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MESH.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MESH
* Problem:
* ********
* The goodness of a finite element grid is characterized by the
* smallest angle of all triangles. Given a triangulation of a domain
* in R**2. Find a topological equivalent triangulation so, that the
* smallest angel becomes as large as possible. Topological equivalent
* means shifting the edges of the grid only in such a way that
* neighbouring triangles remain neighbours.
* Source: Prof. Dr. Michael Kraetzschmar, Institut fuer Angewandte
* Mathematik der Fachhochschule Flensburg, Kanzleistrasse 91-93,
* D-24943 FLENSBURG, GERMANY
* SIF input: Prof. Dr. Michael Kraetzschmar
* classification OOR2-AY-41-48
* Problem data
RE omega1 1.0D3
RE omega2 -1.0D3
RE omega3 -1.0D5
RE s 0.700000
RF pi ARCCOS -1.0
RF sqrt3/2 SQRT 0.75
R* h sqrt3/2 s
RE drei 3.0
R/ pi/3 pi drei
IE 1 1
IE np 5
IE nk 8
IE nd 4
VARIABLES
DO i 1 np
X x(i)
X y(i)
OD i
DO i 1 nk
X l(i)
OD i
DO i 1 nd
X alpha(i)
X beta(i)
X gamma(i)
X delta(i)
X f(i)
OD i
deltamin
fmin
fmax
GROUPS
XN obj1 deltamin 1.0
ZN obj1 'SCALE' omega1
XN obj2 fmax 1.0 fmin -1.0
ZN obj2 'SCALE' omega2
XN obj3
ZN obj3 'SCALE' omega3
DO i 1 nk
XE seit(i)
OD i
DO i 1 nd
XE skal(i)
XE skbe(i)
OD i
DO i 1 nd
XE doppf(i) f(i) -1.0
OD i
DO i 1 nd
XE wisum(i) alpha(i) 1.0 beta(i) 1.0
XE wisum(i) gamma(i) 1.0
OD i
DO i 1 nd
XG alphd(i) alpha(i) 1.0 delta(i) -1.0
XG betad(i) beta(i) 1.0 delta(i) -1.0
XG gammd(i) gamma(i) 1.0 delta(i) -1.0
XG deltd(i) delta(i) 1.0 deltamin -1.0
OD i
DO i 1 nd
XG fmind(i) f(i) 1.0 fmin -1.0
XG fmaxd(i) fmax 1.0 f(i) -1.0
OD i
CONSTANTS
DO i 1 nd
Z MESH wisum(i) pi
OD i
BOUNDS
ZU MESH deltamin pi
XX MESH x1 0.000000
XX MESH y1 0.000000
XX MESH x2 0.000000
XX MESH y2 1.000000
XX MESH x3 1.000000
XX MESH y3 1.000000
XX MESH x4 1.000000
XX MESH y4 0.000000
XR MESH x5
XR MESH y5
DO i 1 nd
ZU MESH alpha(i) pi
ZU MESH beta(i) pi
ZU MESH gamma(i) pi
ZU MESH delta(i) pi
OD i
ZU MESH deltamin pi
START POINT
XV MESH x1 0.000000
XV MESH y1 0.000000
XV MESH x2 0.000000
XV MESH y2 1.000000
XV MESH x3 1.000000
XV MESH y3 1.000000
XV MESH x4 1.000000
XV MESH y4 0.000000
XV MESH x5 0.350000
XV MESH y5 0.606218
XV MESH l1 0.700000
XV MESH l2 0.526844
XV MESH l3 1.000000
XV MESH l4 0.759977
XV MESH l5 1.000000
XV MESH l6 0.888819
XV MESH l7 1.000000
XV MESH l8 1.000000
XV MESH alpha1 0.523599
XV MESH beta1 1.891392
XV MESH gamma1 0.726602
XV MESH delta1 0.523599
XV MESH f1 0.350000
XV MESH alpha2 0.844195
XV MESH beta2 1.752711
XV MESH gamma2 0.544687
XV MESH delta2 0.544687
XV MESH f2 0.393782
XV MESH alpha3 1.026109
XV MESH beta3 1.295247
XV MESH gamma3 0.820236
XV MESH delta3 0.820236
XV MESH f3 0.650000
XV MESH alpha4 0.750560
XV MESH beta4 1.343835
XV MESH gamma4 1.047198
XV MESH delta4 0.750560
XV MESH f4 0.606218
XV MESH deltamin 0.523599
XV MESH fmin 0.350000
XV MESH fmax 0.650000
ELEMENT TYPE
EV diffsq winkel minwi
IV diffsq dif
EV laenge lp1x lp1y
EV laenge lp2x lp2y
EV laenge llaenge
IV laenge lp1p2x lp1p2y
IV laenge ll
EV vekprod vp1x vp1y
EV vekprod vp2x vp2y
EV vekprod vp3x vp3y
IV vekprod vp2p1x vp2p1y
IV vekprod vp2p3x vp2p3y
EV sklprod sp1x sp1y
EV sklprod sp2x sp2y
EV sklprod sp3x sp3y
IV sklprod sp2p1x sp2p1y
IV sklprod sp2p3x sp2p3y
EV cosprod cl1 cl2
EV cosprod cw
ELEMENT USES
DO i 1 nd
XT aldsq(i) diffsq
ZV aldsq(i) winkel alpha(i)
ZV aldsq(i) minwi delta(i)
XT bedsq(i) diffsq
ZV bedsq(i) winkel beta(i)
ZV bedsq(i) minwi delta(i)
XT gadsq(i) diffsq
ZV gadsq(i) winkel gamma(i)
ZV gadsq(i) minwi delta(i)
OD i
DO i 1 nk
XT laeng(i) laenge
OD i
ZV laeng1 lp1x x1
ZV laeng1 lp1y y1
ZV laeng1 lp2x x5
ZV laeng1 lp2y y5
ZV laeng1 llaenge l1
ZV laeng2 lp1x x5
ZV laeng2 lp1y y5
ZV laeng2 lp2x x2
ZV laeng2 lp2y y2
ZV laeng2 llaenge l2
ZV laeng3 lp1x x2
ZV laeng3 lp1y y2
ZV laeng3 lp2x x1
ZV laeng3 lp2y y1
ZV laeng3 llaenge l3
ZV laeng4 lp1x x5
ZV laeng4 lp1y y5
ZV laeng4 lp2x x3
ZV laeng4 lp2y y3
ZV laeng4 llaenge l4
ZV laeng5 lp1x x3
ZV laeng5 lp1y y3
ZV laeng5 lp2x x2
ZV laeng5 lp2y y2
ZV laeng5 llaenge l5
ZV laeng6 lp1x x5
ZV laeng6 lp1y y5
ZV laeng6 lp2x x4
ZV laeng6 lp2y y4
ZV laeng6 llaenge l6
ZV laeng7 lp1x x4
ZV laeng7 lp1y y4
ZV laeng7 lp2x x3
ZV laeng7 lp2y y3
ZV laeng7 llaenge l7
ZV laeng8 lp1x x1
ZV laeng8 lp1y y1
ZV laeng8 lp2x x4
ZV laeng8 lp2y y4
ZV laeng8 llaenge l8
DO i 1 nd
XT sal(i) sklprod
OD i
ZV sal1 sp1x x2
ZV sal1 sp1y y2
ZV sal1 sp2x x1
ZV sal1 sp2y y1
ZV sal1 sp3x x5
ZV sal1 sp3y y5
ZV sal2 sp1x x3
ZV sal2 sp1y y3
ZV sal2 sp2x x2
ZV sal2 sp2y y2
ZV sal2 sp3x x5
ZV sal2 sp3y y5
ZV sal3 sp1x x4
ZV sal3 sp1y y4
ZV sal3 sp2x x3
ZV sal3 sp2y y3
ZV sal3 sp3x x5
ZV sal3 sp3y y5
ZV sal4 sp1x x1
ZV sal4 sp1y y1
ZV sal4 sp2x x4
ZV sal4 sp2y y4
ZV sal4 sp3x x5
ZV sal4 sp3y y5
DO i 1 nd
XT cal(i) cosprod
OD i
ZV cal1 cl1 l3
ZV cal1 cl2 l1
ZV cal1 cw alpha1
ZV cal2 cl1 l5
ZV cal2 cl2 l2
ZV cal2 cw alpha2
ZV cal3 cl1 l7
ZV cal3 cl2 l4
ZV cal3 cw alpha3
ZV cal4 cl1 l8
ZV cal4 cl2 l6
ZV cal4 cw alpha4
DO i 1 nd
XT sbe(i) sklprod
OD i
ZV sbe1 sp1x x1
ZV sbe1 sp1y y1
ZV sbe1 sp2x x5
ZV sbe1 sp2y y5
ZV sbe1 sp3x x2
ZV sbe1 sp3y y2
ZV sbe2 sp1x x2
ZV sbe2 sp1y y2
ZV sbe2 sp2x x5
ZV sbe2 sp2y y5
ZV sbe2 sp3x x3
ZV sbe2 sp3y y3
ZV sbe3 sp1x x3
ZV sbe3 sp1y y3
ZV sbe3 sp2x x5
ZV sbe3 sp2y y5
ZV sbe3 sp3x x4
ZV sbe3 sp3y y4
ZV sbe4 sp1x x4
ZV sbe4 sp1y y4
ZV sbe4 sp2x x5
ZV sbe4 sp2y y5
ZV sbe4 sp3x x1
ZV sbe4 sp3y y1
DO i 1 nd
XT cbe(i) cosprod
OD i
ZV cbe1 cl1 l1
ZV cbe1 cl2 l2
ZV cbe1 cw beta1
ZV cbe2 cl1 l2
ZV cbe2 cl2 l4
ZV cbe2 cw beta2
ZV cbe3 cl1 l4
ZV cbe3 cl2 l6
ZV cbe3 cw beta3
ZV cbe4 cl1 l6
ZV cbe4 cl2 l1
ZV cbe4 cw beta4
DO i 1 nd
XT flae(i) vekprod
OD i
ZV flae1 vp1x x1
ZV flae1 vp1y y1
ZV flae1 vp2x x5
ZV flae1 vp2y y5
ZV flae1 vp3x x2
ZV flae1 vp3y y2
ZV flae2 vp1x x2
ZV flae2 vp1y y2
ZV flae2 vp2x x5
ZV flae2 vp2y y5
ZV flae2 vp3x x3
ZV flae2 vp3y y3
ZV flae3 vp1x x3
ZV flae3 vp1y y3
ZV flae3 vp2x x5
ZV flae3 vp2y y5
ZV flae3 vp3x x4
ZV flae3 vp3y y4
ZV flae4 vp1x x4
ZV flae4 vp1y y4
ZV flae4 vp2x x5
ZV flae4 vp2y y5
ZV flae4 vp3x x1
ZV flae4 vp3y y1
GROUP TYPE
GV square alpha
GROUP USES
XT obj1 square
XT obj2 square
DO i 1 nd
XE obj3 aldsq(i) 1.0
XE obj3 bedsq(i) 1.0
XE obj3 gadsq(i) 1.0
OD i
DO i 1 nk
XE seit(i) laeng(i) 1.0
OD i
DO i 1 nd
XE skal(i) sal(i) 1.0 cal(i) -1.0
XE skbe(i) sbe(i) 1.0 cbe(i) -1.0
OD i
DO i 1 nd
XE doppf(i) flae(i) 1.0
OD i
OBJECT BOUND
* Solution
*LO SOLTN 5.9213448D-4
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MESH
TEMPORARIES
R cosa
R sina
R prod2
R prod3
M cos
M sin
INDIVIDUALS
T diffsq
R dif winkel 1.0 minwi -1.0
F dif * dif
G dif dif + dif
H dif dif 2.0
T laenge
R lp1p2x lp1x 1.0 lp2x -1.0
R lp1p2y lp1y 1.0 lp2y -1.0
R ll llaenge 1.0
F ll * ll
F+ - lp1p2x * lp1p2x - lp1p2y * lp1p2y
G ll ll + ll
G lp1p2x - (lp1p2x + lp1p2x)
G lp1p2y - (lp1p2y + lp1p2y)
H ll ll 2.0
H ll lp1p2x 0.0
H ll lp1p2y 0.0
H lp1p2x lp1p2y 0.0
H lp1p2x lp1p2x -2.0
H lp1p2y lp1p2y -2.0
T vekprod
R vp2p1x vp1x 1.0 vp2x -1.0
R vp2p1y vp1y 1.0 vp2y -1.0
R vp2p3x vp3x 1.0 vp2x -1.0
R vp2p3y vp3y 1.0 vp2y -1.0
F vp2p3x * vp2p1y - vp2p1x * vp2p3y
G vp2p1x -vp2p3y
G vp2p1y vp2p3x
G vp2p3x vp2p1y
G vp2p3y -vp2p1x
H vp2p3x vp2p1y 1.0
H vp2p1x vp2p3y -1.0
T sklprod
R sp2p1x sp1x 1.0 sp2x -1.0
R sp2p1y sp1y 1.0 sp2y -1.0
R sp2p3x sp3x 1.0 sp2x -1.0
R sp2p3y sp3y 1.0 sp2y -1.0
F sp2p1x * sp2p3x + sp2p1y * sp2p3y
G sp2p1x sp2p3x
G sp2p1y sp2p3y
G sp2p3x sp2p1x
G sp2p3y sp2p1y
H sp2p1x sp2p3x 1.0
H sp2p1y sp2p3y 1.0
T cosprod
A cosa cos(cw)
A sina sin(cw)
A prod2 cl1 * cl2
A prod3 prod2 * cosa
F prod3
G cl1 cl2 * cosa
G cl2 cl1 * cosa
G cw -sina * prod2
H cl1 cl2 cosa
H cl1 cw -sina * cl2
H cl2 cw -sina * cl1
H cw cw -prod3
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS MESH
INDIVIDUALS
T square
F alpha * alpha
G alpha + alpha
H 2.0
ENDATA