*********************************************** DESCRIPTION *********************************************** 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. *********************************************** COMPILATION: *********************************************** 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. *********************************************** USAGE: *********************************************** 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. *********************************************** EXAMPLE *********************************************** 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