487 lines
20 KiB
C
487 lines
20 KiB
C
/*********************************************************************************/
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/* */
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/* Animation of wave equation in a planar domain */
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/* */
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/* N. Berglund, december 2012, may 2021 */
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/* */
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/* UPDATE 24/04: distinction between damping and "elasticity" parameters */
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/* UPDATE 27/04: new billiard shapes, bug in color scheme fixed */
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/* UPDATE 28/04: code made more efficient, with help of Marco Mancini */
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/* */
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/* Feel free to reuse, but if doing so it would be nice to drop a */
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/* line to nils.berglund@univ-orleans.fr - Thanks! */
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/* */
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/* compile with */
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/* gcc -o wave_billiard wave_billiard.c */
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/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
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/* */
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/* OMP acceleration may be more effective after executing */
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/* export OMP_NUM_THREADS=2 in the shell before running the program */
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/* */
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/* To make a video, set MOVIE to 1 and create subfolder tif_wave */
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/* It may be possible to increase parameter PAUSE */
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/* */
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/* create movie using */
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/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
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/* */
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/*********************************************************************************/
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/*********************************************************************************/
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/* */
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/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
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/* One could make it much faster by using a GPU */
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/* */
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/*********************************************************************************/
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#include <math.h>
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#include <string.h>
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#include <GL/glut.h>
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#include <GL/glu.h>
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#include <unistd.h>
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#include <sys/types.h>
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#include <tiffio.h> /* Sam Leffler's libtiff library. */
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#include <omp.h>
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#define MOVIE 0 /* set to 1 to generate movie */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 1280 /* number of grid points on x axis */
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#define NY 720 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.0 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
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#define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */
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#define CIRCLE_PATTERN_B 10 /* pattern of circles, see list in global_pdes.c */
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#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
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#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */
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#define MU 0.03 /* parameter controlling the dimensions of domain */
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#define MUB 0.03 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 4 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NGRIDX 15 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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/* You can add more billiard tables by adapting the functions */
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/* 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 */
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#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
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#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
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#define OMEGA 0.0035 /* frequency of periodic excitation */
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#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
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#define COURANT 0.02 /* Courant number */
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#define COURANTB 0.0075 /* 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-5 /* 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-6 /* damping factor on boundary */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
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#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 */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* 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 6000 /* number of frames of movie */
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#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 200 /* time after which to start saving frames */
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#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
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#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 1
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/* Color schemes */
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#define BLACK 1 /* background */
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#define COLOR_SCHEME 1 /* 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 1.5 /* 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 2000.0 /* scaling factor for energy representation */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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#include "global_pdes.c" /* constants and global variables */
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#include "sub_wave.c" /* common functions for wave_billiard, heat and schrodinger */
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#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
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#include "sub_wave_comp.c" /* some functions specific to wave_comparison */
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double courant2, courantb2; /* Courant parameters squared */
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/*********************/
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/* animation part */
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/*********************/
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void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
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short int *xy_in[NX])
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/* time step of field evolution */
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/* phi is value of field at time t, psi at time t-1 */
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{
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int i, j, iplus, iminus, jplus, jminus, jmid = NY/2;
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double delta, x, y, c, cc, gamma;
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static long time = 0;
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time++;
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#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y)
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for (i=0; i<NX; i++){
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for (j=0; j<NY; j++){
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if (xy_in[i][j])
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{
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c = COURANT;
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cc = courant2;
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gamma = GAMMA;
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}
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else if (TWOSPEEDS)
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{
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c = COURANTB;
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cc = courantb2;
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gamma = GAMMAB;
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}
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if (((TWOSPEEDS)&&(xy_in[i][j] != 2))||(xy_in[i][j] == 1)){
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/* discretized Laplacian for various boundary conditions */
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if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING)||(B_COND == BC_ABS_REFLECT))
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{
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iplus = (i+1); if (iplus == NX) iplus = NX-1;
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iminus = (i-1); if (iminus == -1) iminus = 0;
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jplus = (j+1);
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if (jplus == NY) jplus = NY-1;
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else if (jplus == jmid) jplus = jmid-1;
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jminus = (j-1);
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if (jminus == -1) jminus = 0;
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else if (jminus == jmid-1) jminus = jmid;
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}
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else if (B_COND == BC_PERIODIC)
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{
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iplus = (i+1) % NX;
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iminus = (i-1) % NX;
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if (iminus < 0) iminus += NX;
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if (j < jmid) /* lower half */
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{
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jplus = (j+1) % jmid;
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jminus = (j-1) % jmid;
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if (jminus < 0) jminus += jmid;
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}
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else /* upper half */
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{
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jplus = j+1;
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if (jplus >= NY) jplus -= jmid;
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jminus = j-1;
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if (jminus < jmid) jminus += jmid;
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}
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}
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else if (B_COND == BC_VPER_HABS)
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{
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iplus = (i+1); if (iplus == NX) iplus = NX-1;
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iminus = (i-1); if (iminus == -1) iminus = 0;
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if (j < jmid) /* lower half */
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{
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jplus = (j+1) % jmid;
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jminus = (j-1) % jmid;
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if (jminus < 0) jminus += jmid;
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}
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else /* upper half */
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{
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jplus = j+1;
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if (jplus >= NY) jplus -= jmid;
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jminus = j-1;
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if (jminus < jmid) jminus += jmid;
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}
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}
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/* imposing linear wave on top and bottom by making Laplacian 1d */
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if (OSCILLATE_TOPBOT)
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{
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if (j == NY-1) jminus = NY-1;
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else if (j == 0) jplus = 0;
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}
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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];
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x = phi_in[i][j];
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y = psi_in[i][j];
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/* 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)||(B_COND == BC_ABS_REFLECT))
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{
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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 */
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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 */
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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 */
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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 */
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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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}
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else if (B_COND == BC_VPER_HABS)
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{
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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 */
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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 */
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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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}
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/* add oscillating boundary condition on the left */
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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)
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{
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if (phi_out[i][j] > VMAX) phi_out[i][j] = VMAX;
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if (phi_out[i][j] < -VMAX) phi_out[i][j] = -VMAX;
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if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
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if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
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}
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}
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}
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}
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// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
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}
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void evolve_wave(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 */
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/* phi is value of field at time t, psi at time t-1 */
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{
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evolve_wave_half(phi, psi, phi_tmp, psi_tmp, xy_in);
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evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
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}
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void animation()
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{
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double time, scale, energies[6], top_energy, bottom_energy;
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double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX];
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short int *xy_in[NX];
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int i, j, s;
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/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
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for (i=0; i<NX; i++)
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{
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phi[i] = (double *)malloc(NY*sizeof(double));
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psi[i] = (double *)malloc(NY*sizeof(double));
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phi_tmp[i] = (double *)malloc(NY*sizeof(double));
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psi_tmp[i] = (double *)malloc(NY*sizeof(double));
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xy_in[i] = (short int *)malloc(NY*sizeof(short int));
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}
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/* initialise positions and radii of circles */
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printf("initializing circle configuration\n");
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if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN_B == D_CIRCLES)) init_circle_config_comp();
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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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int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);
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// int_planar_wave_comp(XMIN + 0.5, 0.0, phi, psi, xy_in);
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printf("initializing wave\n");
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// int_planar_wave_comp(XMIN + 0.1, 0.0, phi, psi, xy_in);
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// int_planar_wave_comp(XMIN + 1.0, 0.0, phi, psi, xy_in);
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// init_wave(-1.5, 0.0, phi, psi, xy_in);
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// init_wave(0.0, 0.0, phi, psi, xy_in);
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/* add a drop at another point */
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// add_drop_to_wave(1.0, 0.7, 0.0, phi, psi);
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// add_drop_to_wave(1.0, -0.7, 0.0, phi, psi);
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// add_drop_to_wave(1.0, 0.0, -0.7, phi, psi);
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/* initialize energies */
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if (COMPUTE_ENERGIES)
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{
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compute_energy_tblr(phi, psi, xy_in, energies);
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top_energy = energies[0] + energies[1] + energies[2];
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bottom_energy = energies[3] + energies[4] + energies[5];
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}
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blank();
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glColor3f(0.0, 0.0, 0.0);
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printf("drawing wave\n");
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draw_wave_comp(phi, psi, xy_in, 1.0, 0);
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printf("drawing billiard\n");
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draw_billiard_comp();
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glutSwapBuffers();
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sleep(SLEEP1);
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for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
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{
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//printf("%d\n",i);
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/* compute the variance of the field to adjust color scheme */
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/* the color depends on the field divided by sqrt(1 + variance) */
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if (SCALE)
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{
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scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
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// printf("Scaling factor: %5lg\n", scale);
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}
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else scale = 1.0;
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draw_wave_comp(phi, psi, xy_in, scale, i);
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draw_billiard_comp();
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if (COMPUTE_ENERGIES)
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{
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compute_energy_tblr(phi, psi, xy_in, energies);
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if (i < INITIAL_TIME)
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{
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top_energy = energies[0] + energies[1] + energies[2];
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bottom_energy = energies[3] + energies[4] + energies[5];
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}
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print_energies(energies, top_energy, bottom_energy);
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}
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for (j=0; j<NVID; j++)
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{
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evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
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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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}
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glutSwapBuffers();
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if (MOVIE)
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{
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if (i >= INITIAL_TIME) save_frame();
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else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
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/* it seems that saving too many files too fast can cause trouble with the file system */
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/* so this is to make a pause from time to time - parameter PAUSE may need adjusting */
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if (i % PAUSE == PAUSE - 1)
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{
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printf("Making a short pause\n");
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sleep(PSLEEP);
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s = system("mv wave*.tif tif_wave/");
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}
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}
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|
|
|
}
|
|
|
|
if (MOVIE)
|
|
{
|
|
for (i=0; i<20; i++) save_frame();
|
|
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(xy_in[i]);
|
|
}
|
|
|
|
}
|
|
|
|
|
|
void display(void)
|
|
{
|
|
glPushMatrix();
|
|
|
|
blank();
|
|
glutSwapBuffers();
|
|
blank();
|
|
glutSwapBuffers();
|
|
|
|
animation();
|
|
sleep(SLEEP2);
|
|
|
|
glPopMatrix();
|
|
|
|
glutDestroyWindow(glutGetWindow());
|
|
|
|
}
|
|
|
|
|
|
int main(int argc, char** argv)
|
|
{
|
|
glutInit(&argc, argv);
|
|
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
|
|
glutInitWindowSize(WINWIDTH,WINHEIGHT);
|
|
glutCreateWindow("Wave equation in a planar domain");
|
|
|
|
init();
|
|
|
|
glutDisplayFunc(display);
|
|
|
|
glutMainLoop();
|
|
|
|
return 0;
|
|
}
|
|
|