740 lines
27 KiB
C
740 lines
27 KiB
C
/*********************************************************************************/
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/* */
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/* Animation of Schrödinger equation in a planar domain */
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/* */
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/* N. Berglund, May 2021 */
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/* */
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/* Feel free to reuse, but if doing so it would be nice to drop a */
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/* line to nils.berglund@univ-orleans.fr - Thanks! */
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/* */
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/* compile with */
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/* gcc -o schrodinger schrodinger.c */
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/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
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/* */
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/* To make a video, set MOVIE to 1 and create subfolder tif_schrod */
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/* It may be possible to increase parameter PAUSE */
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/* */
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/* create movie using */
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/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
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/* */
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/*********************************************************************************/
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/*********************************************************************************/
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/* */
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/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
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/* One could make it much faster by using a GPU */
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/* */
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/*********************************************************************************/
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#include <math.h>
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#include <string.h>
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#include <GL/glut.h>
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#include <GL/glu.h>
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#include <unistd.h>
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#include <sys/types.h>
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#include <tiffio.h> /* Sam Leffler's libtiff library. */
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#include <omp.h>
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#define MOVIE 0 /* set to 1 to generate movie */
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#define SAVE_MEMORY 0 /* set to 1 to save memory when writing tiff images */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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// #define NX 1280 /* number of grid points on x axis */
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// #define NX 720 /* number of grid points on x axis */
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#define NX 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.0 /* scaling for Julia sets */
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/* Choice of the billiard table, see list in global_pdes.c */
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#define B_DOMAIN 10 /* choice of domain shape */
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#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */
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#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
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#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
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#define LAMBDA 0.1 /* parameter controlling the dimensions of domain */
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#define MU 0.03 /* parameter controlling the dimensions of domain */
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#define NPOLY 6 /* number of sides of polygon */
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 5 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NGRIDX 15 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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#define X_SHOOTER -0.2
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#define Y_SHOOTER -0.6
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#define X_TARGET 0.4
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#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
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#define ISO_XSHIFT_LEFT -1.65
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#define ISO_XSHIFT_RIGHT 0.4
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#define ISO_YSHIFT_LEFT -0.05
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#define ISO_YSHIFT_RIGHT -0.05
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#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard in sub_wave.c */
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/* Physical patameters of wave equation */
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#define DT 0.00000001
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// #define DT 0.00000001
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// #define DT 0.000000005
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// #define DT 0.000000005
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#define HBAR 1.0
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 1
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/* Parameters for length and speed of simulation */
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#define NSTEPS 2500 /* number of frames of movie */
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// #define NVID 2000 /* number of iterations between images displayed on screen */
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#define NVID 1200 /* number of iterations between images displayed on screen */
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#define NSEG 100 /* number of segments of boundary */
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#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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#define END_FRAMES 100 /* still frames at end of movie */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 11
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/* Color schemes, see list in global_pdes.c */
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#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* black background */
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#define COLOR_SCHEME 3 /* choice of color scheme */
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#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define E_SCALE 150.0 /* scaling factor for energy representation */
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#define LOG_SCALE 1.0 /* scaling factor for energy log representation */
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#define LOG_SHIFT 0.0 /* shift of colors on log scale */
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#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP 180.0 /* amplitude of variation of hue for color scheme C_HUE */
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#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
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#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */
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#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
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/* the following constants are only used by wave_billiard and wave_3d so far */
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#define COMPARISON 0 /* set to 1 to compare two different patterns */
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#define B_DOMAIN_B 20 /* second domain shape, for comparisons */
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#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */
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#define OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */
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#define ACHIRP 0.2 /* acceleration coefficient in chirp */
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#define DAMPING 0.0 /* damping of periodic excitation */
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#define OMEGA 0.001 /* frequency of periodic excitation */
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#define AMPLITUDE 0.8 /* amplitude of periodic excitation */
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/* end of constants only used by wave_billiard and wave_3d */
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/* for compatibility with sub_wave and sub_maze */
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#define NXMAZE 7 /* width of maze */
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#define NYMAZE 7 /* height of maze */
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#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
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#define RAND_SHIFT 24 /* seed of random number generator */
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#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
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#define ADD_POTENTIAL 0
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#define POT_MAZE 7
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#define POTENTIAL 0
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/* end of constants only used by sub_wave and sub_maze */
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#include "global_pdes.c"
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#include "sub_maze.c"
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#include "sub_wave.c"
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double courant2; /* Courant parameter squared */
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double dx2; /* spatial step size squared */
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double intstep; /* integration step */
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double intstep1; /* integration step used in absorbing boundary conditions */
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void init_coherent_state(double x, double y, double px, double py, double scalex, double *phi[NX],
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double *psi[NX], short int *xy_in[NX])
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/* initialise field with coherent state of position (x,y) and momentum (px, py) */
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/* phi is real part, psi is imaginary part */
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{
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int i, j;
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double xy[2], dist2, module, phase, scale2;
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scale2 = scalex*scalex;
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for (i=0; i<NX; i++)
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for (j=0; j<NY; j++)
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{
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ij_to_xy(i, j, xy);
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xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
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if (xy_in[i][j])
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{
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dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
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module = exp(-dist2/scale2);
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if (module < 1.0e-15) module = 1.0e-15;
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phase = (px*(xy[0]-x) + py*(xy[1]-y))/scalex;
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phi[i][j] = module*cos(phase);
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psi[i][j] = module*sin(phase);
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}
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else
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{
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phi[i][j] = 0.0;
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psi[i][j] = 0.0;
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}
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}
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}
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/*********************/
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/* animation part */
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/*********************/
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void schrodinger_color_scheme(double phi, double psi, double scale, int time, double rgb[3])
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// double phi, psi, scale, rgb[3];
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// int time;
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{
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double phase, amp, lum;
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if (PLOT == P_MODULE)
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color_scheme(COLOR_SCHEME, 2.0*module2(phi, psi)-1.0, scale, time, rgb);
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else if (PLOT == P_PHASE)
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{
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amp = module2(phi,psi);
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// if (amp < 1.0e-10) amp = 1.0e-10;
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phase = argument(phi/amp, psi/amp);
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if (phase < 0.0) phase += DPI;
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lum = (color_amplitude(amp, scale, time))*0.5;
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if (lum < 0.0) lum = 0.0;
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hsl_to_rgb(phase*360.0/DPI, 0.9, lum, rgb);
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}
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else if (PLOT == P_REAL) color_scheme(COLOR_SCHEME, phi, scale, time, rgb);
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else if (PLOT == P_IMAGINARY) color_scheme(COLOR_SCHEME, psi, scale, time, rgb);
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}
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void draw_wave(double *phi[NX], double *psi[NX], short int *xy_in[NX], double scale, int time)
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/* draw the field */
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{
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int i, j;
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double rgb[3], xy[2], x1, y1, x2, y2, amp, phase;
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glBegin(GL_QUADS);
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for (i=0; i<NX; i++)
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for (j=0; j<NY; j++)
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{
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if (xy_in[i][j])
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{
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schrodinger_color_scheme(phi[i][j],psi[i][j], scale, time, rgb);
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glVertex2i(i, j);
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glVertex2i(i+1, j);
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glVertex2i(i+1, j+1);
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glVertex2i(i, j+1);
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}
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}
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glEnd ();
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}
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void evolve_wave_half_old(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
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short int *xy_in[NX])
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// void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
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// /* time step of field evolution */
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// /* phi is real part, psi is imaginary part */
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// double *phi_in[NX], *psi_in[NX], *phi_out[NX], *psi_out[NX]; short int *xy_in[NX];
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{
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int i, j, iplus, iminus, jplus, jminus;
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double delta1, delta2, x, y;
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#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta1,delta2,x,y)
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for (i=0; i<NX; i++){
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for (j=0; j<NY; j++){
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if (xy_in[i][j]){
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/* discretized Laplacian depending on boundary conditions */
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if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING))
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{
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iplus = (i+1); if (iplus == NX) iplus = NX-1;
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iminus = (i-1); if (iminus == -1) iminus = 0;
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jplus = (j+1); if (jplus == NY) jplus = NY-1;
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jminus = (j-1); if (jminus == -1) jminus = 0;
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}
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else if (B_COND == BC_PERIODIC)
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{
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iplus = (i+1) % NX;
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iminus = (i-1) % NX;
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if (iminus < 0) iminus += NX;
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jplus = (j+1) % NY;
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jminus = (j-1) % NY;
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if (jminus < 0) jminus += NY;
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}
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delta1 = phi_in[iplus][j] + phi_in[iminus][j] + phi_in[i][jplus] + phi_in[i][jminus] - 4.0*phi_in[i][j];
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delta2 = psi_in[iplus][j] + psi_in[iminus][j] + psi_in[i][jplus] + psi_in[i][jminus] - 4.0*psi_in[i][j];
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x = phi_in[i][j];
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y = psi_in[i][j];
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/* evolve phi and psi */
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if (B_COND != BC_ABSORBING)
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{
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phi_out[i][j] = x - intstep*delta2;
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psi_out[i][j] = y + intstep*delta1;
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}
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else /* case of absorbing b.c. - this is only an approximation of correct way of implementing */
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{
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/* in the bulk */
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if ((i>0)&&(i<NX-1)&&(j>0)&&(j<NY-1))
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{
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phi_out[i][j] = x - intstep*delta2;
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psi_out[i][j] = y + intstep*delta1;
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}
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/* right border */
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else if (i==NX-1)
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{
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phi_out[i][j] = x - intstep1*(y - psi_in[i-1][j]);
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psi_out[i][j] = y + intstep1*(x - phi_in[i-1][j]);
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}
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/* upper border */
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else if (j==NY-1)
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{
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phi_out[i][j] = x - intstep1*(y - psi_in[i][j-1]);
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psi_out[i][j] = y + intstep1*(x - phi_in[i][j-1]);
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}
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/* left border */
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else if (i==0)
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{
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phi_out[i][j] = x - intstep1*(y - psi_in[1][j]);
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psi_out[i][j] = y + intstep1*(x - phi_in[1][j]);
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}
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/* lower border */
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else if (j==0)
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{
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phi_out[i][j] = x - intstep1*(y - psi_in[i][1]);
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psi_out[i][j] = y + intstep1*(x - phi_in[i][1]);
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}
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}
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if (FLOOR)
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{
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if (phi_out[i][j] > VMAX) phi_out[i][j] = VMAX;
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if (phi_out[i][j] < -VMAX) phi_out[i][j] = -VMAX;
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if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
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if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
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}
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}
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}
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}
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// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
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}
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void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
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short int *xy_in[NX])
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// void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
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// /* time step of field evolution */
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// /* phi is real part, psi is imaginary part */
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{
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int i, j, iplus, iminus, jplus, jminus;
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double delta1, delta2, x, y;
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#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta1,delta2,x,y)
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for (i=1; i<NX-1; i++){
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for (j=1; j<NY-1; j++){
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if (xy_in[i][j]){
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x = phi_in[i][j];
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y = psi_in[i][j];
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delta1 = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
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delta2 = psi_in[i+1][j] + psi_in[i-1][j] + psi_in[i][j+1] + psi_in[i][j-1] - 4.0*y;
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/* evolve phi and psi */
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phi_out[i][j] = x - intstep*delta2;
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psi_out[i][j] = y + intstep*delta1;
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}
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}
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}
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/* left boundary */
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for (j=1; j<NY-1; j++){
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if (xy_in[0][j]){
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x = phi_in[0][j];
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y = psi_in[0][j];
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switch (B_COND) {
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case (BC_DIRICHLET):
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{
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delta1 = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
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delta2 = psi_in[1][j] + psi_in[0][j+1] + psi_in[0][j-1] - 3.0*y;
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phi_out[0][j] = x - intstep*delta2;
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psi_out[0][j] = y + intstep*delta1;
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break;
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}
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case (BC_PERIODIC):
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{
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delta1 = phi_in[1][j] + phi_in[NX-1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 4.0*x;
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delta2 = psi_in[1][j] + psi_in[NX-1][j] + psi_in[0][j+1] + psi_in[0][j-1] - 4.0*y;
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phi_out[0][j] = x - intstep*delta2;
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psi_out[0][j] = y + intstep*delta1;
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break;
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}
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}
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}
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}
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/* right boundary */
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for (j=1; j<NY-1; j++){
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if (xy_in[0][j]){
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x = phi_in[NX-1][j];
|
|
y = psi_in[NX-1][j];
|
|
|
|
switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
delta1 = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
|
|
delta2 = psi_in[NX-2][j] + psi_in[NX-1][j+1] + psi_in[NX-1][j-1] - 3.0*y;
|
|
phi_out[NX-1][j] = x - intstep*delta2;
|
|
psi_out[NX-1][j] = y + intstep*delta1;
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
delta1 = phi_in[NX-2][j] + phi_in[0][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 4.0*x;
|
|
delta2 = psi_in[NX-2][j] + psi_in[0][j] + psi_in[NX-1][j+1] + psi_in[NX-1][j-1] - 4.0*y;
|
|
phi_out[NX-1][j] = x - intstep*delta2;
|
|
psi_out[NX-1][j] = y + intstep*delta1;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* top boundary */
|
|
for (i=0; i<NX; i++){
|
|
if (xy_in[i][NY-1]){
|
|
x = phi_in[i][NY-1];
|
|
y = psi_in[i][NY-1];
|
|
|
|
switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
iplus = i+1; if (iplus == NX) iplus = NX-1;
|
|
iminus = i-1; if (iminus == -1) iminus = 0;
|
|
|
|
delta1 = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] - 3.0*x;
|
|
delta2 = psi_in[iplus][NY-1] + psi_in[iminus][NY-1] + psi_in[i][NY-2] - 3.0*x;
|
|
phi_out[i][NY-1] = x - intstep*delta2;
|
|
psi_out[i][NY-1] = y + intstep*delta1;
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
iplus = (i+1) % NX;
|
|
iminus = (i-1) % NX;
|
|
if (iminus < 0) iminus += NX;
|
|
|
|
delta1 = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] + phi_in[i][0] - 4.0*x;
|
|
delta2 = psi_in[iplus][NY-1] + psi_in[iminus][NY-1] + psi_in[i][NY-2] + psi_in[i][0] - 4.0*y;
|
|
phi_out[i][NY-1] = x - intstep*delta2;
|
|
psi_out[i][NY-1] = y + intstep*delta1;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* bottom boundary */
|
|
for (i=0; i<NX; i++){
|
|
if (xy_in[i][0]){
|
|
x = phi_in[i][0];
|
|
y = psi_in[i][0];
|
|
|
|
switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
iplus = i+1; if (iplus == NX) iplus = NX-1;
|
|
iminus = i-1; if (iminus == -1) iminus = 0;
|
|
|
|
delta1 = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] - 3.0*x;
|
|
delta2 = psi_in[iplus][0] + psi_in[iminus][0] + psi_in[i][1] - 3.0*x;
|
|
phi_out[i][0] = x - intstep*delta2;
|
|
psi_out[i][0] = y + intstep*delta1;
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
iplus = (i+1) % NX;
|
|
iminus = (i-1) % NX;
|
|
if (iminus < 0) iminus += NX;
|
|
|
|
delta1 = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] + phi_in[i][NY-1] - 4.0*x;
|
|
delta2 = psi_in[iplus][0] + psi_in[iminus][0] + psi_in[i][1] + psi_in[i][NY-1] - 4.0*y;
|
|
phi_out[i][0] = x - intstep*delta2;
|
|
psi_out[i][0] = y + intstep*delta1;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* for debugging purposes/if there is a risk of blow-up */
|
|
if (FLOOR) for (i=0; i<NX; i++){
|
|
for (j=0; j<NY; j++){
|
|
if (xy_in[i][j] != 0)
|
|
{
|
|
if (phi_out[i][j] > VMAX) phi_out[i][j] = VMAX;
|
|
if (phi_out[i][j] < -VMAX) phi_out[i][j] = -VMAX;
|
|
if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
|
|
if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void evolve_wave(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *psi_tmp[NX], short int *xy_in[NX])
|
|
/* time step of field evolution */
|
|
/* phi is real part, psi is imaginary part */
|
|
{
|
|
evolve_wave_half(phi, psi, phi_tmp, psi_tmp, xy_in);
|
|
evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
|
|
}
|
|
|
|
|
|
double compute_variance(double *phi[NX], double *psi[NX], short int *xy_in[NX])
|
|
// double compute_variance(phi, psi, xy_in)
|
|
/* compute the variance (total probability) of the field */
|
|
// double *phi[NX], *psi[NX]; short int * xy_in[NX];
|
|
{
|
|
int i, j, n = 0;
|
|
double variance = 0.0;
|
|
|
|
for (i=1; i<NX; i++)
|
|
for (j=1; j<NY; j++)
|
|
{
|
|
if (xy_in[i][j])
|
|
{
|
|
n++;
|
|
variance += phi[i][j]*phi[i][j] + psi[i][j]*psi[i][j];
|
|
}
|
|
}
|
|
if (n==0) n=1;
|
|
return(variance/(double)n);
|
|
}
|
|
|
|
void renormalise_field(double *phi[NX], double *psi[NX], short int *xy_in[NX], double variance)
|
|
/* renormalise variance of field */
|
|
{
|
|
int i, j;
|
|
double stdv;
|
|
|
|
stdv = sqrt(variance);
|
|
|
|
for (i=1; i<NX; i++)
|
|
for (j=1; j<NY; j++)
|
|
{
|
|
if (xy_in[i][j])
|
|
{
|
|
phi[i][j] = phi[i][j]/stdv;
|
|
psi[i][j] = psi[i][j]/stdv;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void draw_color_bar(int plot, double range)
|
|
{
|
|
if (ROTATE_COLOR_SCHEME) draw_color_scheme(-1.0, -0.8, XMAX - 0.1, -1.0, plot, -range, range);
|
|
else draw_color_scheme(1.7, YMIN + 0.1, 1.9, YMAX - 0.1, plot, -range, range);
|
|
}
|
|
|
|
|
|
void animation()
|
|
{
|
|
double time, scale, dx, var;
|
|
double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX];
|
|
short int *xy_in[NX];
|
|
int i, j, s;
|
|
|
|
/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
|
|
for (i=0; i<NX; i++)
|
|
{
|
|
phi[i] = (double *)malloc(NY*sizeof(double));
|
|
psi[i] = (double *)malloc(NY*sizeof(double));
|
|
phi_tmp[i] = (double *)malloc(NY*sizeof(double));
|
|
psi_tmp[i] = (double *)malloc(NY*sizeof(double));
|
|
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
|
|
}
|
|
|
|
/* initialise polyline for von Koch and simular domains */
|
|
npolyline = init_polyline(MDEPTH, polyline);
|
|
// for (i=0; i<npolyline; i++) printf("vertex %i: (%.3f, %.3f)\n", i, polyline[i].x, polyline[i].y);
|
|
|
|
dx = (XMAX-XMIN)/((double)NX);
|
|
intstep = DT/(dx*dx*HBAR);
|
|
intstep1 = DT/(dx*HBAR);
|
|
|
|
printf("Integration step %.3lg\n", intstep);
|
|
|
|
/* initialize wave wave function */
|
|
init_coherent_state(-0.5, 0.0, 15.0, 0.0, 0.15, phi, psi, xy_in);
|
|
// init_coherent_state(0.0, 0.0, 0.0, 5.0, 0.03, phi, psi, xy_in);
|
|
// init_coherent_state(-0.5, 0.0, 1.0, 1.0, 0.05, phi, psi, xy_in);
|
|
|
|
|
|
|
|
if (SCALE)
|
|
{
|
|
var = compute_variance(phi,psi, xy_in);
|
|
scale = sqrt(1.0 + var);
|
|
renormalise_field(phi, psi, xy_in, var);
|
|
}
|
|
|
|
blank();
|
|
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
|
|
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
|
|
glutSwapBuffers();
|
|
|
|
sleep(SLEEP1);
|
|
|
|
for (i=0; i<=NSTEPS; i++)
|
|
{
|
|
/* compute the variance of the field to adjust color scheme */
|
|
/* the color depends on the field divided by sqrt(1 + variance) */
|
|
if (SCALE)
|
|
{
|
|
var = compute_variance(phi,psi, xy_in);
|
|
scale = sqrt(1.0 + var);
|
|
// printf("Norm: %5lg\t Scaling factor: %5lg\n", var, scale);
|
|
renormalise_field(phi, psi, xy_in, var);
|
|
}
|
|
else scale = 1.0;
|
|
|
|
draw_wave(phi, psi, xy_in, scale, i);
|
|
|
|
// printf("Wave drawn\n");
|
|
|
|
for (j=0; j<NVID; j++) evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
|
|
|
|
draw_billiard(0, 1.0);
|
|
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
|
|
|
|
glutSwapBuffers();
|
|
|
|
if (MOVIE)
|
|
{
|
|
save_frame();
|
|
|
|
/* it seems that saving too many files too fast can cause trouble with the file system */
|
|
/* so this is to make a pause from time to time - parameter PAUSE may need adjusting */
|
|
if (i % PAUSE == PAUSE - 1)
|
|
{
|
|
printf("Making a short pause\n");
|
|
sleep(PSLEEP);
|
|
s = system("mv wave*.tif tif_schrod/");
|
|
}
|
|
}
|
|
}
|
|
|
|
if (MOVIE)
|
|
{
|
|
for (i=0; i<END_FRAMES; i++) save_frame();
|
|
s = system("mv wave*.tif tif_schrod/");
|
|
}
|
|
|
|
for (i=0; i<NX; i++)
|
|
{
|
|
free(phi[i]);
|
|
free(psi[i]);
|
|
free(phi_tmp[i]);
|
|
free(psi_tmp[i]);
|
|
free(xy_in[i]);
|
|
}
|
|
|
|
}
|
|
|
|
|
|
void display(void)
|
|
{
|
|
glPushMatrix();
|
|
|
|
blank();
|
|
glutSwapBuffers();
|
|
blank();
|
|
glutSwapBuffers();
|
|
|
|
animation();
|
|
sleep(SLEEP2);
|
|
|
|
glPopMatrix();
|
|
|
|
glutDestroyWindow(glutGetWindow());
|
|
|
|
}
|
|
|
|
|
|
int main(int argc, char** argv)
|
|
{
|
|
glutInit(&argc, argv);
|
|
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
|
|
glutInitWindowSize(WINWIDTH,WINHEIGHT);
|
|
glutCreateWindow("Schrodinger equation in a planar domain");
|
|
|
|
init();
|
|
|
|
glutDisplayFunc(display);
|
|
|
|
glutMainLoop();
|
|
|
|
return 0;
|
|
}
|
|
|