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nilsberglund-orleans
2021-06-20 23:31:23 +02:00
committed by GitHub
parent bd6aa073a7
commit 279a6e8801
7 changed files with 2149 additions and 141 deletions
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204
wave_billiard.c
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@@ -46,8 +46,10 @@
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
#define NX 640 /* number of grid points on x axis */
#define NY 360 /* number of grid points on y axis */
#define NX 1280 /* number of grid points on x axis */
#define NY 720 /* number of grid points on y axis */
// #define NX 640 /* number of grid points on x axis */
// #define NY 360 /* number of grid points on y axis */
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
/* but will multiply run time by 4 */
@@ -57,9 +59,11 @@
#define YMIN -1.125
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
#define JULIA_SCALE 1.1 /* scaling for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 8 /* choice of domain shape */
#define B_DOMAIN 16 /* choice of domain shape */
#define D_RECTANGLE 0 /* rectangular domain */
#define D_ELLIPSE 1 /* elliptical domain */
@@ -74,21 +78,39 @@
#define D_GRATING 10 /* diffraction grating */
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
#define D_MENGER 15 /* Menger-Sierpinski carpet */
#define D_JULIA_INT 16 /* interior of Julia set */
/* Billiard tables for heat equation */
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
#define D_MANDELBROT 24 /* Mandelbrot set */
#define D_JULIA 25 /* Julia set */
#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
#define MU 0.05 /* parameter controlling the dimensions of domain */
#define NPOLY 8 /* number of sides of polygon */
#define APOLY 1.0 /* 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 */
/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard below */
/* Physical patameters of wave equation */
/* Physical parameters of wave equation */
#define OMEGA 0.9 /* frequency of periodic excitation */
#define COURANT 0.01 /* Courant number */
#define GAMMA 0.0 /* damping factor in wave equation */
// #define GAMMA 5.0e-10 /* damping factor in wave equation */
#define KAPPA 5.0e-6 /* "elasticity" term enforcing oscillations */
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
// #define KAPPA 5.0e-6 /* "elasticity" term enforcing oscillations */
// #define KAPPA 5.0e-9 /* "elasticity" term enforcing oscillations */
// #define KAPPA 5.0e-8 /* "elasticity" term enforcing oscillations */
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
@@ -96,13 +118,22 @@
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
/* Boundary conditions */
#define B_COND 2
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
#define BC_PERIODIC 1 /* periodic boundary conditions */
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
/* For debugging purposes only */
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
#define VMAX 10.0 /* max value of wave amplitude */
/* Parameters for length and speed of simulation */
#define NSTEPS 5000 /* number of frames of movie */
#define NSTEPS 4000 /* number of frames of movie */
#define NVID 25 /* number of iterations between images displayed on screen */
#define NSEG 100 /* number of segments of boundary */
@@ -120,7 +151,7 @@
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
#define C_HUE 1 /* color scheme modifies hue */
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
@@ -128,8 +159,8 @@
#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 100.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP 80.0 /* amplitude of variation of hue for color scheme C_HUE */
#define HUEMEAN 230.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP 50.0 /* amplitude of variation of hue for color scheme C_HUE */
// #define HUEMEAN 320.0 /* mean value of hue for color scheme C_HUE */
// #define HUEAMP 100.0 /* amplitude of variation of hue for color scheme C_HUE */
@@ -139,6 +170,10 @@
#define DPI 6.283185307
#define PID 1.570796327
double julia_x = -0.5, julia_y = 0.5; /* parameters for Julia sets */
// double julia_x = 0.33267, julia_y = 0.06395; /* parameters for Julia sets */
// double julia_x = 0.37468, julia_y = 0.21115; /* parameters for Julia sets */
#include "sub_wave.c"
double courant2; /* Courant parameter squared */
@@ -162,6 +197,24 @@ void init_wave(x, y, phi, psi, xy_in)
}
}
void init_wave_flat(phi, psi, xy_in)
/* initialise flat field - phi is wave height, psi is phi at time t-1 */
double *phi[NX], *psi[NX]; short int * xy_in[NX];
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
void add_drop_to_wave(factor, x, y, phi, psi)
/* add drop at (x,y) to the field with given prefactor */
double factor, x, y, *phi[NX], *psi[NX];
@@ -178,6 +231,33 @@ double factor, x, y, *phi[NX], *psi[NX];
}
}
void oscillate_linear_wave(amplitude, t, x1, y1, x2, y2, phi, psi)
/* oscillating boundary condition at (x,y) */
double amplitude, t, x1, y1, x2, y2, *phi[NX], *psi[NX];
{
int i, j, ij1[2], ij2[2], imin, imax, jmin, jmax, d = 5;
double xy[2], dist2;
xy_to_ij(x1, y1, ij1);
xy_to_ij(x2, y2, ij2);
imin = ij1[0] - d; if (imin < 0) imin = 0;
imax = ij2[0] + d; if (imax >= NX) imax = NX-1;
jmin = ij1[1] - d; if (jmin < 0) jmin = 0;
jmax = ij2[1] + d; if (jmax >= NY) jmax = NY-1;
for (i = imin; i < imax; i++)
for (j = jmin; j < jmax; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x1)*(xy[0]-x1); /* to be improved */
// dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
// if (dist2 < 0.01)
if (dist2 < 0.001)
phi[i][j] = amplitude*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01)*cos(t*OMEGA);
// phi[i][j] += 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01)*cos(t*OMEGA);
}
}
@@ -215,7 +295,92 @@ int time;
glEnd ();
}
void evolve_wave(phi, psi, xy_in)
void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
double *phi_in[NX], *psi_in[NX], *phi_out[NX], *psi_out[NX]; short int *xy_in[NX];
{
int i, j, iplus, iminus, jplus, jminus;
double delta, x, y, c, cc;
c = COURANT;
cc = courant2;
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (xy_in[i][j]){
/* discretized Laplacian */
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;
}
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_ABSORBING) phi_out[i][j] = -y + 2*x + cc*delta - KAPPA*x - GAMMA*(x-y);
else
{
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*x - GAMMA*(x-y);
/* lower border */
else if (j==0)
phi_out[i][j] = x - c*(x - phi_in[i][1]) - KAPPA*x - GAMMA*(x-y);
/* right border */
if (i==NX-1)
phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA*x - GAMMA*(x-y);
/* left border */
else if (i==0)
phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA*x - GAMMA*(x-y);
}
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(phi, psi, phi_tmp, psi_tmp, xy_in)
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX]; short int *xy_in[NX];
{
evolve_wave_half(phi, psi, phi_tmp, psi_tmp, xy_in);
evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
}
void old_evolve_wave(phi, psi, xy_in)
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
double *phi[NX], *psi[NX]; short int *xy_in[NX];
@@ -286,7 +451,7 @@ double compute_variance(phi, psi, xy_in)
void animation()
{
double time, scale;
double *phi[NX], *psi[NX];
double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX];
short int *xy_in[NX];
int i, j, s;
@@ -295,12 +460,15 @@ void animation()
{
phi[i] = (double *)malloc(NY*sizeof(double));
psi[i] = (double *)malloc(NY*sizeof(double));
phi_tmp[i] = (double *)malloc(NY*sizeof(double));
psi_tmp[i] = (double *)malloc(NY*sizeof(double));
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
}
courant2 = COURANT*COURANT;
/* initialize wave with a drop at one point, zero elsewhere */
// init_wave_flat(phi, psi, xy_in);
init_wave(0.0, 0.0, phi, psi, xy_in);
/* add a drop at another point */
@@ -329,12 +497,19 @@ void animation()
scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
// printf("Scaling factor: %5lg\n", scale);
}
else scale = 1.0;
// /* TO BE ADAPTED */
// scale = 1.0;
draw_wave(phi, psi, xy_in, scale, i);
for (j=0; j<NVID; j++) evolve_wave(phi, psi, xy_in);
for (j=0; j<NVID; j++)
{
evolve_wave(phi, psi, phi_tmp, 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);
}
// for (j=0; j<NVID; j++) evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
draw_billiard();
@@ -365,6 +540,9 @@ void animation()
{
free(phi[i]);
free(psi[i]);
free(phi_tmp[i]);
free(psi_tmp[i]);
free(xy_in[i]);
}
}