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DESCRIPTION
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This program is related to the paper
M. Novaga - E. Paolini: "A computational approach to fractures in crystal
growth", Rend. Mat. Acc. Lincei, Vol. 10, N. 31, pages 46--56.
also available at http://cvgmt.sns.it/papers/novpao98/
Given a polygon F we want to minimize the functional
E(xi) = Integral_F (div xi)^2
among all vector fields xi: F -> R^2 such that xi has given normal
component on the boundary of F.
This program implements a finite element method. The function xi
is interpolated on a triangulation of F.
The resulting functions xi and div xi are plotted on a PostScript file.
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COMPILATION:
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The program has been tested on a "Debian GNU/Linux" system with
"gcc 2.95.4" GNU C++ compiler.
1. obtain the file "divano-*.tgz" ('*' is the version number)
2. decompress the package:
tar -xzf divano-*.tgz
3. enter the source directory:
cd divano-*.tgz
4. compile
make
The compilation should not report error nor warnings.
You can move the executable file "divano" wherever you want.
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USAGE:
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SYNOPSIS
divano [options]
where [options] are
polygon:
n-agonal wulff shape (see "n")
doubleseat:
double-seat shaped wulff shape
hexagon:
enloged hexagonal wulff shape
seat:
seat shaped wulff shape
load:
load wulff shape from file (see "file")
file <filaname>:
load or save from file <filename>
psfile <filename>:
write PS pictures to file <filename>
n <integer>:
number of edges of polygon
m <integer>:
half number of edges of polygon
eps <float>:
size of triangulation
dt <float>:
time step
s <float>:
enlonge parameter for hexagon
fine <float>:
refinement parameter
level:
draw level curves
csi:
draw vector field
step <float>:
distance between level curves
The program is menu-driven. Always press <return> after each choice.
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EXAMPLE
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Here is an example session
$ make
g++ -c divano.C
g++ divano.o vector2.o -lm -o divano
$ ./divano seat
divano ver. 1.0 written by E.Paolini
Seat
4-agonal wulff shape
Triangulating
Computing matrices
7 6 5 4 3 2 1
Vertices: 7 Triangles: 5 Edges: 11
Area: 1.25
Energy: 37.75 dt: 0.1 eps: 100
a) choose dt
b) evolve with fixed dt
c) evolve
d) draw
e) save
f) triangulate
g) adjust
h) check
x) exit
Your choice: f
eps= 0.3
[...]
Your choice: c
Energy: 33.2564 dt: 0.0513158
Energy increases!
[...]
Your choice: d
Writing picture on Postscript file out.ps
[...]
Your choice: x
