RJ H
ZX GRIDGENA X(E7,J) X
XX GRIDGENA Y(E7,J) 7.0
OD J
DO I E8+1 E10
RI RI I
R* Y RI H
XX GRIDGENA X(I,E8) 8.0
ZX GRIDGENA Y(I,E8) Y
OD I
DO J E4 E8-1
RI RJ J
R* X RJ H
ZX GRIDGENA X(E10,J) X
XX GRIDGENA Y(E10,J) 10.0
OD J
* Top part of the boundary
DO I E8 E10-1
RI RI I
R* Y RI H
XX GRIDGENA X(I,E4) 4.0
ZX GRIDGENA Y(I,E4) Y
OD I
DO J E2 E4-1
RI RJ J
R* X RJ H
ZX GRIDGENA X(E8,J) X
XX GRIDGENA Y(E8,J) 8.0
OD J
DO I E8+1 E10
RI RI I
R* Y RI H
XX GRIDGENA X(I,E2) 2.0
ZX GRIDGENA Y(I,E2) Y
OD I
DO J 0 E2-1
RI RJ J
R* X RJ H
ZX GRIDGENA X(E10,J) X
XX GRIDGENA Y(E10,J) 10.0
OD J
* Left side of the boundary
DO I E6 E10-1
RI RI I
R* Y RI H
XX GRIDGENA X(I,0) 0.0
ZX GRIDGENA Y(I,0) Y
OD I
DO J 1 E2
RI RJ J
R* X RJ H
ZX GRIDGENA X(E6,J) X
XX GRIDGENA Y(E6,J) 6.0
OD J
DO I E2 E6-1
RI RI I
R* Y RI H
XX GRIDGENA X(I,E2) 2.0
ZX GRIDGENA Y(I,E2) Y
OD I
DO J 0 E2-1
RI RJ J
R* X RJ H
ZX GRIDGENA X(E2,J) X
XX GRIDGENA Y(E2,J) 2.0
OD J
DO I 1 E2-1
RI RI I
R* Y RI H
XX GRIDGENA X(I,0) 0.0
ZX GRIDGENA Y(I,0) Y
OD I
START POINT
* First vertical slice (2 parts)
DO J 0 E2-1
DO I 0 E2
RI RJ J
R* X RJ H
R+ XX X PERT
RI RI I
R* Y RI H
Z GRIDGENA X(I,J) XX
Z GRIDGENA Y(I,J) Y
OD I
DO I E6 E10
RI RJ J
R* X RJ H
RI RI I
R* Y RI H
Z GRIDGENA X(I,J) X
Z GRIDGENA Y(I,J) Y
OD I
OD J
* Vertical line at x = 2
DO I 0 E10
RI RI I
R* Y RI H
X GRIDGENA X(I,E2) 2.0
Z GRIDGENA Y(I,E2) Y
OD I
* Second vertical slice
DO J E2+1 E4-1
DO I 0 E8
RI RJ J
R* X RJ H
R+ XX X PERT
RI RI I
R* Y RI H
R+ YY Y PERT
Z GRIDGENA X(I,J) XX
Z GRIDGENA Y(I,J) YY
OD I
OD J
* Third vertical slide
DO J E4 E6
DO I 0 E10
RI RJ J
R* X RJ H
R+ XX X PERT
RI RI I
R* Y RI H
R+ YY Y PERT
Z GRIDGENA X(I,J) XX
Z GRIDGENA Y(I,J) YY
OD I
OD J
* Fourth vertical slice (2 parts)
DO J E6+1 E8
DO I 0 E3
RI RJ J
R* X RJ H
RI RI I
R* Y RI H
Z GRIDGENA X(I,J) X
Z GRIDGENA Y(I,J) Y
OD I
DO I E7 E10
RI RJ J
R* X RJ H
RI RI I
R* Y RI H
Z GRIDGENA X(I,J) X
Z GRIDGENA Y(I,J) Y
OD I
OD J
ELEMENT TYPE
* All elements correspond to the Ivanienko functional for a triangle.
* This functional only depends ob the RELATIVE positions of
* the grid nodes, hence the internal variables corresponding to
* node coordinates differences.
EV IVNKO XA YA
EV IVNKO XB YB
EV IVNKO XC YC
IV IVNKO XBA YBA
IV IVNKO XCA YCA
ELEMENT USES
T 'DEFAULT' IVNKO
* First slice (2 parts)
DO J 0 E2-1
IA J+1 J 1
DO I 0 E2-1
IA I+1 I 1
ZV A(I,J) XA X(I,J)
ZV A(I,J) YA Y(I,J)
ZV A(I,J) XB X(I,J+1)
ZV A(I,J) YB Y(I,J+1)
ZV A(I,J) XC X(I+1,J)
ZV A(I,J) YC Y(I+1,J)
ZV B(I,J) XA X(I,J+1)
ZV B(I,J) YA Y(I,J+1)
ZV B(I,J) XB X(I+1,J+1)
ZV B(I,J) YB Y(I+1,J+1)
ZV B(I,J) XC X(I,J)
ZV B(I,J) YC Y(I,J)
ZV C(I,J) XA X(I+1,J+1)
ZV C(I,J) YA Y(I+1,J+1)
ZV C(I,J) XB X(I+1,J)
ZV C(I,J) YB Y(I+1,J)
ZV C(I,J) XC X(I,J+1)
ZV C(I,J) YC Y(I,J+1)
ZV D(I,J) XA X(I+1,J)
ZV D(I,J) YA Y(I+1,J)
ZV D(I,J) XB X(I,J)
ZV D(I,J) YB Y(I,J)
ZV D(I,J) XC X(I+1,J+1)
ZV D(I,J) YC Y(I+1,J+1)
OD I
DO I E6 E10-1
IA I+1 I 1
ZV A(I,J) XA X(I,J)
ZV A(I,J) YA Y(I,J)
ZV A(I,J) XB X(I,J+1)
ZV A(I,J) YB Y(I,J+1)
ZV A(I,J) XC X(I+1,J)
ZV A(I,J) YC Y(I+1,J)
ZV B(I,J) XA X(I,J+1)
ZV B(I,J) YA Y(I,J+1)
ZV B(I,J) XB X(I+1,J+1)
ZV B(I,J) YB Y(I+1,J+1)
ZV B(I,J) XC X(I,J)
ZV B(I,J) YC Y(I,J)
ZV C(I,J) XA X(I+1,J+1)
ZV C(I,J) YA Y(I+1,J+1)
ZV C(I,J) XB X(I+1,J)
ZV C(I,J) YB Y(I+1,J)
ZV C(I,J) XC X(I,J+1)
ZV C(I,J) YC Y(I,J+1)
ZV D(I,J) XA X(I+1,J)
ZV D(I,J) YA Y(I+1,J)
ZV D(I,J) XB X(I,J)
ZV D(I,J) YB Y(I,J)
ZV D(I,J) XC X(I+1,J+1)
ZV D(I,J) YC Y(I+1,J+1)
OD I
OD J
* Second vertical slice
DO J E2 E4-1
IA J+1 J 1
DO I 0 E8-1
IA I+1 I 1
ZV A(I,J) XA X(I,J)
ZV A(I,J) YA Y(I,J)
ZV A(I,J) XB X(I,J+1)
ZV A(I,J) YB Y(I,J+1)
ZV A(I,J) XC X(I+1,J)
ZV A(I,J) YC Y(I+1,J)
ZV B(I,J) XA X(I,J+1)
ZV B(I,J) YA Y(I,J+1)
ZV B(I,J) XB X(I+1,J+1)
ZV B(I,J) YB Y(I+1,J+1)
ZV B(I,J) XC X(I,J)
ZV B(I,J) YC Y(I,J)
ZV C(I,J) XA X(I+1,J+1)
ZV C(I,J) YA Y(I+1,J+1)
ZV C(I,J) XB X(I+1,J)
ZV C(I,J) YB Y(I+1,J)
ZV C(I,J) XC X(I,J+1)
ZV C(I,J) YC Y(I,J+1)
ZV D(I,J) XA X(I+1,J)
ZV D(I,J) YA Y(I+1,J)
ZV D(I,J) XB X(I,J)
ZV D(I,J) YB Y(I,J)
ZV D(I,J) XC X(I+1,J+1)
ZV D(I,J) YC Y(I+1,J+1)
OD I
OD J
* Third vertical slice
DO J E4 E6-1
IA J+1 J 1
DO I 0 E10-1
IA I+1 I 1
ZV A(I,J) XA X(I,J)
ZV A(I,J) YA Y(I,J)
ZV A(I,J) XB X(I,J+1)
ZV A(I,J) YB Y(I,J+1)
ZV A(I,J) XC X(I+1,J)
ZV A(I,J) YC Y(I+1,J)
ZV B(I,J) XA X(I,J+1)
ZV B(I,J) YA Y(I,J+1)
ZV B(I,J) XB X(I+1,J+1)
ZV B(I,J) YB Y(I+1,J+1)
ZV B(I,J) XC X(I,J)
ZV B(I,J) YC Y(I,J)
ZV C(I,J) XA X(I+1,J+1)
ZV C(I,J) YA Y(I+1,J+1)
ZV C(I,J) XB X(I+1,J)
ZV C(I,J) YB Y(I+1,J)
ZV C(I,J) XC X(I,J+1)
ZV C(I,J) YC Y(I,J+1)
ZV D(I,J) XA X(I+1,J)
ZV D(I,J) YA Y(I+1,J)
ZV D(I,J) XB X(I,J)
ZV D(I,J) YB Y(I,J)
ZV D(I,J) XC X(I+1,J+1)
ZV D(I,J) YC Y(I+1,J+1)
OD I
OD J
* Fourth vertical slice (2 parts)
DO J E6 E8-1
IA J+1 J 1
DO I 0 E3-1
IA I+1 I 1
ZV A(I,J) XA X(I,J)
ZV A(I,J) YA Y(I,J)
ZV A(I,J) XB X(I,J+1)
ZV A(I,J) YB Y(I,J+1)
ZV A(I,J) XC X(I+1,J)
ZV A(I,J) YC Y(I+1,J)
ZV B(I,J) XA X(I,J+1)
ZV B(I,J) YA Y(I,J+1)
ZV B(I,J) XB X(I+1,J+1)
ZV B(I,J) YB Y(I+1,J+1)
ZV B(I,J) XC X(I,J)
ZV B(I,J) YC Y(I,J)
ZV C(I,J) XA X(I+1,J+1)
ZV C(I,J) YA Y(I+1,J+1)
ZV C(I,J) XB X(I+1,J)
ZV C(I,J) YB Y(I+1,J)
ZV C(I,J) XC X(I,J+1)
ZV C(I,J) YC Y(I,J+1)
ZV D(I,J) XA X(I+1,J)
ZV D(I,J) YA Y(I+1,J)
ZV D(I,J) XB X(I,J)
ZV D(I,J) YB Y(I,J)
ZV D(I,J) XC X(I+1,J+1)
ZV D(I,J) YC Y(I+1,J+1)
OD I
DO I E7 E10-1
IA I+1 I 1
ZV A(I,J) XA X(I,J)
ZV A(I,J) YA Y(I,J)
ZV A(I,J) XB X(I,J+1)
ZV A(I,J) YB Y(I,J+1)
ZV A(I,J) XC X(I+1,J)
ZV A(I,J) YC Y(I+1,J)
ZV B(I,J) XA X(I,J+1)
ZV B(I,J) YA Y(I,J+1)
ZV B(I,J) XB X(I+1,J+1)
ZV B(I,J) YB Y(I+1,J+1)
ZV B(I,J) XC X(I,J)
ZV B(I,J) YC Y(I,J)
ZV C(I,J) XA X(I+1,J+1)
ZV C(I,J) YA Y(I+1,J+1)
ZV C(I,J) XB X(I+1,J)
ZV C(I,J) YB Y(I+1,J)
ZV C(I,J) XC X(I,J+1)
ZV C(I,J) YC Y(I,J+1)
ZV D(I,J) XA X(I+1,J)
ZV D(I,J) YA Y(I+1,J)
ZV D(I,J) XB X(I,J)
ZV D(I,J) YB Y(I,J)
ZV D(I,J) XC X(I+1,J+1)
ZV D(I,J) YC Y(I+1,J+1)
OD I
OD J
GROUP USES
* First vertical slice (2 parts)
DO J 0 E2-1
DO I 0 E2-1
XE OBJ A(I,J) B(I,J)
XE OBJ C(I,J) D(I,J)
OD I
DO I E6 E10-1
XE OBJ A(I,J) B(I,J)
XE OBJ C(I,J) D(I,J)
OD I
OD J
* Second vertical slice
DO J E2 E4-1
DO I 0 E8-1
XE OBJ A(I,J) B(I,J)
XE OBJ C(I,J) D(I,J)
OD I
OD J
* Third vertical slice
DO J E4 E6-1
DO I 0 E10-1
XE OBJ A(I,J) B(I,J)
XE OBJ C(I,J) D(I,J)
OD I
OD J
* Fourth vertical slice (2 parts)
DO J E6 E8-1
DO I 0 E3-1
XE OBJ A(I,J) B(I,J)
XE OBJ C(I,J) D(I,J)
OD I
DO I E7 E10-1
XE OBJ A(I,J) B(I,J)
XE OBJ C(I,J) D(I,J)
OD I
OD J
OBJECT BOUND
LO GRIDGENA 0.0
* Solution
*LO SOLTN(1) 480.0
*LO SOLTN(2) 1920.0
*LO SOLTN(3) 4320.0
*LO SOLTN(4) 7680.0
*LO SOLTN(5) 12000.0
*LO SOLTN(6) 17280.0
*LO SOLTN(7) 23520.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GRIDGENA
TEMPORARIES
R N
R D
R D2
R D3
INDIVIDUALS
* Ivanienko functional for a triangle
T IVNKO
R XBA XB 1.0 XA -1.0
R YBA YB 1.0 YA -1.0
R XCA XC 1.0 XA -1.0
R YCA YC 1.0 YA -1.0
A N XBA * XBA + YCA * YCA + YBA * YBA
A+ + XCA * XCA
A D XBA * YCA - YBA * XCA
A D2 D * D
A D3 D * D2
F N / D
G XBA 2.0 * XBA / D - N * YCA / D2
G YBA 2.0 * YBA / D + N * XCA / D2
G XCA 2.0 * XCA / D + N * YBA / D2
G YCA 2.0 * YCA / D - N * XBA / D2
H XBA XBA 2.0 / D + 2.0 * N * YCA * YCA / D3
H+ - 4.0 * XBA * YCA / D2
H XBA YBA 2.0 * ( XBA * XCA - YBA * YCA ) / D2
H+ - 2.0 * N * YCA * XCA / D3
H XBA XCA 2.0 * ( XBA * YBA - XCA * YCA ) / D2
H+ - 2.0 * N * YCA * YBA / D3
H XBA YCA - 2.0 * ( XBA * XBA + YCA * YCA ) / D2
H+ + 2.0 * N * YCA * XBA / D3 - N / D2
H YBA YBA 2.0 / D + 2.0 * N * XCA * XCA / D3
H+ + 4.0 * YBA * XCA / D2
H YBA XCA 2.0 * ( YBA * YBA + XCA * XCA ) / D2
H+ + 2.0 * N * XCA * YBA / D3 + N / D2
H YBA YCA - 2.0 * ( YBA * XBA - YCA * XCA ) / D2
H+ - 2.0 * N * XCA * XBA / D3
H XCA XCA 2.0 / D + 2.0 * N * YBA * YBA / D3
H+ + 4.0 * XCA * YBA / D2
H XCA YCA - 2.0 * ( XCA * XBA - YCA * YBA ) / D2
H+ - 2.0 * N * YBA * XBA / D3
H YCA YCA 2.0 / D + 2.0 * N * XBA * XBA / D3
H+ - 4.0 * YCA * XBA / D2
ENDATA