1102 lines
46 KiB
C
1102 lines
46 KiB
C
/*********************************************************************************/
|
|
/* */
|
|
/* Animation of wave equation in a planar domain */
|
|
/* */
|
|
/* N. Berglund, december 2012, may 2021 */
|
|
/* */
|
|
/* UPDATE 24/04: distinction between damping and "elasticity" parameters */
|
|
/* UPDATE 27/04: new billiard shapes, bug in color scheme fixed */
|
|
/* UPDATE 28/04: code made more efficient, with help of Marco Mancini */
|
|
/* */
|
|
/* Feel free to reuse, but if doing so it would be nice to drop a */
|
|
/* line to 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 */
|
|
/* */
|
|
/* OMP acceleration may be more effective after executing */
|
|
/* export OMP_NUM_THREADS=2 in the shell before running the program */
|
|
/* */
|
|
/* To make a video, set MOVIE to 1 and create subfolder tif_wave */
|
|
/* It may be possible to increase parameter PAUSE */
|
|
/* */
|
|
/* create movie using */
|
|
/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
|
|
/* */
|
|
/*********************************************************************************/
|
|
|
|
/*********************************************************************************/
|
|
/* */
|
|
/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
|
|
/* One could make it much faster by using a GPU */
|
|
/* */
|
|
/*********************************************************************************/
|
|
|
|
#include <math.h>
|
|
#include <string.h>
|
|
#include <GL/glut.h>
|
|
#include <GL/glu.h>
|
|
#include <unistd.h>
|
|
#include <sys/types.h>
|
|
#include <tiffio.h> /* Sam Leffler's libtiff library. */
|
|
#include <omp.h>
|
|
#include <time.h>
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
#define SAVE_MEMORY 1 /* set to 1 to save memory when writing tiff images */
|
|
|
|
#define WINWIDTH 1920 /* window width */
|
|
#define WINHEIGHT 1150 /* window height */
|
|
#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */
|
|
|
|
#define NX 3840 /* number of grid points on x axis */
|
|
#define NY 2300 /* number of grid points on y axis */
|
|
#define YMID 1150 /* mid point of display */
|
|
|
|
#define XMIN -2.0
|
|
#define XMAX 2.0 /* x interval */
|
|
#define YMIN -1.125
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 947 /* choice of domain shape, see list in global_pdes.c */
|
|
#define B_DOMAIN_B 947 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
#define CIRCLE_PATTERN 2 /* pattern of circles, see list in global_pdes.c */
|
|
#define CIRCLE_PATTERN_B 11 /* pattern of circles, see list in global_pdes.c */
|
|
#define IMAGE_FILE 5 /* for option D_IMAGE */
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
#define PDISC_FACTOR 3.25 /* controls density of Poisson disc process (default: 3.25) */
|
|
#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
|
|
#define RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */
|
|
#define PDISC_CONNECT_FACTOR 1.5 /* controls which discs are connected for D_CIRCLE_LATTICE_POISSON domain */
|
|
|
|
#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */
|
|
#define XDEP_POLY_ANGLE_B 1 /* set to 1 to rotate polygons depending on x coordinate */
|
|
#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */
|
|
#define HEX_NONUNIF_COMPRESSSION 0.15 /* compression factor for HEX_NONUNIF pattern */
|
|
#define HEX_NONUNIF_COMPRESSSION_B -0.15 /* compression factor for HEX_NONUNIF pattern */
|
|
|
|
#define LAMBDA 0.6 /* parameter controlling the dimensions of domain */
|
|
#define MU 0.075 /* parameter controlling the dimensions of domain */
|
|
#define MUB 1.0 /* parameter controlling the dimensions of domain */
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
#define APOLY_B 0.335 /* angle by which to turn polygon, in units of Pi/2 */
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define NGRIDX 6 /* number of grid point for grid of disks */
|
|
#define NGRIDY 12 /* number of grid point for grid of disks */
|
|
#define WALL_WIDTH 0.013 /* width of wall separating lenses */
|
|
#define WALL_WIDTH_B 0.01 /* width of wall separating lenses */
|
|
#define WALL_WIDTH_RND 0.0 /* proportion of width of width for random arrangements */
|
|
#define RADIUS_FACTOR 0.3 /* controls inner radius for C_RING arrangements */
|
|
#define WALL_WIDTH_ASYM 1.25 /* asymmetry of wall width (D_CIRCLE_LATTICE_NONISO) */
|
|
#define WALL_WIDTH_ASYM_B 0.75 /* asymmetry of wall width (D_CIRCLE_LATTICE_HEX_NONISO) */
|
|
|
|
|
|
#define X_SHOOTER -0.2
|
|
#define Y_SHOOTER -0.6
|
|
#define X_TARGET 0.4
|
|
#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
|
|
|
|
#define ISO_XSHIFT_LEFT -1.65
|
|
#define ISO_XSHIFT_RIGHT 0.4
|
|
#define ISO_YSHIFT_LEFT -0.05
|
|
#define ISO_YSHIFT_RIGHT -0.05
|
|
#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
#define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
#define OMEGA 0.0125 /* frequency of periodic excitation */
|
|
#define AMPLITUDE 0.5 /* amplitude of periodic excitation */
|
|
#define COURANT 0.1 /* Courant number */
|
|
#define COURANTB 0.035 /* Courant number in medium B */
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
#define GAMMAB 0.0 /* damping factor in wave equation */
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
|
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
|
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
|
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
|
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
|
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
|
|
|
#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */
|
|
#define OSCILLATING_SOURCE_PERIOD 12.5 /* period of oscillating source */
|
|
#define ALTERNATE_OSCILLATING_SOURCE 1 /* set to 1 to alternate sign of oscillating source */
|
|
#define N_SOURCES 1 /* number of sources, for option draw_sources */
|
|
#define ALTERNATE_SOURCE_PHASES 0 /* set to 1 to alternate initial phases of sources */
|
|
#define MAX_PULSING_TIME 500 /* max time for adding pulses */
|
|
|
|
/* Boundary conditions, see list in global_pdes.c */
|
|
|
|
// #define B_COND 2
|
|
#define B_COND 3
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 4500 /* number of frames of movie */
|
|
#define NVID 8 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define INITIAL_TIME 0 /* time after which to start saving frames */
|
|
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
|
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 1 /* final sleeping time */
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
/* Parameters of initial condition */
|
|
|
|
#define INITIAL_AMP 0.75 /* amplitude of initial condition */
|
|
#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */
|
|
#define INITIAL_WAVELENGTH 0.025 /* wavelength of initial condition */
|
|
|
|
/* Plot type, see list in global_pdes.c */
|
|
|
|
#define PLOT 0
|
|
|
|
/* Color schemes */
|
|
|
|
#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */
|
|
|
|
#define BLACK 1 /* background */
|
|
#define BLACK_TEXT 0 /* set to 1 to write text in black instead of white */
|
|
|
|
#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
#define SLOPE 1.5 /* sensitivity of color on wave amplitude */
|
|
#define COLOR_RANGE 1.0 /* max range of color (default: 1.0) */
|
|
#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */
|
|
#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
#define VSHIFT_AMPLITUDE 0.0 /* additional shift for wave amplitude */
|
|
#define VSCALE_AMPLITUDE 0.5 /* additional scaling factor for wave amplitude */
|
|
#define E_SCALE 20.0 /* scaling factor for energy representation */
|
|
#define PLOT_ESCALE 1.0e-3 /* vertical scale for energy plot */
|
|
#define PLOT_ESCALE_LOG 0.1 /* vertical scale for log energy plot */
|
|
#define PLOT_ESCALE_LOG_SHIFT 0.5 /* shift of log energy plot */
|
|
#define LOG_SCALE 1.5 /* scaling factor for energy log representation */
|
|
#define LOG_SHIFT 1.0 /* shift of colors on log scale */
|
|
#define FLUX_SCALE 1.0e4 /* scaling factor for enegy flux represtnation */
|
|
#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
|
|
|
|
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */
|
|
#define COLORBAR_RANGE 4.0 /* scale of color scheme bar */
|
|
#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */
|
|
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
|
|
|
|
/* For debugging purposes only */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
#define VMAX 5.0 /* max value of wave amplitude */
|
|
|
|
/* the following constants are only used by wave_billiard and wave_3d so far */
|
|
#define COMPARISON 0 /* set to 1 to compare two different patterns */
|
|
#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */
|
|
#define ACHIRP 0.2 /* acceleration coefficient in chirp */
|
|
#define DAMPING 0.0 /* damping of periodic excitation */
|
|
/* end of constants only used by wave_billiard and wave_3d */
|
|
|
|
/* for compatibility with sub_wave and sub_maze */
|
|
#define NXMAZE 7 /* width of maze */
|
|
#define NYMAZE 7 /* height of maze */
|
|
#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
|
|
#define RAND_SHIFT 24 /* seed of random number generator */
|
|
#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
|
|
#define ADD_POTENTIAL 0
|
|
#define POT_MAZE 7
|
|
#define POTENTIAL 0
|
|
#define MAZE_WIDTH 0.02 /* half width of maze walls */
|
|
#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */
|
|
#define IOR 7 /* choice of index of refraction, see list in global_pdes.c */
|
|
#define IOR_TOTAL_TURNS 1.5 /* total angle of rotation for IOR_PERIODIC_WELLS_ROTATING */
|
|
#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */
|
|
#define WAVE_PACKET_SOURCE_TYPE 1 /* type of wave packet sources */
|
|
#define N_WAVE_PACKETS 15 /* number of wave packets */
|
|
#define OSCIL_LEFT_YSHIFT 40.0 /* y-dependence of left oscillation (for non-horizontal waves) */
|
|
#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
|
|
#define MU_B 1.0 /* parameter controlling the dimensions of domain */
|
|
#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
|
|
#define VERTICAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
|
|
#define DRAW_WAVE_TIMESERIES 0 /* set to 1 to draw a time series of the wave */
|
|
#define RADIUS_FACTOR 0.3 /* controls inner radius for C_RING arrangements */
|
|
#define OSCIL_YMAX 0.35 /* defines oscillation range */
|
|
#define MESSAGE_LDASH 14 /* length of dash for Morse code message */
|
|
#define MESSAGE_LDOT 8 /* length of dot for Morse code message */
|
|
#define MESSAGE_LINTERVAL 54 /* length of interval between dashes/dots for Morse code message */
|
|
#define MESSAGE_LINTERLETTER 60 /* length of interval between letters for Morse code message */
|
|
#define MESSAGE_LSPACE 48 /* length of space for Morse code message */
|
|
#define MESSAGE_INITIAL_TIME 100 /* initial time before starting message for Morse code message */
|
|
#define AVRG_E_FACTOR 0.95 /* controls time window size in P_AVERAGE_ENERGY scheme */
|
|
#define HORIZONTAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
|
|
#define WAVE_PROFILE_X 2.1 /* value of x to sample wave profile */
|
|
#define WAVE_PROFILE_Y -1.0 /* value of y to sample wave profile */
|
|
#define PROFILE_AT_BOTTOM 1 /* draw wave profile at bottom instead of top */
|
|
#define AVERAGE_WAVE_PROFILE 1 /* set to 1 to draw time-average of wave profile squared*/
|
|
#define TIMESERIES_NVALUES 400 /* number of values plotted in time series */
|
|
#define DRAW_WAVE_SOURCE 0 /* set to 1 to draw source of wave at (wave_source_x, wave_source_y) */
|
|
#define HRES 1 /* dummy, only used by rde.c */
|
|
#define INITIAL_SHIFT 20.0 /* time shift of initial wave packet (in oscillation periods) */
|
|
#define WAVE_PACKET_SHIFT 200.0 /* time shift between wave packets (in oscillation periods) */
|
|
#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */
|
|
#define SHADE_2D 1 /* set to 1 to add pseudo-3d shading effect */
|
|
#define SHADE_SCALE_2D 0.01 /* lower value increases sensitivity of shading */
|
|
#define N_SOURCES 1 /* number of sources, for option draw_sources */
|
|
#define XYIN_INITIALISED (B_DOMAIN == D_IMAGE)
|
|
double light[2] = {0.40824829, 0.816496581}; /* location of light source for SHADE_2D option*/
|
|
/* end of constants only used by sub_wave and sub_maze */
|
|
|
|
#include "global_pdes.c" /* constants and global variables */
|
|
#include "sub_maze.c" /* support for generating mazes */
|
|
#include "sub_wave.c" /* common functions for wave_billiard, heat and schrodinger */
|
|
#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
|
|
#include "sub_wave_comp.c" /* some functions specific to wave_comparison */
|
|
|
|
double courant2, courantb2; /* Courant parameters squared */
|
|
|
|
double compute_energy_x(int i, double *phi[NX], double *psi[NX], short int *xy_in[NX])
|
|
/* compute energy in column i */
|
|
{
|
|
double energy = 0.0;
|
|
int j;
|
|
|
|
for (j=0; j<NY/2; j++)
|
|
energy += compute_energy(phi, psi, xy_in, i, j);
|
|
|
|
return(energy);
|
|
}
|
|
|
|
double logscale_y(double energy)
|
|
{
|
|
static double ymid, yscale;
|
|
static int first = 1;
|
|
|
|
if (first)
|
|
{
|
|
ymid = 0.5*(YMIN + YMAX);
|
|
yscale = (YMAX - YMIN)*0.5/2.25;
|
|
first = 0;
|
|
}
|
|
|
|
return(ymid + yscale*(PLOT_ESCALE_LOG_SHIFT + 0.2*log(energy)));
|
|
// return(ymid + 0.5*(1.0 + 0.2*log(energy)));
|
|
}
|
|
|
|
void draw_wave_energy(double *phi[NX], double *psi[NX], short int *xy_in[NX], double scale, int time)
|
|
/* draw the field */
|
|
{
|
|
int i, j, k, iplus, iminus, jplus, jminus, size = 1;
|
|
double rgb[3], xy[2], x, y, x1, y1, x2, y2, velocity, energy, gradientx, gradienty, gradientx2, gradienty2, pos[2], norm, pscal, ca, vscale2, escale;
|
|
double energies[NX], ymid, *values, *shade, *rgbvals;
|
|
static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
|
|
char message[50];
|
|
|
|
|
|
values = (double *)malloc(NX*NY*sizeof(double));
|
|
rgbvals = (double *)malloc(3*NX*NY*sizeof(double));
|
|
ymid = 0.5*(YMIN + YMAX);
|
|
|
|
// printf("dtinverse = %.5lg\n", dtinverse);
|
|
|
|
#pragma omp parallel for private(i,j,rgb)
|
|
for (i=0; i<NX; i++)
|
|
for (j=0; j<NY/2; j++)
|
|
{
|
|
if (((TWOSPEEDS)&&(xy_in[i][j] != 2))||(xy_in[i][j] == 1)) {
|
|
switch (PLOT) {
|
|
case (P_AMPLITUDE):
|
|
{
|
|
values[i*NY+j] = phi[i][j];
|
|
/* make wave luminosity larger inside obstacles */
|
|
if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
|
|
else color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
|
|
break;
|
|
}
|
|
case (P_ENERGY):
|
|
{
|
|
energy = compute_energy(phi, psi, xy_in, i, j);
|
|
values[i*NY+j] = energy;
|
|
/* adjust energy to color palette */
|
|
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym(COLOR_SCHEME, energy, scale, time, rgb);
|
|
else color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
|
|
break;
|
|
}
|
|
case (P_MIXED):
|
|
{
|
|
if (j > NY/2)
|
|
{
|
|
values[i*NY+j] = phi[i][j];
|
|
color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
|
|
}
|
|
else
|
|
{
|
|
energy = compute_energy(phi, psi, xy_in, i, j);
|
|
values[i*NY+j] = energy;
|
|
color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
rgbvals[i*NY+j] = rgb[0];
|
|
rgbvals[NX*NY+i*NY+j] = rgb[1];
|
|
rgbvals[2*NX*NY+i*NY+j] = rgb[2];
|
|
}
|
|
}
|
|
|
|
if (SHADE_2D)
|
|
{
|
|
vscale2 = SHADE_SCALE_2D*SHADE_SCALE_2D;
|
|
shade = (double *)malloc(NX*NY*sizeof(double));
|
|
#pragma omp parallel for private(i,j,gradientx,gradienty,norm,pscal,ca)
|
|
for (i=0; i<NX-size; i+=size)
|
|
{
|
|
for (j=0; j<NY/2-size; j+=size)
|
|
{
|
|
gradientx = values[(i+1)*NY+j] - values[i*NY+j];
|
|
gradienty = values[i*NY+j+1] - values[i*NY+j];
|
|
norm = sqrt(vscale2 + gradientx*gradientx + gradienty*gradienty);
|
|
pscal = -gradientx*light[0] - gradienty*light[1] + SHADE_SCALE_2D;
|
|
ca = pscal/norm;
|
|
ca = (ca + 1.0)*0.4 + 0.2;
|
|
for (k=0; k<3; k++) rgbvals[k*NX*NY+i*NY+j] *= ca;
|
|
}
|
|
}
|
|
}
|
|
|
|
glBegin(GL_QUADS);
|
|
|
|
for (i=0; i<NX; i+=size)
|
|
for (j=0; j<NY/2; j+=size)
|
|
{
|
|
if ((TWOSPEEDS)||(xy_in[i][j]))
|
|
{
|
|
|
|
glColor3f(rgbvals[i*NY+j], rgbvals[NX*NY+i*NY+j], rgbvals[2*NX*NY+i*NY+j]);
|
|
|
|
glVertex2i(i, j);
|
|
glVertex2i(i+size, j);
|
|
glVertex2i(i+size, j+size);
|
|
glVertex2i(i, j+size);
|
|
}
|
|
}
|
|
|
|
glEnd ();
|
|
|
|
if (SHADE_2D) free(shade);
|
|
|
|
|
|
/* compute and plot energies */
|
|
for (i=0; i<NX; i++) energies[i] = compute_energy_x(i, phi, psi, xy_in);
|
|
|
|
glEnable(GL_SCISSOR_TEST);
|
|
glScissor(0.0, YMID/(HIGHRES+1), NX, YMID/(HIGHRES+1));
|
|
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
glBegin(GL_QUADS);
|
|
glVertex2i(0, NY/2);
|
|
glVertex2i(NX, NY/2);
|
|
glVertex2i(NX, NY);
|
|
glVertex2i(0, NY);
|
|
glEnd();
|
|
|
|
/* log coordinate lines */
|
|
glLineWidth(1);
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
for (i=-2; i<6; i++)
|
|
{
|
|
energy = pow(10.0, (double)i);
|
|
y = logscale_y(energy);
|
|
glBegin(GL_LINE_STRIP);
|
|
x = XMIN;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
x = XMAX;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
}
|
|
glColor3f(0.5, 0.5, 0.5);
|
|
for (i=-2; i<6; i++)
|
|
{
|
|
for (j=2; j<10; j++)
|
|
{
|
|
energy = (double)j*pow(10.0, (double)i);
|
|
y = logscale_y(energy);
|
|
glBegin(GL_LINE_STRIP);
|
|
x = XMIN;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
x = XMAX;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
}
|
|
}
|
|
|
|
erase_area_hsl(XMAX - 0.4, YMAX - 0.1, 0.35, 0.07, 0.0, 1.0, 0.0);
|
|
erase_area_hsl(XMAX - 0.4, YMAX - 0.2, 0.35, 0.07, 0.0, 1.0, 0.0);
|
|
|
|
sprintf(message, "Energy (log scale)");
|
|
glColor3f(0.0, 0.5, 1.0);
|
|
xy_to_pos(XMAX - 0.7, YMAX - 0.13, pos);
|
|
write_text(pos[0], pos[1], message);
|
|
sprintf(message, "Energy (linear scale)");
|
|
glColor3f(1.0, 0.0, 0.0);
|
|
xy_to_pos(XMAX - 0.7, YMAX - 0.23, pos);
|
|
write_text(pos[0], pos[1], message);
|
|
|
|
/* log of energy */
|
|
glLineWidth(3);
|
|
glColor3f(0.0, 0.5, 1.0);
|
|
glBegin(GL_LINE_STRIP);
|
|
for (i=0; i<NX; i++)
|
|
{
|
|
x = XMIN + ((double)i)*(XMAX-XMIN)/((double)NX);
|
|
y = logscale_y(energies[i]);
|
|
if (y < ymid) y = ymid;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd();
|
|
|
|
/* y axis labels */
|
|
for (i=-2; i<6; i++)
|
|
{
|
|
y = logscale_y(pow(10.0, (double)i));
|
|
erase_area_hsl(XMIN + 0.06, y + 0.025, 0.12, 0.02, 0.0, 1.0, 0.0);
|
|
sprintf(message, "%d dB", (i-2)*10);
|
|
xy_to_pos(XMIN + 0.02, y + 0.01, pos);
|
|
glColor3f(0.7, 0.7, 0.7);
|
|
write_text_fixedwidth(pos[0], pos[1], message);
|
|
}
|
|
|
|
/* energy */
|
|
glColor3f(1.0, 0.0, 0.0);
|
|
escale = PLOT_ESCALE;
|
|
glBegin(GL_LINE_STRIP);
|
|
for (i=0; i<NX; i++)
|
|
{
|
|
x = XMIN + ((double)i)*(XMAX-XMIN)/((double)NX);
|
|
y = ymid + escale*energies[i];
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd();
|
|
|
|
glDisable(GL_SCISSOR_TEST);
|
|
|
|
/* draw horizontal mid line */
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
glBegin(GL_LINE_STRIP);
|
|
xy_to_pos(XMIN, 0.5*(YMIN+YMAX), pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(XMAX, 0.5*(YMIN+YMAX), pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
|
|
free(values);
|
|
free(rgbvals);
|
|
}
|
|
|
|
/*********************/
|
|
/* animation part */
|
|
/*********************/
|
|
|
|
void evolve_wave_half_old(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 */
|
|
{
|
|
int i, j, iplus, iminus, jplus, jminus, jmid = NY/2;
|
|
double delta, x, y, c, cc, gamma;
|
|
static long time = 0;
|
|
|
|
time++;
|
|
|
|
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y,c,cc,gamma)
|
|
for (i=0; i<NX; i++){
|
|
for (j=0; j<NY/2; j++){
|
|
if (xy_in[i][j])
|
|
{
|
|
c = COURANT;
|
|
cc = courant2;
|
|
gamma = GAMMA;
|
|
}
|
|
else if (TWOSPEEDS)
|
|
{
|
|
c = COURANTB;
|
|
cc = courantb2;
|
|
gamma = GAMMAB;
|
|
}
|
|
|
|
if (((TWOSPEEDS)&&(xy_in[i][j] != 2))||(xy_in[i][j] == 1)){
|
|
/* discretized Laplacian for various boundary conditions */
|
|
if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING)||(B_COND == BC_ABS_REFLECT))
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
jplus = (j+1); if (jplus == jmid) jplus = jmid-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) % jmid;
|
|
jminus = (j-1) % jmid; if (jminus < 0) jminus += jmid;
|
|
}
|
|
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); if (jplus >= jmid) jplus -= jmid;
|
|
jminus = (j-1); if (jminus < 0) jminus += jmid;
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
|
|
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 */
|
|
if ((B_COND == BC_PERIODIC)||(B_COND == BC_DIRICHLET))
|
|
phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - gamma*(x-y);
|
|
else if ((B_COND == BC_ABSORBING)||(B_COND == BC_ABS_REFLECT))
|
|
{
|
|
if ((i>0)&&(i<NX-1)&&(j>0)&&(j<NY-1))
|
|
phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - gamma*(x-y);
|
|
|
|
/* upper border */
|
|
else if (j==NY-1)
|
|
phi_out[i][j] = x - c*(x - phi_in[i][NY-2]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
|
|
|
|
/* lower border */
|
|
else if (j==0)
|
|
phi_out[i][j] = x - c*(x - phi_in[i][1]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
|
|
|
|
/* right border */
|
|
if (i==NX-1)
|
|
phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
|
|
/* left border */
|
|
else if (i==0)
|
|
phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
}
|
|
else if (B_COND == BC_VPER_HABS)
|
|
{
|
|
if ((i>0)&&(i<NX-1))
|
|
phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - gamma*(x-y);
|
|
|
|
/* right border */
|
|
else if (i==NX-1)
|
|
phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
|
|
/* left border */
|
|
else if (i==0)
|
|
phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
}
|
|
|
|
/* add oscillating boundary condition on the left */
|
|
if ((i == 0)&&(OSCILLATE_LEFT))
|
|
phi_out[0][j] = oscillating_bc(time, j);
|
|
// phi_out[i][j] = AMPLITUDE*cos((double)time*OMEGA);
|
|
|
|
psi_out[i][j] = x;
|
|
|
|
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]);
|
|
}
|
|
|
|
|
|
void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_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 */
|
|
{
|
|
int i, j, iplus, iminus, jplus, jminus, jmid = NY/2;
|
|
double delta, x, y, c, cc, gamma, tb_shift;
|
|
static long time = 0;
|
|
static double tc[NX][NY/2], tcc[NX][NY/2], tgamma[NX][NY/2];
|
|
static short int first = 1;
|
|
|
|
time++;
|
|
|
|
if (OSCILLATE_TOPBOT) tb_shift = (int)((XMAX - XMIN)*(double)NX/(XMAX - XMIN));
|
|
|
|
/* initialize tables with wave speeds and dissipation */
|
|
if (first)
|
|
{
|
|
for (i=0; i<NX; i++){
|
|
for (j=0; j<jmid; j++){
|
|
if (xy_in[i][j])
|
|
{
|
|
tc[i][j] = COURANT;
|
|
tcc[i][j] = courant2;
|
|
tgamma[i][j] = GAMMA;
|
|
}
|
|
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,c,cc,gamma)
|
|
/* evolution in the bulk */
|
|
for (i=1; i<NX-1; i++){
|
|
for (j=1; j<jmid-1; j++){
|
|
if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
|
|
x = phi_in[i][j];
|
|
y = psi_in[i][j];
|
|
|
|
/* discretized Laplacian */
|
|
delta = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
|
|
|
|
/* evolve phi */
|
|
phi_out[i][j] = -y + 2*x + tcc[i][j]*delta - KAPPA*x - tgamma[i][j]*(x-y);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* left boundary */
|
|
if (OSCILLATE_LEFT) for (j=1; j<jmid; j++)
|
|
phi_out[0][j] = oscillating_bc(time, j);
|
|
// phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
|
|
else for (j=1; j<jmid-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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* right boundary */
|
|
for (j=1; j<jmid-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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* top 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];
|
|
|
|
if ((OSCILLATE_TOPBOT)&&(i < tb_shift)&&(i<NX-1)&&(i>0))
|
|
{
|
|
iplus = i+1;
|
|
iminus = i-1; if (iminus < 0) iminus = 0;
|
|
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + - 2.0*x;
|
|
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
|
|
}
|
|
|
|
else switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
iplus = i+1; if (iplus == NX) iplus = NX-1;
|
|
iminus = i-1; if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][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);
|
|
// 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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* 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);
|
|
}
|
|
|
|
/* for debugging purposes/if there is a risk of blow-up */
|
|
if (FLOOR) for (i=0; i<NX; i++){
|
|
for (j=0; j<jmid; 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_old(phi, psi, phi_tmp, psi_tmp, xy_in);
|
|
// evolve_wave_half_old(phi_tmp, psi_tmp, phi, psi, xy_in);
|
|
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 animation()
|
|
{
|
|
double time, scale, energies[6], top_energy, bottom_energy, source_amp[N_SOURCES], source_periods[N_SOURCES], sign[N_SOURCES];
|
|
double *phi[NX], *psi[NX], *tmp[NX];
|
|
short int *xy_in[NX];
|
|
int i, j, s, source, source_period, source_shift[N_SOURCES], phase, dperiod, add_counter[N_SOURCES];
|
|
|
|
/* 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_energy(circles);
|
|
else if (B_DOMAIN == D_POLYGONS) init_polygon_config(polygons);
|
|
|
|
npolyline = init_poly(MDEPTH, polyline, polyrect, polyrectrot, polyarc, circles, &npolyrect, &npolyrect_rot, &npolyarc, &ncircles, 1);
|
|
|
|
courant2 = COURANT*COURANT;
|
|
courantb2 = COURANTB*COURANTB;
|
|
|
|
for (i=0; i<N_SOURCES; i++) add_counter[i] = 0;
|
|
if (ALTERNATE_SOURCE_PHASES) for (i=0; i<N_SOURCES; i++) sign[i] = pow(-1.0,(double)i);
|
|
else for (i=0; i<N_SOURCES; i++) sign[i] = 1.0;
|
|
|
|
/* 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);
|
|
|
|
|
|
blank();
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
printf("drawing wave\n");
|
|
draw_wave_energy(phi, psi, xy_in, 1.0, 0);
|
|
|
|
printf("drawing billiard\n");
|
|
draw_billiard_half(B_DOMAIN, CIRCLE_PATTERN, 0, 0, 1.0);
|
|
|
|
glutSwapBuffers();
|
|
|
|
|
|
|
|
sleep(SLEEP1);
|
|
|
|
for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
|
|
{
|
|
//printf("%d\n",i);
|
|
/* compute the variance of the field to adjust color scheme */
|
|
/* the color depends on the field divided by sqrt(1 + variance) */
|
|
if (SCALE)
|
|
{
|
|
scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
|
|
// printf("Scaling factor: %5lg\n", scale);
|
|
}
|
|
else scale = 1.0;
|
|
|
|
draw_wave_energy(phi, psi, xy_in, scale, i);
|
|
|
|
draw_billiard_half(B_DOMAIN, CIRCLE_PATTERN, 0, 0, 1.0);
|
|
|
|
/* add oscillating waves */
|
|
wave_source_x[0] = -1.0;
|
|
wave_source_y[0] = 0.5*YMIN;
|
|
source_periods[0] = OSCILLATING_SOURCE_PERIOD;
|
|
source_amp[0] = INITIAL_AMP;
|
|
for (source = 0; source < N_SOURCES; source++)
|
|
{
|
|
dperiod = source_periods[source];
|
|
phase = i - (int)(dperiod*(double)((int)((double)i/dperiod)));
|
|
if ((ADD_OSCILLATING_SOURCE)&&(phase == 1)&&(i<MAX_PULSING_TIME))
|
|
{
|
|
printf("Source %i: Adding pulse %i\n", source, add_counter[source]);
|
|
add_counter[source]++;
|
|
if (ALTERNATE_OSCILLATING_SOURCE) sign[source] = -sign[source];
|
|
add_circular_wave_comp(-sign[source]*source_amp[source], wave_source_x[source], wave_source_y[source], phi, psi, xy_in, 0);
|
|
}
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
glutSwapBuffers();
|
|
|
|
if (MOVIE)
|
|
{
|
|
if (i >= INITIAL_TIME) save_frame();
|
|
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)
|
|
{
|
|
for (i=0; i<END_FRAMES; i++) save_frame();
|
|
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)
|
|
{
|
|
time_t rawtime;
|
|
struct tm * timeinfo;
|
|
|
|
time(&rawtime);
|
|
timeinfo = localtime(&rawtime);
|
|
|
|
glPushMatrix();
|
|
|
|
blank();
|
|
glutSwapBuffers();
|
|
blank();
|
|
glutSwapBuffers();
|
|
|
|
animation();
|
|
sleep(SLEEP2);
|
|
|
|
glPopMatrix();
|
|
|
|
glutDestroyWindow(glutGetWindow());
|
|
|
|
printf("Start local time and date: %s", asctime(timeinfo));
|
|
time(&rawtime);
|
|
timeinfo = localtime(&rawtime);
|
|
printf("Current local time and date: %s", asctime(timeinfo));
|
|
}
|
|
|
|
|
|
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;
|
|
}
|