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wave_comparison.c
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wave_comparison.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 1 /* set to 1 for a variable index of refraction */
#define IOR 10 /* 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 */
#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */
#define TIME_LAPSE_FACTOR 4 /* factor of time-lapse movie */
#define WINWIDTH 1920 /* window width */
#define WINHEIGHT 1150 /* window height */
// #define NX 1920 /* number of grid points on x axis */
// #define NY 1000 /* number of grid points on y axis */
// #define YMID 500 /* mid point of display */
#define NX 3840 /* number of grid points on x axis */
#define NY 2300 /* number of grid points on y axis */
#define YMID 1150 /* mid point of display */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -1.197916667
#define YMAX 1.197916667 /* y interval for 9/16 aspect ratio */
// #define WINWIDTH 1280 /* window width */
// #define WINHEIGHT 720 /* window height */
// #define NX 1280 /* number of grid points on x axis */
// #define NY 720 /* number of grid points on y axis */
// #define YMID 360 /* mid point of display */
// #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 HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 63 /* choice of domain shape, see list in global_pdes.c */
#define B_DOMAIN_B 63 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 13 /* pattern of circles, see list in global_pdes.c */
#define CIRCLE_PATTERN_B 13 /* pattern of circles, see list in global_pdes.c */
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
#define PDISC_FACTOR 3.25 /* controls density of Poisson disc process (default: 3.25) */
#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
#define RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */
#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */
#define XDEP_POLY_ANGLE_B 0 /* set to 1 to rotate polygons depending on x coordinate */
#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */
#define HEX_NONUNIF_COMPRESSSION 0.15 /* compression factor for HEX_NONUNIF pattern */
#define HEX_NONUNIF_COMPRESSSION_B -0.15 /* compression factor for HEX_NONUNIF pattern */
#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */
#define MU 0.7 /* parameter controlling the dimensions of domain */
#define MUB 0.2 /* parameter controlling the dimensions of domain */
#define NPOLY 3 /* number of sides of polygon */
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
#define APOLY_B 2.0 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 4 /* 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 20 /* number of grid point for grid of disks */
#define NGRIDY 20 /* 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 -1.65
#define ISO_XSHIFT_RIGHT 0.4
#define ISO_YSHIFT_LEFT -0.05
#define ISO_YSHIFT_RIGHT -0.05
#define ISO_SCALE 0.85 /* 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 1 /* set to 1 to replace hardcore boundary by medium with different speed */
#define OSCILLATE_LEFT 0 /* 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 OMEGA 0.024 /* frequency of periodic excitation */
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
#define DAMPING 0.0 /* damping of periodic excitation */
#define COURANT 0.1 /* Courant number */
#define COURANTB 0.063 /* 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 */
/* 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 1 /* set to 1 to add an oscillating wave source */
#define OSCILLATING_SOURCE_PERIOD 20 /* period of oscillating source */
#define ALTERNATE_OSCILLATING_SOURCE 1 /* set to 1 to alternate sign of oscillating source */
#define NSOURCES 48 /* number of sources */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 4
/* Parameters for length and speed of simulation */
// #define NSTEPS 500 /* number of frames of movie */
#define NSTEPS 2600 /* number of frames of movie */
#define NVID 7 /* number of iterations between images displayed on screen */
#define NSEG 100 /* number of segments of boundary */
#define INITIAL_TIME 100 /* time after which to start saving frames */
#define COMPUTE_ENERGIES 0 /* set to 1 to compute and print energies */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
#define PAUSE 100 /* 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 50 /* number of still frames between movies */
#define END_FRAMES 300 /* 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 1.0 /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.00001 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.025 /* wavelength of initial condition */
/* Plot type, see list in global_pdes.c */
#define PLOT 0
#define PLOT_B 5
/* Color schemes */
#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */
#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */
#define BLACK 1 /* background */
#define BLACK_TEXT 1 /* set to 1 to write text in black instead of white */
#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 VSHIFT_AMPLITUDE 0.0 /* additional shift for wave amplitude */
#define VSCALE_AMPLITUDE 0.5 /* additional scaling factor for wave amplitude */
#define E_SCALE 100.0 /* scaling factor for energy representation */
#define LOG_SCALE 1.0 /* scaling factor for energy log representation */
#define LOG_SHIFT 2.0 /* 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 220.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */
#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 12.5 /* scale of color scheme bar for 2nd part */
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
/* For debugging purposes only */
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
#define VMAX 5.0 /* max value of wave amplitude */
/* the following constants are only used by wave_billiard and wave_3d so far */
#define COMPARISON 0 /* set to 1 to compare two different patterns */
#define OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */
#define ACHIRP 0.2 /* acceleration coefficient in chirp */
#define DAMPING 0.0 /* damping of periodic excitation */
/* end of constants only used by wave_billiard and wave_3d */
/* for compatibility with sub_wave and sub_maze */
#define NXMAZE 7 /* width of maze */
#define NYMAZE 7 /* height of maze */
#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
#define RAND_SHIFT 24 /* seed of random number generator */
#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
#define ADD_POTENTIAL 0
#define POT_MAZE 7
#define POTENTIAL 0
#define MAZE_WIDTH 0.02 /* half width of maze walls */
#define WAVE_PACKET_SOURCE_TYPE 1 /* type of wave packet sources */
#define N_WAVE_PACKETS 15 /* number of wave packets */
#define OSCIL_LEFT_YSHIFT 0.0 /* y-dependence of left oscillation (for non-horizontal waves) */
#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
#define MU_B 1.0 /* parameter controlling the dimensions of domain */
#define VERTICAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
#define DRAW_WAVE_TIMESERIES 0 /* set to 1 to draw a time series of the wave */
#define WALL_WIDTH 0.1 /* width of wall separating lenses */
#define RADIUS_FACTOR 0.3 /* controls inner radius for C_RING arrangements */
#define OSCIL_YMAX 0.35 /* defines oscillation range */
#define MESSAGE_LDASH 14 /* length of dash for Morse code message */
#define MESSAGE_LDOT 8 /* length of dot for Morse code message */
#define MESSAGE_LINTERVAL 54 /* length of interval between dashes/dots for Morse code message */
#define MESSAGE_LINTERLETTER 60 /* length of interval between letters for Morse code message */
#define MESSAGE_LSPACE 48 /* length of space for Morse code message */
#define MESSAGE_INITIAL_TIME 100 /* initial time before starting message for Morse code message */
#define AVRG_E_FACTOR 0.95 /* controls time window size in P_AVERAGE_ENERGY scheme */
#define HORIZONTAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
#define WAVE_PROFILE_X 2.1 /* value of x to sample wave profile */
#define WAVE_PROFILE_Y -1.0 /* value of y to sample wave profile */
#define PROFILE_AT_BOTTOM 1 /* draw wave profile at bottom instead of top */
#define AVERAGE_WAVE_PROFILE 1 /* set to 1 to draw time-average of wave profile squared*/
#define TIMESERIES_NVALUES 400 /* number of values plotted in time series */
#define DRAW_WAVE_SOURCE 0 /* set to 1 to draw source of wave at (wave_source_x, wave_source_y) */
#define HRES 1 /* dummy, only used by rde.c */
#define INITIAL_SHIFT 20.0 /* time shift of initial wave packet (in oscillation periods) */
#define WAVE_PACKET_SHIFT 200.0 /* time shift between wave packets (in oscillation periods) */
#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */
#define SHADE_2D 0 /* set to 1 to add pseudo-3d shading effect */
#define SHADE_SCALE_2D 0.05 /* lower value increases sensitivity of shading */
#define N_SOURCES 1 /* number of sources, for option draw_sources */
#define XYIN_INITIALISED (B_DOMAIN == D_IMAGE)
double light[2] = {0.40824829, 0.816496581}; /* location of light source for SHADE_2D option*/
/* end of constants only used by sub_wave and sub_maze */
#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 */
#include "sub_wave_comp.c" /* some functions specific to wave_comparison */
double courant2, courantb2; /* Courant parameters squared */
FILE *monitor_sources;
/*********************/
/* animation part */
/*********************/
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 */
{
int i, j, iplus, iminus, jplus, jminus, jmid = NY/2;
double delta, x, y, c, cc, gamma;
static long time = 0;
static double tc[NX][NY], tgamma[NX][NY];
static short int first = 1;
time++;
/* 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;
if (!VARIABLE_IOR) tcc[i][j] = courantb2;
tgamma[i][j] = GAMMAB;
}
}
}
first = 0;
}
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y,c,cc,gamma)
/* evolution in the bulk */
for (i=1; i<NX-1; i++){
for (j=1; j<jmid-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);
}
}
for (j=jmid+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);
}
}
}
/* left boundary */
if (OSCILLATE_LEFT) {
for (j=1; j<jmid-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
for (j=jmid+1; j<NY-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
}
else for (j=1; j<NY-1; j++) if ((j!=jmid-1)&&(j!=jmid)) {
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;
}
case (BC_ABS_REFLECT):
{
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;
}
}
}
}
/* right boundary */
for (j=1; j<NY-1; j++) if ((j!=jmid-1)&&(j!=jmid)) {
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;
}
case (BC_ABS_REFLECT):
{
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;
}
}
}
}
/* top mid boundary */
for (i=0; i<NX; i++){
if ((TWOSPEEDS)||(xy_in[i][jmid-1] != 0)){
x = phi_in[i][jmid-1];
y = psi_in[i][jmid-1];
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][jmid-1] + phi_in[iminus][jmid-1] + phi_in[i][jmid-2] - 3.0*x;
phi_out[i][jmid-1] = -y + 2*x + tcc[i][jmid-1]*delta - KAPPA*x - tgamma[i][jmid-1]*(x-y);
break;
}
case (BC_PERIODIC):
{
iplus = (i+1) % NX;
iminus = (i-1) % NX; if (iminus < 0) iminus += NX;
delta = phi_in[iplus][jmid-1] + phi_in[iminus][jmid-1] + phi_in[i][jmid-2] + phi_in[i][0] - 4.0*x;
phi_out[i][jmid-1] = -y + 2*x + tcc[i][jmid-1]*delta - KAPPA*x - tgamma[i][jmid-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][jmid-1] + phi_in[iminus][jmid-1] + phi_in[i][jmid-2] - 3.0*x;
phi_out[i][jmid-1] = x - tc[i][jmid-1]*(x - phi_in[i][jmid-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][jmid-1] + phi_in[iminus][jmid-1] + phi_in[i][jmid-2] + phi_in[i][0] - 4.0*x;
if (i==0) phi_out[0][jmid-1] = x - tc[0][jmid-1]*(x - phi_in[1][jmid-1]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
else phi_out[i][jmid-1] = -y + 2*x + tcc[i][jmid-1]*delta - KAPPA*x - tgamma[i][jmid-1]*(x-y);
break;
}
case (BC_ABS_REFLECT):
{
iplus = i+1; if (iplus == NX) iplus = NX-1;
iminus = i-1; if (iminus == -1) iminus = 0;
delta = phi_in[iplus][jmid-1] + phi_in[iminus][jmid-1] + phi_in[i][jmid-2] - 3.0*x;
phi_out[i][jmid-1] = -y + 2*x + tcc[i][jmid-1]*delta - KAPPA*x - tgamma[i][jmid-1]*(x-y);
break;
}
}
}
}
/* 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];
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][jmid-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][jmid-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;
}
case (BC_ABS_REFLECT):
{
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;
}
}
}
}
/* 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];
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][jmid] - 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][jmid] - 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;
}
case (BC_ABS_REFLECT):
{
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;
}
}
}
}
/* bottom mid boundary */
for (i=0; i<NX; i++){
if ((TWOSPEEDS)||(xy_in[i][jmid] != 0)){
x = phi_in[i][jmid];
y = psi_in[i][jmid];
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][jmid] + phi_in[iminus][jmid] + phi_in[i][jmid+1] - 3.0*x;
phi_out[i][jmid] = -y + 2*x + tcc[i][jmid]*delta - KAPPA*x - tgamma[i][jmid]*(x-y);
break;
}
case (BC_PERIODIC):
{
iplus = (i+1) % NX;
iminus = (i-1) % NX; if (iminus < 0) iminus += NX;
delta = phi_in[iplus][jmid] + phi_in[iminus][jmid] + phi_in[i][jmid+1] + phi_in[i][NY-1] - 4.0*x;
phi_out[i][jmid] = -y + 2*x + tcc[i][jmid]*delta - KAPPA*x - tgamma[i][jmid]*(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][jmid] + phi_in[iminus][jmid] + phi_in[i][jmid+1] - 3.0*x;
phi_out[i][jmid] = x - tc[i][jmid]*(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][jmid] + phi_in[iminus][jmid] + phi_in[i][jmid+1] + phi_in[i][NY-1] - 4.0*x;
if (i==0) phi_out[0][jmid] = x - tc[0][jmid]*(x - phi_in[1][jmid]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
else phi_out[i][jmid] = -y + 2*x + tcc[i][jmid]*delta - KAPPA*x - tgamma[i][jmid]*(x-y);
break;
}
case (BC_ABS_REFLECT):
{
iplus = i+1; if (iplus == NX) iplus = NX-1;
iminus = i-1; if (iminus == -1) iminus = 0;
delta = phi_in[iplus][jmid] + phi_in[iminus][jmid] + phi_in[i][jmid+1] - 3.0*x;
phi_out[i][jmid] = -y + 2*x + tcc[i][jmid]*delta - KAPPA*x - tgamma[i][jmid]*(x-y);
break;
}
}
}
}
/* add oscillating boundary condition on the left corners */
if ((i == 0)&&(OSCILLATE_LEFT))
{
phi_out[i][0] = AMPLITUDE*cos((double)time*OMEGA);
phi_out[i][jmid-1] = AMPLITUDE*cos((double)time*OMEGA);
phi_out[i][jmid] = AMPLITUDE*cos((double)time*OMEGA);
phi_out[i][NY-1] = AMPLITUDE*cos((double)time*OMEGA);
}
/* 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;
}
}
}
// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
}
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 */
{
evolve_wave_half(phi, psi, tmp, xy_in, tcc_table);
evolve_wave_half(tmp, phi, psi, xy_in, tcc_table);
evolve_wave_half(psi, tmp, phi, xy_in, tcc_table);
}
// 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);
// }
void draw_color_bar_palette(int plot, double range, int palette, 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
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, energies[6], top_energy, bottom_energy, omega, angle, fade_value, sign = 1.0, ior_angle = 0.0;
double *phi[NX], *psi[NX], *tmp[NX], *total_energy[NX], *tcc_table[NX];
short int *xy_in[NX];
int i, j, s, counter = 0, k, first_source = 1, fade, resol = HIGHRES + 1;
t_wave_source wave_source[NSOURCES];
monitor_sources = fopen("monitor_sources.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));
tcc_table[i] = (double *)malloc(NX*sizeof(double));
}
/* initialise positions and radii of circles */
printf("initializing circle configuration\n");
if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN_B == D_CIRCLES)) init_circle_config_comp(circles);
if ((B_DOMAIN == D_POLYGONS)|(B_DOMAIN_B == D_POLYGONS)) init_polygon_config_comp(polygons);
// for (i=0; i<ncircles; i++) printf("polygon %i at (%.3f, %.3f) radius %.3f\n", i, polygons[i].xc, polygons[i].yc, polygons[i].radius);
/* 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);
/* 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;
courant2 = COURANT*COURANT;
courantb2 = COURANTB*COURANTB;
/* initialize wave with a drop at one point, zero elsewhere */
init_wave_flat_comp(phi, psi, xy_in);
// int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);
// int_planar_wave_comp(XMIN + 0.5, 0.0, phi, psi, xy_in);
printf("initializing wave\n");
// int_planar_wave_comp(XMIN + 0.1, 0.0, phi, psi, xy_in);
// int_planar_wave_comp(XMIN + 1.0, 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);
if (VARIABLE_IOR) init_ior_2d_comp(xy_in, tcc_table, ior_angle);
/* initialize energies */
if (COMPUTE_ENERGIES)
{
printf("computing energies\n");
compute_energy_tblr(phi, psi, xy_in, energies);
top_energy = energies[0] + energies[1] + energies[2];
bottom_energy = energies[3] + energies[4] + energies[5];
printf("computed energies\n");
}
blank();
glColor3f(0.0, 0.0, 0.0);
printf("drawing wave\n");
draw_wave_comp(phi, psi, xy_in, 1.0, 0, PLOT);
printf("drawing billiard\n");
draw_billiard_comp(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, fade, fade_value);
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_comp(phi, psi, xy_in, scale, i, PLOT);
draw_wave_comp_highres_palette(resol, phi, psi, total_energy, xy_in, scale, i, PLOT, COLOR_PALETTE, 0, 1.0);
for (j=0; j<NVID; j++)
{
evolve_wave(phi, psi, tmp, xy_in, tcc_table);
// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
}
/* add oscillating waves */
if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == 1))
{
if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
add_circular_wave(sign, -1.75, 0.16, phi, psi, xy_in);
add_circular_wave(sign, -1.75, -0.16, phi, psi, xy_in);
// if (first_source) for (k=0; k<NSOURCES; k++)
// {
// omega = DPI/(double)NSOURCES;
// wave_source[k].xc = 0.05*cos(((double)k + 0.5)*omega);;
// wave_source[k].yc = 0.05*sin(((double)k + 0.5)*omega);
// if (wave_source[k].yc < 0.0)
// {
// wave_source[k].xc *= 0.5;
// wave_source[k].yc *= 0.5;
// }
// // wave_source[k].phase = 0.99 - 1.4*sin(0.35*(1.0 + wave_source[k].xc/0.1));
// // wave_source[k].phase = 0.99 - 1.4*sin(0.7*(1.0 + wave_source[k].xc/0.1));
// // wave_source[k].phase = 0.99 - 1.4*sin(0.7*(1.0 + wave_source[k].xc/0.05));
// wave_source[k].phase = 0.99 - 1.4*sin(0.35*(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;
// wave_source[k].sign = 1;
//
// first_source = 0;
// }
//
// fprintf(monitor_sources, "Frame %i\n\n", i);
//
// for (k=0; k<NSOURCES; k++) /*if (wave_source[k].xc > 0.0) */
// {
// wave_source[k].phase += 0.06;
// // if (k==1) printf("x = %.3lg, phase = %.3lg\n", wave_source[k].xc, wave_source[k].phase);
// // fprintf(monitor_sources, "x = %.3lg, y = %.3lg, phase = %.3lg\n", wave_source[k].xc, wave_source[k].yc, wave_source[k].phase);
// if (wave_source[k].phase > 1.0)
// {
// add_circular_wave_comp((double)wave_source[k].sign*wave_source[k].amp, wave_source[k].xc, wave_source[k].yc, phi, psi, xy_in, (wave_source[k].yc > 0));
// fprintf(monitor_sources, "x = %.3lg, y = %.3lg, phase = %.3lg\n", wave_source[k].xc, wave_source[k].yc, wave_source[k].phase);
// printf("Adding wave at (%.2lg, %.2lg)\n", wave_source[k].xc, wave_source[k].yc);
// fprintf(monitor_sources, "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;
// }
// }
}
draw_billiard_comp(0, 1.0);
if (COMPUTE_ENERGIES)
{
compute_energy_tblr(phi, psi, xy_in, energies);
if (i < INITIAL_TIME)
{
top_energy = energies[0] + energies[1] + energies[2];
bottom_energy = energies[3] + energies[4] + energies[5];
}
print_energies(energies, top_energy, bottom_energy);
}
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, fade, fade_value);
if (!((NO_EXTRA_BUFFER_SWAP)&&(MOVIE))) glutSwapBuffers();
if (MOVIE)
{
if (i >= INITIAL_TIME) save_frame();
if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
{
// save_frame();
if ((TIME_LAPSE)&&((i - INITIAL_TIME)%TIME_LAPSE_FACTOR == 0))
{
save_frame_counter(NSTEPS + END_FRAMES + (i - INITIAL_TIME)/TIME_LAPSE_FACTOR);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, 0, 1.0);
counter++;
}
else /*if (DOUBLE_MOVIE)*/
{
// draw_wave_comp(phi, psi, xy_in, scale, i, PLOT_B);
draw_wave_comp_highres_palette(resol, phi, psi, total_energy, xy_in, scale, i, PLOT_B, COLOR_PALETTE_B, 0, 1.0);
draw_billiard_comp(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, 0, 1.0);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
counter++;
}
}
else if (NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
// else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
/* 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_comp(phi, psi, xy_in, scale, i, PLOT);
draw_wave_comp_highres_palette(resol, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE, 0, 1.0);
draw_billiard_comp(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, 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;
draw_wave_comp_highres_palette(resol, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE, 1, fade_value);
draw_billiard_comp(1, fade_value);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE, 1, fade_value);
if (!NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
save_frame_counter(NSTEPS + i + 1);
}
if (DOUBLE_MOVIE)
{
// draw_wave_comp(phi, psi, xy_in, scale, i, PLOT_B);
draw_wave_comp_highres_palette(resol, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B, 0, 1.0);
draw_billiard_comp(0, 1.0);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, 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;
draw_wave_comp_highres_palette(resol, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B, 1, fade_value);
draw_billiard_comp(1, fade_value);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, 1, fade_value);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
}
}
if (TIME_LAPSE) for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + END_FRAMES + NSTEPS/TIME_LAPSE_FACTOR + i);
s = system("mv wave*.tif tif_wave/");
}
for (i=0; i<NX; i++)
{
free(phi[i]);
free(psi[i]);
free(tmp[i]);
free(total_energy[i]);
free(xy_in[i]);
free(tcc_table[i]);
}
}