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nilsberglund-orleans
2022-04-12 19:20:18 +02:00
committed by GitHub
parent 6d878e89dd
commit 65aa6866be
14 changed files with 3174 additions and 448 deletions
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282
wave_billiard.c
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@@ -47,34 +47,38 @@
/* General geometrical parameters */
/* uncomment for higher resolution version */
// #define WINWIDTH 1920 /* window width */
// #define WINHEIGHT 1000 /* window height */
#define WINWIDTH 1920 /* window width */
#define WINHEIGHT 1000 /* window height */
// #define NX 1920 /* number of grid points on x axis */
// #define NY 1000 /* number of grid points on y axis */
#define NX 3840 /* number of grid points on x axis */
#define NY 2000 /* number of grid points on y axis */
#define XMIN -1.25
#define XMAX 2.75 /* x interval */
#define YMIN -1.041666667
#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */
// #define WINWIDTH 1280 /* window width */
// #define WINHEIGHT 720 /* window height */
//
// #define XMIN -2.0
// #define XMAX 2.0 /* x interval */
// #define YMIN -1.041666667
// #define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
/* comment out for higher resolution version */
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
#define NX 1280 /* number of grid points on x axis */
#define NY 720 /* number of grid points on y axis */
#define 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 NX 1280 /* number of grid points on x axis */
// // #define NY 720 /* number of grid points on y axis */
// #define NX 2560 /* number of grid points on x axis */
// #define NY 1440 /* number of grid points on y axis */
//
// #define XMIN -1.25
// #define XMAX 2.75 /* 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 41 /* choice of domain shape, see list in global_pdes.c */
#define B_DOMAIN 3 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */
@@ -82,8 +86,8 @@
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
#define LAMBDA 1.1 /* parameter controlling the dimensions of domain */
#define MU 1.0 /* parameter controlling the dimensions of domain */
#define LAMBDA 0.75 /* parameter controlling the dimensions of domain */
#define MU 0.2 /* parameter controlling the dimensions of domain */
#define NPOLY 3 /* number of sides of polygon */
#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 6 /* depth of computation of Menger gasket */
@@ -110,16 +114,18 @@
/* Physical parameters of wave equation */
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */
#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
#define OMEGA 0.002 /* frequency of periodic excitation */
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
#define COURANT 0.03 /* Courant number */
#define COURANTB 0.01 /* Courant number in medium B */
#define OMEGA 0.005 /* frequency of periodic excitation */
#define AMPLITUDE 0.8 /* amplitude of periodic excitation */
#define DAMPING 2.5e-5 /* damping of periodic excitation */
#define COURANT 0.05 /* Courant number */
#define COURANTB 0.0375 /* Courant number in medium B */
// #define COURANTB 0.016363636 /* Courant number in medium B */
#define GAMMA 0.0 /* damping factor in wave equation */
#define GAMMAB 5.0e-4 /* damping factor in wave equation */
#define GAMMAB 0.0 /* damping factor in wave equation */
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
@@ -130,18 +136,19 @@
/* 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 ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */
#define OSCILLATING_SOURCE_PERIOD 100 /* period of oscillating source */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 2
#define B_COND 3
// #define B_COND 2
/* Parameters for length and speed of simulation */
#define NSTEPS 2200 /* number of frames of movie */
#define NSTEPS 2700 /* number of frames of movie */
// #define NSTEPS 100 /* number of frames of movie */
#define NVID 25 /* number of iterations between images displayed on screen */
#define NVID 30 /* number of iterations between images displayed on screen */
#define NSEG 1000 /* number of segments of boundary */
#define INITIAL_TIME 0 /* time after which to start saving frames */
#define BOUNDARY_WIDTH 1 /* width of billiard boundary */
@@ -151,7 +158,7 @@
#define SLEEP1 1 /* initial sleeping time */
#define SLEEP2 1 /* final sleeping time */
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
#define END_FRAMES 50 /* number of still frames at end of movie */
#define END_FRAMES 100 /* number of still frames at end of movie */
/* Parameters of initial condition */
@@ -162,23 +169,28 @@
/* Plot type, see list in global_pdes.c */
#define PLOT 0
// #define PLOT 3
// #define PLOT 1
#define PLOT_B 5 /* plot type for second movie */
#define PLOT_B 3 /* plot type for second movie */
/* Color schemes */
#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */
#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */
#define BLACK 1 /* background */
#define 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 0.2 /* sensitivity of color on wave amplitude */
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */
#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 150.0 /* scaling factor for energy representation */
#define LOG_SCALE 1.5 /* scaling factor for energy log representation */
#define LOG_SHIFT 0.0 /* shift of colors on log scale */
#define E_SCALE 300.0 /* scaling factor for energy representation */
#define LOG_SCALE 1.0 /* scaling factor for energy log representation */
#define LOG_SHIFT 1.0 /* shift of colors on log scale */
#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 */
@@ -189,8 +201,8 @@
#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */
#define COLORBAR_RANGE 1.0 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 5.0 /* scale of color scheme bar for 2nd part */
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */
@@ -211,137 +223,6 @@ double courant2, courantb2; /* Courant parameters squared */
/* 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;
double delta, x, y, c, cc, gamma;
static long time = 0;
time++;
// c = COURANT;
// cc = courant2;
#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; j++){
// if (xy_in[i][j])
// {
// c = COURANT;
// cc = courant2;
// gamma = GAMMA;
// }
if (xy_in[i][j] != 0)
{
c = COURANT;
cc = courant2;
if (xy_in[i][j] == 1) gamma = GAMMA;
else gamma = GAMMAB;
}
else if (TWOSPEEDS)
{
c = COURANTB;
cc = courantb2;
gamma = GAMMAB;
}
if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
/* discretized Laplacian for various boundary conditions */
if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING))
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
}
else if (B_COND == BC_PERIODIC)
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
jplus = (j+1) % NY;
jminus = (j-1) % NY;
if (jminus < 0) jminus += NY;
}
else if (B_COND == BC_VPER_HABS)
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1) % NY;
jminus = (j-1) % NY;
if (jminus < 0) jminus += NY;
}
/* 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)
{
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);
}
psi_out[i][j] = x;
/* add oscillating boundary condition on the left */
if ((i == 0)&&(OSCILLATE_LEFT)) 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], double *psi_out[NX],
@@ -400,7 +281,7 @@ void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX
}
/* left boundary */
if (OSCILLATE_LEFT) for (j=1; j<NY-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
if (OSCILLATE_LEFT) for (j=1; j<NY-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA)*exp(-(double)time*DAMPING);
else for (j=1; j<NY-1; j++){
if ((TWOSPEEDS)||(xy_in[0][j] != 0)){
x = phi_in[0][j];
@@ -575,8 +456,8 @@ void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX
/* add oscillating boundary condition on the left corners */
if (OSCILLATE_LEFT)
{
phi_out[0][0] = AMPLITUDE*cos((double)time*OMEGA);
phi_out[0][NY-1] = AMPLITUDE*cos((double)time*OMEGA);
phi_out[0][0] = AMPLITUDE*cos((double)time*OMEGA)*exp(-(double)time*DAMPING);
phi_out[0][NY-1] = AMPLITUDE*cos((double)time*OMEGA)*exp(-(double)time*DAMPING);
}
/* for debugging purposes/if there is a risk of blow-up */
@@ -606,10 +487,15 @@ void evolve_wave(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *
void draw_color_bar(int plot, double range)
{
if (ROTATE_COLOR_SCHEME) draw_color_scheme(-1.0, -0.8, XMAX - 0.1, -1.0, plot, -range, range);
else draw_color_scheme(1.7, YMIN + 0.1, 1.9, YMAX - 0.1, plot, -range, range);
else draw_color_scheme(XMAX - 0.3, YMIN + 0.1, XMAX - 0.1, YMAX - 0.1, plot, -range, range);
// else draw_color_scheme(1.7, YMIN + 0.25, 1.9, YMAX - 0.25, plot, -range, range);
}
void draw_color_bar_palette(int plot, double range, int palette)
{
if (ROTATE_COLOR_SCHEME) draw_color_scheme_palette(-1.0, -0.8, XMAX - 0.1, -1.0, plot, -range, range, palette);
else draw_color_scheme_palette(XMAX - 0.3, YMIN + 0.1, XMAX - 0.1, YMAX - 0.1, plot, -range, range, palette);
}
void animation()
{
@@ -682,16 +568,18 @@ void animation()
// xy_to_ij(startright[0], startright[1], sample_right);
// printf("xleft = (%.3f, %.3f) xright = (%.3f, %.3f)\n", xin_left, yin_left, xin_right, yin_right);
// init_wave_flat(phi, psi, xy_in);
init_wave_flat(phi, psi, xy_in);
// init_wave_plus(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);
// init_wave(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);
// init_circular_wave(X_SHOOTER, Y_SHOOTER, phi, psi, xy_in);
// printf("Initializing wave\n");
// init_circular_wave(-1.0, 0.0, phi, psi, xy_in);
// init_circular_wave(-0.5, 0.0, phi, psi, xy_in);
// printf("Wave initialized\n");
init_circular_wave(0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in);
period++;
// init_circular_wave(0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in);
// period++;
// for (i=0; i<3; i++)
// {
// add_circular_wave(-1.0, 0.6*cos(PID + (double)(i)*DPI/3.0), 0.6*sin(PID + (double)(i)*DPI/3.0), phi, psi, xy_in);
@@ -718,12 +606,13 @@ void animation()
blank();
glColor3f(0.0, 0.0, 0.0);
// draw_wave(phi, psi, xy_in, 1.0, 0, PLOT);
draw_wave_e(phi, psi, total_energy, color_scale, xy_in, 1.0, 0, PLOT);
// draw_wave_highres(2, phi, psi, total_energy, xy_in, 1.0, 0, PLOT);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, xy_in, 1.0, 0, PLOT, COLOR_PALETTE);
else draw_wave_epalette(phi, psi, total_energy, color_scale, xy_in, 1.0, 0, PLOT, COLOR_PALETTE);
draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE);
glutSwapBuffers();
@@ -744,8 +633,8 @@ void animation()
else scale = 1.0;
// draw_wave(phi, psi, xy_in, scale, i, PLOT);
draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, i, PLOT);
// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, i, PLOT);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, xy_in, scale, i, PLOT, COLOR_PALETTE);
else draw_wave_epalette(phi, psi, total_energy, color_scale, xy_in, scale, i, PLOT, COLOR_PALETTE);
for (j=0; j<NVID; j++)
{
evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
@@ -763,7 +652,7 @@ void animation()
draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE);
/* add oscillating waves */
if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == OSCILLATING_SOURCE_PERIOD - 1))
@@ -783,12 +672,13 @@ void animation()
if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
{
// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, i, PLOT_B);
// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, i, PLOT_B);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, xy_in, scale, i, PLOT_B, COLOR_PALETTE_B);
else draw_wave_epalette(phi, psi, total_energy, color_scale, xy_in, scale, i, PLOT_B, COLOR_PALETTE_B);
draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B);
glutSwapBuffers();
save_frame_counter(NSTEPS + 21 + counter);
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
// save_frame_counter(NSTEPS + 21 + counter);
counter++;
}
@@ -809,20 +699,20 @@ void animation()
if (DOUBLE_MOVIE)
{
// draw_wave(phi, psi, xy_in, scale, i, PLOT);
draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, NSTEPS, PLOT);
// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE);
else draw_wave_epalette(phi, psi, total_energy, color_scale, xy_in, scale, NSTEPS, PLOT, COLOR_PALETTE);
draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT, COLORBAR_RANGE, COLOR_PALETTE);
glutSwapBuffers();
}
for (i=0; i<MID_FRAMES; i++) save_frame();
if (DOUBLE_MOVIE)
{
// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, NSTEPS, PLOT_B);
// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B);
if (HIGHRES) draw_wave_highres_palette(2, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B);
else draw_wave_epalette(phi, psi, total_energy, color_scale, xy_in, scale, NSTEPS, PLOT_B, COLOR_PALETTE_B);
draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(PLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B);
glutSwapBuffers();
}
for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);