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wave_billiard.c
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wave_billiard.c
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/*********************************************************************************/
/* */
/* Animation of wave equation in a planar domain */
/* */
/* N. Berglund, december 2012, may 2021 */
/* */
/* UPDATE 24/04: distinction between damping and "elasticity" parameters */
/* UPDATE 27/04: new billiard shapes, bug in color scheme fixed */
/* UPDATE 28/04: code made more efficient, with help of Marco Mancini */
/* */
/* Feel free to reuse, but if doing so it would be nice to drop a */
/* line to [email protected] - Thanks! */
/* */
/* compile with */
/* gcc -o wave_billiard wave_billiard.c */
/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
/* */
/* OMP acceleration may be more effective after executing */
/* export OMP_NUM_THREADS=2 in the shell before running the program */
/* */
/* To make a video, set MOVIE to 1 and create subfolder tif_wave */
/* It may be possible to increase parameter PAUSE */
/* */
/* create movie using */
/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
/* */
/**********************************************************************************/
/*********************************************************************************/
/* */
/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
/* One could make it much faster by using a GPU */
/* */
/*********************************************************************************/
#include <math.h>
#include <string.h>
#include <GL/glut.h>
#include <GL/glu.h>
#include <unistd.h>
#include <sys/types.h>
#include <tiffio.h> /* Sam Leffler's libtiff library. */
#include <omp.h>
#include <time.h>
#define MOVIE 0 /* set to 1 to generate movie */
#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
#define SAVE_MEMORY 1 /* set to 1 to save memory when writing tiff images */
#define NO_EXTRA_BUFFER_SWAP 1 /* some OS require one less buffer swap when recording images */
#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */
#define IOR 9 /* choice of index of refraction, see list in global_pdes.c */
#define IOR_TOTAL_TURNS 1.5 /* total angle of rotation for IOR_PERIODIC_WELLS_ROTATING */
#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */
/* General geometrical parameters */
#define WINWIDTH 1920 /* window width */
#define WINHEIGHT 1150 /* window height */
#define NX 3840 /* number of grid points on x axis */
#define NY 2300 /* number of grid points on y axis */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -0.397916667
#define YMAX 1.997916667 /* y interval for 9/16 aspect ratio */
// #define YMIN -1.197916667
// #define YMAX 1.197916667 /* y interval for 9/16 aspect ratio */
#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */
// #define WINWIDTH 1280 /* window width */
// #define WINHEIGHT 720 /* window height */
//
// // #define NX 640 /* number of grid points on x axis */
// // #define NY 360 /* number of grid points on y axis */
// // #define NX 1280 /* number of grid points on x axis */
// // #define NY 720 /* number of grid points on y axis */
// #define NX 2560 /* number of grid points on x axis */
// #define NY 1440 /* number of grid points on y axis */
//
// #define XMIN -2.0
// #define XMAX 2.0 /* x interval */
// #define YMIN -1.125
// #define YMAX 1.125 /* y interval for 9/16 aspect ratio */
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 103 /* pattern of circles or polygons, see list in global_pdes.c */
#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */
#define B_DOMAIN_B 20 /* second domain shape, for comparisons */
#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
#define NPOISSON 1000 /* number of points for Poisson C_RAND_POISSON arrangement */
#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
#define MU 0.005 /* parameter controlling the dimensions of domain */
#define NPOLY 6 /* number of sides of polygon */
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 6 /* depth of computation of Menger gasket */
#define MRATIO 3 /* ratio defining Menger gasket */
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NGRIDX 60 /* number of grid point for grid of disks */
#define NGRIDY 10 /* number of grid point for grid of disks */
// #define NGRIDY 18 /* number of grid point for grid of disks */
#define X_SHOOTER -0.2
#define Y_SHOOTER -0.6
#define X_TARGET 0.4
#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
#define ISO_XSHIFT_LEFT -2.9
#define ISO_XSHIFT_RIGHT 1.4
#define ISO_YSHIFT_LEFT -0.15
#define ISO_YSHIFT_RIGHT -0.15
#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */
/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard below */
/* Physical parameters of wave equation */
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */
#define OMEGA 0.024 /* frequency of periodic excitation */
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
#define ACHIRP 0.25 /* acceleration coefficient in chirp */
#define DAMPING 0.0 /* damping of periodic excitation */
#define COURANT 0.1 /* Courant number */
#define COURANTB 0.01 /* Courant number in medium B */
#define GAMMA 0.0 /* damping factor in wave equation */
#define GAMMAB 0.0 /* damping factor in wave equation */
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
#define OSCIL_LEFT_YSHIFT -400.0 /* y-dependence of left oscillation (for non-horizontal waves) */
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */
#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */
#define ALTERNATE_OSCILLATING_SOURCE 1 /* set to 1 to alternate sign of oscillating source */
#define ADD_WAVE_PACKET_SOURCES 0 /* set to 1 to add several sources emitting wave packets */
#define WAVE_PACKET_SOURCE_TYPE 1 /* type of wave packet sources */
#define N_WAVE_PACKETS 15 /* number of wave packets */
#define WAVE_PACKET_RADIUS 20 /* radius of wave packets */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 2
/* Parameters for length and speed of simulation */
#define NSTEPS 3600 /* number of frames of movie */
// #define NSTEPS 500 /* number of frames of movie */
#define NVID 7 /* number of iterations between images displayed on screen */
#define NSEG 1000 /* number of segments of boundary */
#define INITIAL_TIME 700 /* time after which to start saving frames */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
#define PRINT_SPEED 0 /* print speed of moving source */
#define PRINT_FREQUENCY 0 /* print frequency (for phased array) */
#define PAUSE 200 /* number of frames after which to pause */
#define PSLEEP 1 /* sleep time during pause */
#define SLEEP1 1 /* initial sleeping time */
#define SLEEP2 1 /* final sleeping time */
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
#define END_FRAMES 100 /* number of still frames at end of movie */
#define FADE 1 /* set to 1 to fade at end of movie */
/* Parameters of initial condition */
#define INITIAL_AMP 2.0 /* amplitude of initial condition */
// #define INITIAL_VARIANCE 0.000015 /* variance of initial condition */
#define INITIAL_VARIANCE 0.000025 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */
/* Plot type, see list in global_pdes.c */
#define PLOT 0
// #define PLOT 7
#define PLOT_B 5 /* plot type for second movie */
/* Color schemes */
#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */
// #define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */
#define COLOR_PALETTE_B 12 /* Color palette, see list in global_pdes.c */
#define BLACK 1 /* background */
#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */
#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 50.0 /* scaling factor for energy representation */
#define LOG_SCALE 1.0 /* scaling factor for energy log representation */
#define LOG_SHIFT 1.5 /* shift of colors on log scale */
#define FLUX_SCALE 5.0e3 /* scaling factor for enegy flux represtnation */
#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
#define COLORBAR_RANGE 1.0 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 0.4 /* scale of color scheme bar for 2nd part */
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
#define CIRC_COLORBAR 0 /* set to 1 to draw circular color scheme */
#define CIRC_COLORBAR_B 0 /* set to 1 to draw circular color scheme */
#define DRAW_WAVE_PROFILE 1 /* set to 1 to draw a profile of the wave */
#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */
#define NXMAZE 8 /* width of maze */
#define NYMAZE 32 /* height of maze */
#define MAZE_MAX_NGBH 5 /* max number of neighbours of maze cell */
#define RAND_SHIFT 0 /* seed of random number generator */
#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
#define MAZE_WIDTH 0.02 /* half width of maze walls */
/* for compatibility with sub_wave and sub_maze */
#define ADD_POTENTIAL 0
#define POT_MAZE 7
#define POTENTIAL 0
/* end of constants only used by sub_wave and sub_maze */
/* For debugging purposes only */
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
#define VMAX 10.0 /* max value of wave amplitude */
#define MEAN_FLUX (PLOT == P_TOTAL_ENERGY_FLUX)||(PLOT_B == P_TOTAL_ENERGY_FLUX)
#define REFRESH_IOR ((IOR == IOR_PERIODIC_WELLS_ROTATING)||(IOR == IOR_PERIODIC_WELLS_ROTATING_LARGE))
#include "global_pdes.c" /* constants and global variables */
#include "sub_maze.c" /* support for generating mazes */
#include "sub_wave.c" /* common functions for wave_billiard, heat and schrodinger */
#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
FILE *time_series_left, *time_series_right;
double courant2, courantb2; /* Courant parameters squared */
/*********************/
/* animation part */
/*********************/
// void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
// short int *xy_in[NX])
void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX],
short int *xy_in[NX], double *tcc[NX])
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
/* this version of the function has been rewritten in order to minimize the number of if-branches */
{
int i, j, iplus, iminus, jplus, jminus;
double delta, x, y, c, cc, gamma, tb_shift;
static long time = 0;
static double tc[NX][NY], tgamma[NX][NY];
static short int first = 1;
time++;
// if (OSCILLATE_TOPBOT) tb_shift = (int)((X_SHIFT - XMIN)*(double)NX/(XMAX - XMIN));
if (OSCILLATE_TOPBOT) tb_shift = (int)((XMAX - XMIN)*(double)NX/(XMAX - XMIN));
/* initialize tables with wave speeds and dissipation */
if (first)
{
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (xy_in[i][j] != 0)
{
tc[i][j] = COURANT;
if (!VARIABLE_IOR) tcc[i][j] = courant2;
if (xy_in[i][j] == 1) tgamma[i][j] = GAMMA;
else tgamma[i][j] = GAMMAB;
}
else if (TWOSPEEDS)
{
tc[i][j] = COURANTB;
tcc[i][j] = courantb2;
tgamma[i][j] = GAMMAB;
}
}
}
first = 0;
}
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y)
/* evolution in the bulk */
for (i=1; i<NX-1; i++){
for (j=1; j<NY-1; j++){
if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
x = phi_in[i][j];
y = psi_in[i][j];
/* discretized Laplacian */
delta = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
/* evolve phi */
phi_out[i][j] = -y + 2*x + tcc[i][j]*delta - KAPPA*x - tgamma[i][j]*(x-y);
// psi_out[i][j] = x;
}
}
}
/* left boundary */
if (OSCILLATE_LEFT) for (j=1; j<NY-1; j++) phi_out[0][j] = oscillating_bc(time, j);
else for (j=1; j<NY-1; j++){
if ((TWOSPEEDS)||(xy_in[0][j] != 0)){
x = phi_in[0][j];
y = psi_in[0][j];
switch (B_COND) {
case (BC_DIRICHLET):
{
delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
phi_out[0][j] = -y + 2*x + tcc[0][j]*delta - KAPPA*x - tgamma[0][j]*(x-y);
break;
}
case (BC_PERIODIC):
{
delta = phi_in[1][j] + phi_in[NX-1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 4.0*x;
phi_out[0][j] = -y + 2*x + tcc[0][j]*delta - KAPPA*x - tgamma[0][j]*(x-y);
break;
}
case (BC_ABSORBING):
{
delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
break;
}
case (BC_VPER_HABS):
{
delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
break;
}
}
// psi_out[0][j] = x;
}
}
/* right boundary */
for (j=1; j<NY-1; j++){
if ((TWOSPEEDS)||(xy_in[NX-1][j] != 0)){
x = phi_in[NX-1][j];
y = psi_in[NX-1][j];
switch (B_COND) {
case (BC_DIRICHLET):
{
delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
phi_out[NX-1][j] = -y + 2*x + tcc[NX-1][j]*delta - KAPPA*x - tgamma[NX-1][j]*(x-y);
break;
}
case (BC_PERIODIC):
{
delta = phi_in[NX-2][j] + phi_in[0][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 4.0*x;
phi_out[NX-1][j] = -y + 2*x + tcc[NX-1][j]*delta - KAPPA*x - tgamma[NX-1][j]*(x-y);
break;
}
case (BC_ABSORBING):
{
delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
phi_out[NX-1][j] = x - tc[NX-1][j]*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
break;
}
case (BC_VPER_HABS):
{
delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
phi_out[NX-1][j] = x - tc[NX-1][j]*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
break;
}
}
// psi_out[NX-1][j] = x;
}
}
/* top boundary */
for (i=0; i<NX; i++){
if ((TWOSPEEDS)||(xy_in[i][NY-1] != 0)){
x = phi_in[i][NY-1];
y = psi_in[i][NY-1];
if ((OSCILLATE_TOPBOT)&&(i < tb_shift)&&(i<NX-1)&&(i>0))
{
iplus = i+1;
iminus = i-1; if (iminus < 0) iminus = 0;
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + - 2.0*x;
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
}
else switch (B_COND) {
case (BC_DIRICHLET):
{
iplus = i+1; if (iplus == NX) iplus = NX-1;
iminus = i-1; if (iminus == -1) iminus = 0;
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] - 3.0*x;
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
break;
}
case (BC_PERIODIC):
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] + phi_in[i][0] - 4.0*x;
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
break;
}
case (BC_ABSORBING):
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] - 3.0*x;
phi_out[i][NY-1] = x - tc[i][NY-1]*(x - phi_in[i][NY-2]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
break;
}
case (BC_VPER_HABS):
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] + phi_in[i][0] - 4.0*x;
if (i==0) phi_out[0][NY-1] = x - tc[0][NY-1]*(x - phi_in[1][NY-1]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
else phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
break;
}
}
// psi_out[i][NY-1] = x;
}
}
/* bottom boundary */
for (i=0; i<NX; i++){
if ((TWOSPEEDS)||(xy_in[i][0] != 0)){
x = phi_in[i][0];
y = psi_in[i][0];
if ((OSCILLATE_TOPBOT)&&(i < tb_shift)&&(i<NX-1)&&(i>0))
{
iplus = i+1;
iminus = i-1; if (iminus < 0) iminus = 0;
delta = phi_in[iplus][0] + phi_in[iminus][0] + - 2.0*x;
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
}
else switch (B_COND) {
case (BC_DIRICHLET):
{
iplus = i+1; if (iplus == NX) iplus = NX-1;
iminus = i-1; if (iminus == -1) iminus = 0;
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] - 3.0*x;
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
break;
}
case (BC_PERIODIC):
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] + phi_in[i][NY-1] - 4.0*x;
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
break;
}
case (BC_ABSORBING):
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] - 3.0*x;
phi_out[i][0] = x - tc[i][0]*(x - phi_in[i][1]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
break;
}
case (BC_VPER_HABS):
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] + phi_in[i][NY-1] - 4.0*x;
if (i==0) phi_out[0][0] = x - tc[0][0]*(x - phi_in[1][0]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
else phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
break;
}
}
// psi_out[i][0] = x;
}
}
/* add oscillating boundary condition on the left corners */
if (OSCILLATE_LEFT)
{
phi_out[0][0] = oscillating_bc(time, 0);
phi_out[0][NY-1] = oscillating_bc(time, NY-1);
}
/* 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 *tmp[NX], short int *xy_in[NX], double *tcc_table[NX])
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
{
// For the purpose of these comments w[t], w[t-1], w[t+1] are used to refer
// to phi, psi and the result respectively to avoid confusion with the
// passed parameter names.
// At the beginning w[t] is saved in phi, w[t-1] in psi and tmp is space
// for the next wave state w[t+1]. Take w[t] and w[t-1] to calculate the
// next wave state. Write this new state in temp
evolve_wave_half(phi, psi, tmp, xy_in, tcc_table);
// now w[t] is saved in tmp, w[t-1] in phi and the result is written to psi
evolve_wave_half(tmp, phi, psi, xy_in, tcc_table);
// now w[t] is saved in psi, w[t-1] in tmp and the result is written to phi
evolve_wave_half(psi, tmp, phi, xy_in, tcc_table);
// now w[t] is saved in phi, w[t-1] in psi and tmp is free again to take
// the new wave state w[t+1] in the next call to this function, thus
// matching the given parameter names again
}
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(XMAX - 0.3, YMIN + 0.1, XMAX - 0.1, YMAX - 0.1, plot, -range, range);
// else draw_color_scheme(1.7, YMIN + 0.25, 1.9, YMAX - 0.25, plot, -range, range);
}
void draw_color_bar_palette(int plot, double range, int palette, int circular, int fade, double fade_value)
{
double width = 0.14;
// double width = 0.2;
if (ROTATE_COLOR_SCHEME)
draw_color_scheme_palette_fade(-1.0, -0.8, XMAX - 0.1, -1.0, plot, -range, range, palette, fade, fade_value);
else if (circular)
draw_circular_color_scheme_palette_fade(XMAX - 2.0*width, YMIN + 2.0*width, 1.5*width, plot, -range, range, palette, fade, fade_value);
else
draw_color_scheme_palette_fade(XMAX - 1.5*width, YMIN + 0.1, XMAX - 0.5*width, YMAX - 0.1, plot, -range, range, palette, fade, fade_value);
}
void animation()
{
double time, scale, ratio, startleft[2], startright[2], sign = 1.0, r2, xy[2], fade_value, yshift, speed = 0.0, a, b, c, x, y, angle = 0.0, x1, sign1, ior_angle = 0.0, omega, phase_shift;
double *phi[NX], *psi[NX], *tmp[NX], *total_energy[NX], *color_scale[NX], *total_flux, *tcc_table[NX];
short int *xy_in[NX];
int i, j, k, s, sample_left[2], sample_right[2], period = 0, fade, source_counter = 0, p, q, first_source = 1;
static int counter = 0;
long int wave_value;
t_wave_packet *packet;
t_wave_source wave_source[25];
if (SAVE_TIME_SERIES)
{
time_series_left = fopen("wave_left.dat", "w");
time_series_right = fopen("wave_right.dat", "w");
}
/* 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));
tmp[i] = (double *)malloc(NY*sizeof(double));
total_energy[i] = (double *)malloc(NY*sizeof(double));
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
color_scale[i] = (double *)malloc(NY*sizeof(double));
tcc_table[i] = (double *)malloc(NX*sizeof(double));
}
if (MEAN_FLUX) total_flux = (double *)malloc(4*NX*NY*sizeof(double));
if (ADD_WAVE_PACKET_SOURCES)
{
packet = (t_wave_packet *)malloc(N_WAVE_PACKETS*sizeof(t_wave_packet));
init_wave_packets(packet, WAVE_PACKET_RADIUS);
}
/* initialise positions and radii of circles */
if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN == D_CIRCLES_IN_RECT)) ncircles = init_circle_config(circles);
else if (B_DOMAIN == D_POLYGONS) ncircles = init_polygon_config(polygons);
printf("Polygons initialized\n");
/* initialise polyline for von Koch and similar 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);
npolyrect = init_polyrect(polyrect);
for (i=0; i<npolyrect; i++) printf("polyrect vertex %i: (%.3f, %.3f) - (%.3f, %.3f)\n", i, polyrect[i].x1, polyrect[i].y1, polyrect[i].x2, polyrect[i].y2);
printf("Rectangles initialized\n");
init_polyrect_arc(polyrectrot, polyarc, &npolyrect_rot, &npolyarc);
printf("Rotated rectangles and arcs initialized\n");
printf("%i rotated rectangles, %i arcs\n", npolyrect_rot, npolyarc);
courant2 = COURANT*COURANT;
courantb2 = COURANTB*COURANTB;
c = COURANT*(XMAX - XMIN)/(double)NX;
/* initialize color scale, for option RESCALE_COLOR_IN_CENTER */
if (RESCALE_COLOR_IN_CENTER)
{
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
r2 = xy[0]*xy[0] + xy[1]*xy[1];
color_scale[i][j] = 1.0 - exp(-4.0*r2/LAMBDA*LAMBDA);
}
}
/* initialize wave with a drop at one point, zero elsewhere */
// init_circular_wave(0.0, -LAMBDA, phi, psi, xy_in);
/* initialize total energy table */
if ((PLOT == P_MEAN_ENERGY)||(PLOT_B == P_MEAN_ENERGY)||(PLOT == P_LOG_MEAN_ENERGY)||(PLOT_B == P_LOG_MEAN_ENERGY))
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
total_energy[i][j] = 0.0;
if (MEAN_FLUX)
for (i=0; i<4*NX*NY; i++)
total_flux[i] = 0.0;
if (VARIABLE_IOR) init_ior_2d(xy_in, tcc_table, ior_angle);
ratio = (XMAX - XMIN)/8.4; /* for Tokarsky billiard */
// isospectral_initial_point(0.2, 0.0, startleft, startright); /* for isospectral billiards */
// homophonic_initial_point(0.5, -0.25, 1.5, -0.25, startleft, startright);
// homophonic_initial_point(0.5, -0.25, 1.5, -0.25, startleft, startright);
// printf("xleft = (%.3f, %.3f) xright = (%.3f, %.3f)\n", startleft[0], startleft[1], startright[0], startright[1]);
// xy_to_ij(startleft[0], startleft[1], sample_left);
// xy_to_ij(startright[0], startright[1], sample_right);
// printf("xleft = (%.3f, %.3f) xright = (%.3f, %.3f)\n", xin_left, yin_left, xin_right, yin_right);
init_wave_flat(phi, psi, xy_in);
// init_circular_wave(-0.5, 0.0, phi, psi, xy_in);
// x = XMIN + (XMAX - XMIN)*rand()/RAND_MAX;
// y = YMIN + (YMAX - YMIN)*rand()/RAND_MAX;
// init_circular_wave(0.0, -0.8, phi, psi, xy_in);
// add_circular_wave(-1.0, -1.5, -0.8, phi, psi, xy_in);
// add_circular_wave(-1.0, 1.5, -0.8, phi, psi, xy_in);
// sign = -sign;
// init_circular_wave(2.0*LAMBDA*cos(APOLY*PID), 2.0*LAMBDA*sin(APOLY*PID), phi, psi, xy_in);
// angle = DPI/(double)NPOLY;
// for (j=1; j<NPOLY; j++)
// add_circular_wave(1.0, 2.0*LAMBDA*cos((double)j*angle + APOLY*PID), 2.0*LAMBDA*sin((double)j*angle + APOLY*PID), phi, psi, xy_in);
// init_wave_plus(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);
// init_wave(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);
// init_circular_wave(X_SHOOTER, Y_SHOOTER, phi, psi, xy_in);
// printf("Initializing wave\n");
// init_circular_wave(-0.5, 0.0, phi, psi, xy_in);
// printf("Wave initialized\n");
// init_circular_wave(0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in);
// period++;
// for (i=0; i<3; i++)
// {
// add_circular_wave(-1.0, 0.6*cos(PID + (double)(i)*DPI/3.0), 0.6*sin(PID + (double)(i)*DPI/3.0), phi, psi, xy_in);
// }
// add_circular_wave(-1.0, 0.0, LAMBDA, phi, psi, xy_in);
// add_circular_wave(1.0, -LAMBDA, 0.0, phi, psi, xy_in);
// add_circular_wave(-1.0, 0.0, -LAMBDA, phi, psi, xy_in);
// init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], phi, psi, xy_in);
// init_circular_wave_xplusminus(-0.9, 0.0, 0.81, 0.0, phi, psi, xy_in);
// init_circular_wave(-2.0*ratio, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.015, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.02, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.5, 0.0, phi, psi, xy_in);
// init_wave(-1.5, 0.0, phi, psi, xy_in);
// init_wave(0.0, 0.0, phi, psi, xy_in);
/* add a drop at another point */
// add_drop_to_wave(1.0, 0.7, 0.0, phi, psi);
// add_drop_to_wave(1.0, -0.7, 0.0, phi, psi);
// add_drop_to_wave(1.0, 0.0, -0.7, phi, psi);
blank();
glColor3f(0.0, 0.0, 0.0);
// draw_wave(phi, psi, xy_in, 1.0, 0, PLOT);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, 1.0, 0, PLOT, COLOR_PALETTE, 0, 1.0);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, 1.0, 0, PLOT, COLOR_PALETTE, 0, 1.0);
draw_billiard(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, fade, fade_value);
if (PRINT_SPEED)
{
a = 0.0075;
b = 0.00015;
// speed = a/((double)(NVID)*c);
// speed = 0.55*a/((double)(NVID*OSCILLATING_SOURCE_PERIOD)*c);
speed = a/((double)(3*NVID*OSCILLATING_SOURCE_PERIOD)*c);
/* the factor 3 is due to evolve_wave calling evolve_wave_half 3 times */
print_speed(speed, 0, 1.0);
}
glutSwapBuffers();
sleep(SLEEP1);
for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
{
//printf("%d\n",i);
/* compute the variance of the field to adjust color scheme */
/* the color depends on the field divided by sqrt(1 + variance) */
if (SCALE)
{
scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
// printf("Scaling factor: %5lg\n", scale);
}
else scale = 1.0;
// draw_wave(phi, psi, xy_in, scale, i, PLOT);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, scale, i, PLOT, COLOR_PALETTE, 0, 1.0);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, scale, i, PLOT, COLOR_PALETTE, 0, 1.0);
for (j=0; j<NVID; j++)
{
// evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
evolve_wave(phi, psi, tmp, xy_in, tcc_table);
if (SAVE_TIME_SERIES)
{
wave_value = (long int)(phi[sample_left[0]][sample_left[1]]*1.0e16);
fprintf(time_series_left, "%019ld\n", wave_value);
wave_value = (long int)(phi[sample_right[0]][sample_right[1]]*1.0e16);
fprintf(time_series_right, "%019ld\n", wave_value);
if ((j == 0)&&(i%10 == 0)) printf("Frame %i of %i\n", i, NSTEPS);
// fprintf(time_series_right, "%.15f\n", phi[sample_right[0]][sample_right[1]]);
}
// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
}
draw_billiard(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, fade, fade_value);
/* add oscillating waves */
if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == 1))
{
if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
add_circular_wave(sign, -0.5, 0.0, phi, psi, xy_in);
// p = phased_array_schedule(i);
// phase_shift = 0.02 + 0.06*(double)i/(double)NSTEPS;
// if (first_source) for (k=0; k<25; k++)
// {
// omega = DPI/25.0;
// wave_source[k].xc = 0.05*cos((double)k*omega);;
// wave_source[k].yc = 0.05*sin((double)k*omega);
// wave_source[k].phase = 0.99 - 1.4*sin(0.7*(1.0 + wave_source[k].xc/0.05));
// wave_source[k].amp = 1.0;
// if (wave_source[k].phase) wave_source[k].sign = 1;
// else wave_source[k].sign = -1;
// first_source = 0;
// }
//
// for (k=0; k<25; k++)
// wave_source[k].phase += 1.4*sin(0.7*(1.0 + wave_source[k].xc*cos(angle)/0.05 + wave_source[k].yc*sin(angle)/0.05));
//
// angle = DPI*(double)i/(double)NSTEPS;
//
// for (k=0; k<25; k++)
// {
// wave_source[k].phase += 0.07;
// wave_source[k].phase -= 1.4*sin(0.7*(1.0 + wave_source[k].xc*cos(angle)/0.05 + wave_source[k].yc*sin(angle)/0.05));
//
// if (wave_source[k].phase > 1.0)
// {
// add_circular_wave((double)wave_source[k].sign*wave_source[k].amp, wave_source[k].xc, wave_source[k].yc, phi, psi, xy_in);
// printf("Adding wave at (%.2lg, %.2lg)\n", wave_source[k].xc, wave_source[k].yc);
// wave_source[k].phase -= 1.0;
// wave_source[k].sign *= -1;
// }
// }
// p = 3;
// y = -1.0;
// sign1 = sign;
// printf("p = %i\n", p);
// for (k=-12; k<13; k++)
// {
// x1 = 0.05*((double)source_counter/(double)p + (double)k);
// if ((x1 > 0.1*XMIN)&&(x1 < 0.1*XMAX))
// {
// add_circular_wave(sign1, x1, y, phi, psi, xy_in);
// printf("Adding wave at (%.2lg, %.2lg)\n", x1, y);
// }
// sign1 = -sign1;
// }
// source_counter++;
// if (p > 0) q = p;
// else q = -p;
// if (source_counter >= q)
// {
// source_counter = 0;
// sign = -sign;
// }
// for (j=0; j<NPOLY; j++)
// add_circular_wave(sign, 2.0*LAMBDA*cos((double)j*angle + APOLY*PID), 2.0*LAMBDA*sin((double)j*angle + APOLY*PID), phi, psi, xy_in);
// x = XMIN + (XMAX - XMIN)*rand()/RAND_MAX;
// y = YMIN + (YMAX - YMIN)*rand()/RAND_MAX;
// add_circular_wave(sign, 0.0, 0.0, phi, psi, xy_in);
// add_circular_wave(1.0, -1.5*LAMBDA, 0.0, phi, psi, xy_in);
// add_circular_wave(-1.0, 0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in);
// period++;
//
// yshift = (double)period*a + (double)(period*period)*b;
// add_circular_wave(sign, -1.5 + yshift, 0.0, phi, psi, xy_in);
// // speed = (a + 2.0*(double)(period)*b)/((double)(NVID));
// // speed = 0.55*(a + 2.0*(double)(period)*b)/((double)(NVID*OSCILLATING_SOURCE_PERIOD));
// speed = (a + 2.0*(double)(period)*b)/((double)(3*NVID*OSCILLATING_SOURCE_PERIOD));
// printf("v = %.3lg, c = %.3lg\n", speed, c);
// speed = speed/c;
// speed = 120.0*speed/((double)NVID*COURANT);
}
if (ADD_WAVE_PACKET_SOURCES) add_wave_packets(phi, psi, xy_in, packet, i, WAVE_PACKET_RADIUS, 0, 10, 1);
if (PRINT_SPEED) print_speed(speed, 0, 1.0);
if (PRINT_FREQUENCY) print_frequency(phase_shift, 0, 1.0);
if ((VARIABLE_IOR)&&(REFRESH_IOR)&&(i%3 == 0))
{
ior_angle = ior_angle_schedule(i);
printf("IOR angle = %.5lg\n", ior_angle);
init_ior_2d(xy_in, tcc_table, ior_angle);
printf("speed = %.5lg\n", tcc_table[3*NX/4][NY/2]);
}
if (!((NO_EXTRA_BUFFER_SWAP)&&(MOVIE))) glutSwapBuffers();
if (MOVIE)
{
if (i >= INITIAL_TIME) save_frame();
else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
{
// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
if (HIGHRES)
draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, scale, i, PLOT_B, COLOR_PALETTE_B, 0, 1.0);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, scale, i, PLOT_B, COLOR_PALETTE_B, 0, 1.0);
draw_billiard(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 0, 1.0);
if (PRINT_SPEED) print_speed(speed, 0, 1.0);
if (PRINT_FREQUENCY) print_frequency(phase_shift, 0, 1.0);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
counter++;
}
else if (NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
/* 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_wave/");
}
}
}
if (MOVIE)
{
if (DOUBLE_MOVIE)
{
// draw_wave(phi, psi, xy_in, scale, i, PLOT);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE, 0, 1.0);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE, 0, 1.0);
draw_billiard(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 0, 1.0);
if (PRINT_SPEED) print_speed(speed, 0, 1.0);
if (PRINT_FREQUENCY) print_frequency(phase_shift, 0, 1.0);
glutSwapBuffers();
}
if (!FADE) for (i=0; i<MID_FRAMES; i++) save_frame();
else for (i=0; i<MID_FRAMES; i++)
{
fade_value = 1.0 - (double)i/(double)MID_FRAMES;
if (HIGHRES)
draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE, 1, fade_value);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE, 1, fade_value);
draw_billiard(1, fade_value);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 1, fade_value);
if (PRINT_SPEED) print_speed(speed, 1, fade_value);
if (PRINT_FREQUENCY) print_frequency(phase_shift, 1, fade_value);
if (!NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
save_frame_counter(NSTEPS + i + 1);
}
if (DOUBLE_MOVIE)
{
// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
if (HIGHRES)
draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B, 0, 1.0);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B, 0, 1.0);
draw_billiard(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 0, 1.0);
if (PRINT_SPEED) print_speed(speed, 0, 1.0);
if (PRINT_FREQUENCY) print_frequency(phase_shift, 0, 1.0);
glutSwapBuffers();
if (!FADE) for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
else for (i=0; i<END_FRAMES; i++)
{
fade_value = 1.0 - (double)i/(double)END_FRAMES;
if (HIGHRES)
draw_wave_highres_palette(2, phi, psi, total_energy, total_flux, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B, 1, fade_value);
else draw_wave_epalette(phi, psi, total_energy, total_flux, color_scale, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B, 1, fade_value);
draw_billiard(1, fade_value);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 1, fade_value);
if (PRINT_SPEED) print_speed(speed, 1, fade_value);
if (PRINT_FREQUENCY) print_frequency(phase_shift, 0, 1.0);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
}
}
s = system("mv wave*.tif tif_wave/");
}
for (i=0; i<NX; i++)
{
free(phi[i]);
free(psi[i]);
// free(phi_tmp[i]);
// free(psi_tmp[i]);
free(tmp[i]);
free(total_energy[i]);
free(xy_in[i]);
free(color_scale[i]);
free(tcc_table[i]);
}
if (MEAN_FLUX) free(total_flux);
if (ADD_WAVE_PACKET_SOURCES) free(packet);
if (SAVE_TIME_SERIES)
{
fclose(time_series_left);
fclose(time_series_right);
}