885 lines
38 KiB
C
885 lines
38 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 DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
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#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */
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#define TIME_LAPSE_FACTOR 4 /* factor of time-lapse movie */
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// #define WINWIDTH 1920 /* window width */
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// #define WINHEIGHT 1000 /* window height */
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// #define NX 1920 /* number of grid points on x axis */
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// #define NY 1000 /* number of grid points on y axis */
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// #define YMID 500 /* mid point of display */
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// #define XMIN -0.5
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// #define XMAX 3.5 /* x interval */
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// #define YMIN -1.041666667
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// #define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
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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 YMID 360 /* mid point of display */
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#define XMIN -0.5
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#define XMAX 3.5 /* 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 43 /* choice of domain shape, see list in global_pdes.c */
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#define B_DOMAIN_B 47 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 13 /* pattern of circles, see list in global_pdes.c */
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#define CIRCLE_PATTERN_B 13 /* pattern of circles, see list in global_pdes.c */
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#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
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#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
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#define RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */
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#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */
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#define XDEP_POLY_ANGLE_B 0 /* set to 1 to rotate polygons depending on x coordinate */
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#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */
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#define HEX_NONUNIF_COMPRESSSION 0.15 /* compression factor for HEX_NONUNIF pattern */
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#define HEX_NONUNIF_COMPRESSSION_B -0.15 /* compression factor for HEX_NONUNIF pattern */
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#define LAMBDA -1.1 /* parameter controlling the dimensions of domain */
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#define MU 0.1 /* parameter controlling the dimensions of domain */
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#define MUB 0.1 /* parameter controlling the dimensions of domain */
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// #define MU 0.04665361 /* parameter controlling the dimensions of domain */
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// #define MUB 0.04665361 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define APOLY_B 2.0 /* 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 20 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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#define X_SHOOTER -0.2
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#define Y_SHOOTER -0.6
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#define X_TARGET 0.4
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#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
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#define ISO_XSHIFT_LEFT -1.65
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#define ISO_XSHIFT_RIGHT 0.4
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#define ISO_YSHIFT_LEFT -0.05
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#define ISO_YSHIFT_RIGHT -0.05
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#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical parameters of wave equation */
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#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */
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#define OSCILLATE_LEFT 1 /* 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 0.004 /* 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 0.01154 /* Courant number in medium B */
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// #define COURANTB 0.005 /* Courant number in medium B */
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// #define COURANTB 0.008 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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// #define GAMMA 1.0e-8 /* damping factor in wave equation */
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#define GAMMAB 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 GAMMAB 2.0e-4 /* damping factor in wave equation */
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// #define GAMMAB 2.5e-4 /* 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 0
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/* Parameters for length and speed of simulation */
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#define NSTEPS 2500 /* number of frames of movie */
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// #define NSTEPS 3300 /* 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 20 /* time after which to start saving frames */
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#define COMPUTE_ENERGIES 0 /* 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 100 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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#define MID_FRAMES 20 /* number of still frames between movies */
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#define END_FRAMES 100 /* 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 */
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// #define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */
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#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */
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#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 0
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#define PLOT_B 1
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/* Color schemes */
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#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* background */
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#define BLACK_TEXT 1 /* set to 1 to write text in black instead of white */
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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 1.0 /* sensitivity of color on wave amplitude */
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// #define SLOPE 0.75 /* sensitivity of color on wave amplitude */
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#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */
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#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define E_SCALE 200.0 /* scaling factor for energy representation */
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#define LOG_SCALE 1.5 /* scaling factor for energy log representation */
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#define LOG_SHIFT 1.0 /* shift of colors on log scale */
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#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 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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#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
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#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 2.5 /* scale of color scheme bar for 2nd part */
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#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
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/* 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 5.0 /* max value of wave amplitude */
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/* the following constants are only used by wave_billiard and wave_3d so far */
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#define COMPARISON 0 /* set to 1 to compare two different patterns */
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#define OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */
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#define ACHIRP 0.2 /* acceleration coefficient in chirp */
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#define DAMPING 0.0 /* damping of periodic excitation */
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/* end of constants only used by wave_billiard and wave_3d */
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/* for compatibility with sub_wave and sub_maze */
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#define NXMAZE 7 /* width of maze */
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#define NYMAZE 7 /* height of maze */
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#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
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#define RAND_SHIFT 24 /* seed of random number generator */
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#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
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#define ADD_POTENTIAL 0
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#define POT_MAZE 7
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#define POTENTIAL 0
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/* end of constants only used by sub_wave and sub_maze */
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#include "global_pdes.c" /* constants and global variables */
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#include "sub_maze.c" /* support for generating mazes */
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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],
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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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static double tc[NX][NY], tcc[NX][NY], tgamma[NX][NY];
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static short int first = 1;
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time++;
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/* initialize tables with wave speeds and dissipation */
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if (first)
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{
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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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tc[i][j] = COURANT;
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tcc[i][j] = courant2;
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tgamma[i][j] = GAMMA;
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}
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else if (TWOSPEEDS)
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{
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tc[i][j] = COURANTB;
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tcc[i][j] = courantb2;
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tgamma[i][j] = GAMMAB;
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}
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}
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}
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first = 0;
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}
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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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/* evolution in the bulk */
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for (i=1; i<NX-1; i++){
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for (j=1; j<jmid-1; j++){
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if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
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x = phi_in[i][j];
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y = psi_in[i][j];
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/* discretized Laplacian */
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delta = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
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/* evolve phi */
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phi_out[i][j] = -y + 2*x + tcc[i][j]*delta - KAPPA*x - tgamma[i][j]*(x-y);
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}
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}
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for (j=jmid+1; j<NY-1; j++){
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if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
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x = phi_in[i][j];
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y = psi_in[i][j];
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/* discretized Laplacian */
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delta = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
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/* evolve phi */
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phi_out[i][j] = -y + 2*x + tcc[i][j]*delta - KAPPA*x - tgamma[i][j]*(x-y);
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}
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}
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}
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/* left boundary */
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if (OSCILLATE_LEFT) {
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for (j=1; j<jmid-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
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for (j=jmid+1; j<NY-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
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}
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else for (j=1; j<NY-1; j++) if ((j!=jmid-1)&&(j!=jmid)) {
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if ((TWOSPEEDS)||(xy_in[0][j] != 0)){
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x = phi_in[0][j];
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y = psi_in[0][j];
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switch (B_COND) {
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case (BC_DIRICHLET):
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{
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delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
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phi_out[0][j] = -y + 2*x + tcc[0][j]*delta - KAPPA*x - tgamma[0][j]*(x-y);
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break;
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}
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case (BC_PERIODIC):
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{
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delta = phi_in[1][j] + phi_in[NX-1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 4.0*x;
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phi_out[0][j] = -y + 2*x + tcc[0][j]*delta - KAPPA*x - tgamma[0][j]*(x-y);
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break;
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}
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case (BC_ABSORBING):
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{
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delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
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phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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break;
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}
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case (BC_VPER_HABS):
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{
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delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
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phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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break;
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}
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case (BC_ABS_REFLECT):
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{
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delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
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phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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break;
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}
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}
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}
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}
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/* right boundary */
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for (j=1; j<NY-1; j++) if ((j!=jmid-1)&&(j!=jmid)) {
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if ((TWOSPEEDS)||(xy_in[NX-1][j] != 0)){
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x = phi_in[NX-1][j];
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y = psi_in[NX-1][j];
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switch (B_COND) {
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case (BC_DIRICHLET):
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{
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delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
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phi_out[NX-1][j] = -y + 2*x + tcc[NX-1][j]*delta - KAPPA*x - tgamma[NX-1][j]*(x-y);
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break;
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}
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case (BC_PERIODIC):
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{
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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;
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phi_out[NX-1][j] = -y + 2*x + tcc[NX-1][j]*delta - KAPPA*x - tgamma[NX-1][j]*(x-y);
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break;
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}
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case (BC_ABSORBING):
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{
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delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
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phi_out[NX-1][j] = x - tc[NX-1][j]*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
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break;
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}
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case (BC_VPER_HABS):
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{
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delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
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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])
|
|
/* 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);
|
|
evolve_wave_half(tmp, phi, psi, xy_in);
|
|
evolve_wave_half(psi, tmp, phi, 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(XMAX - 0.3, YMIN + 0.1, XMAX - 0.1, YMAX - 0.1, plot, -range, range);
|
|
}
|
|
|
|
|
|
|
|
void animation()
|
|
{
|
|
double time, scale, energies[6], top_energy, bottom_energy;
|
|
double *phi[NX], *psi[NX], *tmp[NX];
|
|
short int *xy_in[NX];
|
|
int i, j, s, counter = 0;
|
|
|
|
/* 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));
|
|
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
|
|
}
|
|
|
|
/* 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);
|
|
|
|
|
|
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);
|
|
|
|
|
|
/* 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();
|
|
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
|
|
|
|
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_billiard_comp();
|
|
|
|
|
|
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);
|
|
}
|
|
|
|
for (j=0; j<NVID; j++)
|
|
{
|
|
evolve_wave(phi, psi, tmp, xy_in);
|
|
// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
|
|
}
|
|
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
|
|
|
|
glutSwapBuffers();
|
|
|
|
if (MOVIE)
|
|
{
|
|
if (i >= INITIAL_TIME)
|
|
{
|
|
save_frame();
|
|
if ((TIME_LAPSE)&&((i - INITIAL_TIME)%TIME_LAPSE_FACTOR == 0))
|
|
{
|
|
save_frame_counter(NSTEPS + END_FRAMES + (i - INITIAL_TIME)/TIME_LAPSE_FACTOR);
|
|
counter++;
|
|
}
|
|
else if (DOUBLE_MOVIE)
|
|
{
|
|
draw_wave_comp(phi, psi, xy_in, scale, i, PLOT_B);
|
|
draw_billiard_comp();
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
|
|
glutSwapBuffers();
|
|
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
|
|
counter++;
|
|
}
|
|
}
|
|
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_billiard_comp();
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
|
|
glutSwapBuffers();
|
|
}
|
|
for (i=0; i<MID_FRAMES; i++) save_frame();
|
|
if (DOUBLE_MOVIE)
|
|
{
|
|
draw_wave_comp(phi, psi, xy_in, scale, i, PLOT_B);
|
|
draw_billiard_comp();
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
|
|
glutSwapBuffers();
|
|
}
|
|
for (i=0; i<END_FRAMES; i++) 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(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;
|
|
} |