YouTube-simulations/wave_billiard.c

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/*********************************************************************************/
/* */
/* Animation of wave equation in a planar domain */
/* */
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/* N. Berglund, december 2012, may 2021 */
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/* */
/* 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 nils.berglund@univ-orleans.fr - Thanks! */
/* */
/* compile with */
/* gcc -o wave_billiard wave_billiard.c */
/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
/* */
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/* OMP acceleration may be more effective after executing */
/* export OMP_NUM_THREADS=2 in the shell before running the program */
/* */
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/* 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>
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#define MOVIE 1 /* set to 1 to generate movie */
#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
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/* General geometrical parameters */
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#define WINWIDTH 1920 /* window width */
#define WINHEIGHT 1000 /* window height */
#define NX 1920 /* number of grid points on x axis */
#define NY 1000 /* number of grid points on y axis */
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#define XMIN -2.0
#define XMAX 2.0 /* x interval */
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#define YMIN -1.0329
#define YMAX 1.1129 /* 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 NX 2560 /* number of grid points on x axis */
// #define NY 1440 /* number of grid points on y axis */
// #define YMIN -1.125
// #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 */
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#define B_DOMAIN 42 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, 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 */
#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 1.1 /* parameter controlling the dimensions of domain */
#define MU 0.4 /* parameter controlling the dimensions of domain */
#define NPOLY 14 /* number of sides of polygon */
#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 */
#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 10 /* number of grid point for grid of disks */
#define NGRIDY 12 /* number of grid point for grid of disks */
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#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 */
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#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 */
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/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard below */
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/* Physical parameters of wave equation */
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#define TWOSPEEDS 0 /* 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 0.002 /* frequency of periodic excitation */
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
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#define COURANT 0.04 /* Courant number */
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#define COURANTB 0.01 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define GAMMAB 1.0e-6 /* damping factor in wave equation */
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#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
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#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
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#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 */
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/* 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 */
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 3
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/* Parameters for length and speed of simulation */
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#define NSTEPS 2100 /* number of frames of movie */
#define NVID 25 /* 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 INITIAL_TIME 0 /* time after which to start saving frames */
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#define BOUNDARY_WIDTH 3 /* 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 */
#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
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#define END_FRAMES 50 /* number of still frames at end of movie */
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/* Parameters of initial condition */
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#define INITIAL_AMP 0.75 /* amplitude of initial condition */
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#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 1
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#define PLOT_B 0 /* plot type for second movie */
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/* Color schemes */
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#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* background */
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#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 0.5 /* 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 */
#define LOG_SCALE 2.5 /* scaling factor for energy log representation */
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#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 */
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#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 */
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#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 10.0 /* scale of color scheme bar for 2nd part */
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
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#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */
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/* 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 */
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#include "global_pdes.c" /* constants and global variables */
#include "sub_wave.c" /* common functions for wave_billiard, heat and schrodinger */
#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
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FILE *time_series_left, *time_series_right;
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double courant2, courantb2; /* Courant parameters squared */
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/*********************/
/* animation part */
/*********************/
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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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/* 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;
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double delta, x, y, c, cc, gamma;
static long time = 0;
time++;
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// c = COURANT;
// cc = courant2;
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#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y,c,cc,gamma)
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for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
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// if (xy_in[i][j])
// {
// c = COURANT;
// cc = courant2;
// gamma = GAMMA;
// }
if (xy_in[i][j] != 0)
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{
c = COURANT;
cc = courant2;
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if (xy_in[i][j] == 1) gamma = GAMMA;
else gamma = GAMMAB;
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}
else if (TWOSPEEDS)
{
c = COURANTB;
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cc = courantb2;
gamma = GAMMAB;
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}
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if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
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/* discretized Laplacian for various boundary conditions */
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if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING))
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
}
else if (B_COND == BC_PERIODIC)
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
jplus = (j+1) % NY;
jminus = (j-1) % NY;
if (jminus < 0) jminus += NY;
}
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else if (B_COND == BC_VPER_HABS)
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1) % NY;
jminus = (j-1) % NY;
if (jminus < 0) jminus += NY;
}
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/* imposing linear wave on top and bottom by making Laplacian 1d */
if (OSCILLATE_TOPBOT)
{
if (j == NY-1) jminus = NY-1;
else if (j == 0) jplus = 0;
}
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delta = phi_in[iplus][j] + phi_in[iminus][j] + phi_in[i][jplus] + phi_in[i][jminus] - 4.0*phi_in[i][j];
x = phi_in[i][j];
y = psi_in[i][j];
/* evolve phi */
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if ((B_COND == BC_PERIODIC)||(B_COND == BC_DIRICHLET))
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phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - gamma*(x-y);
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else if (B_COND == BC_ABSORBING)
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{
if ((i>0)&&(i<NX-1)&&(j>0)&&(j<NY-1))
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phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - gamma*(x-y);
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/* upper border */
else if (j==NY-1)
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phi_out[i][j] = x - c*(x - phi_in[i][NY-2]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
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/* lower border */
else if (j==0)
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phi_out[i][j] = x - c*(x - phi_in[i][1]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
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/* right border */
if (i==NX-1)
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phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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/* left border */
else if (i==0)
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phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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}
else if (B_COND == BC_VPER_HABS)
{
if ((i>0)&&(i<NX-1))
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phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - gamma*(x-y);
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/* right border */
else if (i==NX-1)
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phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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/* left border */
else if (i==0)
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phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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}
psi_out[i][j] = x;
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/* add oscillating boundary condition on the left */
if ((i == 0)&&(OSCILLATE_LEFT)) phi_out[i][j] = AMPLITUDE*cos((double)time*OMEGA);
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// psi_out[i][j] = x;
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if (FLOOR)
{
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;
}
}
}
}
// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
}
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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])
/* 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;
static long time = 0;
static double tc[NX][NY], tcc[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;
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] = AMPLITUDE*cos((double)time*OMEGA);
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];
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];
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] = AMPLITUDE*cos((double)time*OMEGA);
phi_out[0][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;
if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
}
}
}
}
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void evolve_wave(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *psi_tmp[NX], short int *xy_in[NX])
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/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
{
evolve_wave_half(phi, psi, phi_tmp, psi_tmp, xy_in);
evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
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// evolve_wave_half_old(phi, psi, phi_tmp, psi_tmp, xy_in);
// evolve_wave_half_old(phi_tmp, psi_tmp, phi, psi, xy_in);
}
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);
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}
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void animation()
{
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double time, scale, ratio, startleft[2], startright[2], sign;
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double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX], *total_energy[NX];
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short int *xy_in[NX];
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int i, j, s, sample_left[2], sample_right[2];
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static int counter = 0;
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long int wave_value;
if (SAVE_TIME_SERIES)
{
time_series_left = fopen("wave_left.dat", "w");
time_series_right = fopen("wave_right.dat", "w");
}
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/* 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));
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phi_tmp[i] = (double *)malloc(NY*sizeof(double));
psi_tmp[i] = (double *)malloc(NY*sizeof(double));
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total_energy[i] = (double *)malloc(NY*sizeof(double));
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xy_in[i] = (short int *)malloc(NY*sizeof(short int));
}
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/* initialise positions and radii of circles */
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if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN == D_CIRCLES_IN_RECT)) init_circle_config(circles);
else if (B_DOMAIN == D_POLYGONS) init_polygon_config(polygons);
printf("Polygons initialized\n");
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/* initialise polyline for von Koch and similar domains */
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npolyline = init_polyline(MDEPTH, polyline);
for (i=0; i<npolyline; i++) printf("vertex %i: (%.3f, %.3f)\n", i, polyline[i].x, polyline[i].y);
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courant2 = COURANT*COURANT;
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courantb2 = COURANTB*COURANTB;
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/* initialize wave with a drop at one point, zero elsewhere */
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// init_circular_wave(0.0, -LAMBDA, phi, psi, xy_in);
/* initialize total energy table */
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if ((PLOT == P_MEAN_ENERGY)||(PLOT_B == P_MEAN_ENERGY)||(PLOT == P_LOG_MEAN_ENERGY)||(PLOT_B == P_LOG_MEAN_ENERGY))
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for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
total_energy[i][j] = 0.0;
ratio = (XMAX - XMIN)/8.4; /* for Tokarsky billiard */
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// isospectral_initial_point(0.2, 0.0, startleft, startright); /* for isospectral billiards */
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// homophonic_initial_point(0.5, -0.25, 1.5, -0.25, startleft, startright);
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// 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]);
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// xy_to_ij(startleft[0], startleft[1], sample_left);
// xy_to_ij(startright[0], startright[1], sample_right);
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// printf("xleft = (%.3f, %.3f) xright = (%.3f, %.3f)\n", xin_left, yin_left, xin_right, yin_right);
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// init_wave_flat(phi, psi, xy_in);
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// 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);
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// init_circular_wave(X_SHOOTER, Y_SHOOTER, phi, psi, xy_in);
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// printf("Initializing wave\n");
// init_circular_wave(-1.0, 0.0, phi, psi, xy_in);
// printf("Wave initialized\n");
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init_circular_wave(0.0, 0.0, phi, psi, xy_in);
// 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);
// }
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// 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);
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// init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], phi, psi, xy_in);
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// 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);
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// init_planar_wave(XMIN + 0.015, 0.0, phi, psi, xy_in);
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// init_planar_wave(XMIN + 0.02, 0.0, phi, psi, xy_in);
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// init_planar_wave(XMIN + 0.5, 0.0, phi, psi, xy_in);
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// init_wave(-1.5, 0.0, phi, psi, xy_in);
// init_wave(0.0, 0.0, phi, psi, xy_in);
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/* 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);
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// draw_wave(phi, psi, xy_in, 1.0, 0, PLOT);
draw_wave_e(phi, psi, total_energy, xy_in, 1.0, 0, PLOT);
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
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glutSwapBuffers();
sleep(SLEEP1);
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for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
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{
//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;
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// draw_wave(phi, psi, xy_in, scale, i, PLOT);
draw_wave_e(phi, psi, total_energy, xy_in, scale, i, PLOT);
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for (j=0; j<NVID; j++)
{
evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
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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]]);
}
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// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
}
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
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/* add oscillating waves */
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// if (i%345 == 344)
// {
// add_circular_wave(1.0, -LAMBDA, 0.0, phi, psi, xy_in);
// }
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glutSwapBuffers();
if (MOVIE)
{
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if (i >= INITIAL_TIME) save_frame();
else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
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if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
{
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// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
draw_wave_e(phi, psi, total_energy, xy_in, scale, i, PLOT_B);
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
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draw_billiard();
glutSwapBuffers();
save_frame_counter(NSTEPS + 21 + counter);
counter++;
}
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/* 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/");
}
}
}
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if (MOVIE)
{
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if (DOUBLE_MOVIE)
{
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// draw_wave(phi, psi, xy_in, scale, i, PLOT);
draw_wave_e(phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT);
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
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glutSwapBuffers();
}
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for (i=0; i<MID_FRAMES; i++) save_frame();
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if (DOUBLE_MOVIE)
{
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// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
draw_wave_e(phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B);
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
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glutSwapBuffers();
}
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for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
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s = system("mv wave*.tif tif_wave/");
}
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for (i=0; i<NX; i++)
{
free(phi[i]);
free(psi[i]);
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free(phi_tmp[i]);
free(psi_tmp[i]);
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free(total_energy[i]);
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free(xy_in[i]);
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}
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if (SAVE_TIME_SERIES)
{
fclose(time_series_left);
fclose(time_series_right);
}
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}
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("Wave equation in a planar domain");
init();
glutDisplayFunc(display);
glutMainLoop();
return 0;
}