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nilsberglund-orleans
2021-07-18 15:06:59 +02:00
committed by GitHub
parent 279a6e8801
commit f56b8a0ab4
8 changed files with 951 additions and 425 deletions
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209
heat.c
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@@ -50,46 +50,25 @@
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
/* but will multiply run time by 4 */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
// #define XMIN -1.5
// #define XMAX 2.5 /* x interval */
// #define XMIN -2.0
// #define XMAX 2.0 /* x interval */
#define XMIN -2.5
#define XMAX 1.5 /* x interval */
#define YMIN -1.125
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
#define JULIA_SCALE 1.1 /* scaling for Julia sets */
// #define JULIA_SCALE 0.8 /* scaling for Julia sets */
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 25 /* choice of domain shape */
#define B_DOMAIN 26 /* choice of domain shape, see list in global_pdes.c */
#define D_RECTANGLE 0 /* rectangular domain */
#define D_ELLIPSE 1 /* elliptical domain */
#define D_STADIUM 2 /* stadium-shaped domain */
#define D_SINAI 3 /* Sinai billiard */
#define D_DIAMOND 4 /* diamond-shaped billiard */
#define D_TRIANGLE 5 /* triangular billiard */
#define D_FLAT 6 /* flat interface */
#define D_ANNULUS 7 /* annulus */
#define D_POLYGON 8 /* polygon */
#define D_YOUNG 9 /* Young diffraction slits */
#define D_GRATING 10 /* diffraction grating */
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */
#define D_MENGER 15 /* Menger-Sierpinski carpet */
#define D_JULIA_INT 16 /* interior of Julia set */
#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 */
/* 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 0.7 /* parameter controlling the dimensions of domain */
#define LAMBDA -1.0 /* parameter controlling the dimensions of domain */
#define MU 0.1 /* parameter controlling the dimensions of domain */
#define NPOLY 6 /* number of sides of polygon */
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
@@ -98,6 +77,8 @@
#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 15 /* number of grid point for grid of disks */
#define NGRIDY 20 /* number of grid point for grid of disks */
/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard in sub_wave.c */
@@ -116,13 +97,9 @@
// #define T_IN 2.0 /* inside temperature */
#define SPEED 0.0 /* speed of drift to the right */
/* Boundary conditions */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 0
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
#define BC_PERIODIC 1 /* periodic boundary conditions */
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
#define B_COND 1
/* Parameters for length and speed of simulation */
@@ -142,26 +119,22 @@
/* Field representation */
#define FIELD_REP 0
#define FIELD_REP 1
#define F_INTENSITY 0 /* color represents intensity */
#define F_GRADIENT 1 /* color represents norm of gradient */
#define DRAW_FIELD_LINES 1 /* set to 1 to draw field lines */
#define FIELD_LINE_WIDTH 1 /* width of field lines */
#define N_FIELD_LINES 200 /* number of field lines */
#define N_FIELD_LINES 50 /* number of field lines */
#define FIELD_LINE_FACTOR 100 /* factor controlling precision when computing origin of field lines */
/* Color schemes */
/* Color schemes, see list in global_pdes.c */
#define BLACK 1 /* black background */
#define COLOR_SCHEME 1 /* choice of color scheme */
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
#define C_HUE 1 /* color scheme modifies hue */
#define C_PHASE 2 /* color scheme shows phase */
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
// #define SLOPE 0.1 /* sensitivity of color on wave amplitude */
#define SLOPE 0.3 /* sensitivity of color on wave amplitude */
@@ -171,20 +144,13 @@
#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 280.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -110.0 /* amplitude of variation of hue for color scheme C_HUE */
#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 HUEMEAN 270.0 /* mean value of hue for color scheme C_HUE */
// #define HUEAMP -130.0 /* amplitude of variation of hue for color scheme C_HUE */
/* Basic math */
#define PI 3.141592654
#define DPI 6.283185307
#define PID 1.570796327
double julia_x = 0.0, julia_y = 0.0; /* parameters for Julia sets */
#include "global_pdes.c"
#include "sub_wave.c"
double courant2; /* Courant parameter squared */
@@ -320,12 +286,7 @@ short int *xy_in[NX];
x1 = x1 + delta*nabx/norm;
y1 = y1 + delta*naby/norm;
}
else
{
cont = 0;
// nablax[ij[0]][ij[1]] = 0.0;
// nablay[ij[0]][ij[1]] = 0.0;
}
else cont = 0;
if (!xy_in[ij[0]][ij[1]]) cont = 0;
@@ -361,7 +322,6 @@ int time;
}
/* compute the gradient */
// if (FIELD_REP > 0)
compute_gradient(phi, nablax, nablay);
/* compute the position of origins of field lines */
@@ -371,25 +331,24 @@ int time;
printf("computing linex\n");
x1 = sqrt(3.58);
y1 = 0.0;
x1 = LAMBDA + MU*1.01;
y1 = 1.0;
linex[0] = x1;
liney[0] = y1;
dangle = DPI/((double)(N_FIELD_LINES*FIELD_LINE_FACTOR));
for (i = 1; i < N_FIELD_LINES*FIELD_LINE_FACTOR; i++)
{
// angle = PID + (double)i*dangle;
angle = (double)i*dangle;
x2 = sqrt(3.58)*cos(angle);
y2 = sqrt(1.18)*sin(angle);
x2 = LAMBDA + MU*1.01*cos(angle);
y2 = 0.5 + MU*1.01*sin(angle);
linex[i] = x2;
liney[i] = y2;
distance[i-1] = module2(x2-x1,y2-y1);
x1 = x2;
y1 = y2;
}
distance[N_FIELD_LINES*FIELD_LINE_FACTOR - 1] = module2(x2-sqrt(3.58),y2);
distance[N_FIELD_LINES*FIELD_LINE_FACTOR - 1] = module2(x2-LAMBDA,y2-0.5);
}
dx = (XMAX-XMIN)/((double)NX);
@@ -404,7 +363,6 @@ int time;
value = module2(nablax[i][j], nablay[i][j]);
}
// if ((phi[i][j] - T_IN)*(phi[i][j] - T_OUT) < 0.0)
if (xy_in[i][j] == 1)
{
color_scheme(COLOR_SCHEME, value, scale, time, rgb);
@@ -431,18 +389,14 @@ int time;
else integral[i] = intens;
}
deltaintens = integral[N_FIELD_LINES*FIELD_LINE_FACTOR-1]/((double)N_FIELD_LINES);
// deltaintens = integral[N_FIELD_LINES*FIELD_LINE_FACTOR-1]/((double)N_FIELD_LINES + 1.0);
// deltaintens = integral[N_FIELD_LINES*FIELD_LINE_FACTOR-1]/((double)N_FIELD_LINES);
// printf("delta = %.5lg\n", deltaintens);
i = 0;
// draw_field_line(linex[0], liney[0], nablax, nablay, 0.00002, 100000);
draw_field_line(linex[0], liney[0], xy_in, nablax, nablay, 0.00002, 100000);
for (j = 1; j < N_FIELD_LINES+1; j++)
{
while ((integral[i] <= j*deltaintens)&&(i < N_FIELD_LINES*FIELD_LINE_FACTOR)) i++;
// draw_field_line(linex[i], liney[i], nablax, nablay, 0.00002, 100000);
draw_field_line(linex[i], liney[i], xy_in, nablax, nablay, 0.00002, 100000);
counter++;
}
@@ -459,12 +413,101 @@ int time;
void evolve_wave(phi, xy_in)
void evolve_wave_half(phi_in, phi_out, xy_in)
/* time step of field evolution */
double *phi_in[NX], *phi_out[NX]; short int *xy_in[NX];
{
int i, j, iplus, iminus, jplus, jminus;
double delta1, delta2, x, y;
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta1,delta2,x,y)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (xy_in[i][j] == 1){
/* discretized Laplacian depending on 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;
}
delta1 = 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];
/* evolve phi */
if (B_COND != BC_ABSORBING)
{
phi_out[i][j] = x + intstep*(delta1 - SPEED*(phi_in[iplus][j] - phi_in[i][j]));
}
else /* case of absorbing b.c. - this is only an approximation of correct way of implementing */
{
/* in the bulk */
if ((i>0)&&(i<NX-1)&&(j>0)&&(j<NY-1))
{
phi_out[i][j] = x - intstep*delta2;
}
/* right border */
else if (i==NX-1)
{
phi_out[i][j] = x - intstep1*(x - phi_in[i-1][j]);
}
/* upper border */
else if (j==NY-1)
{
phi_out[i][j] = x - intstep1*(x - phi_in[i][j-1]);
}
/* left border */
else if (i==0)
{
phi_out[i][j] = x - intstep1*(x - phi_in[1][j]);
}
/* lower border */
else if (j==0)
{
phi_out[i][j] = x - intstep1*(x - phi_in[i][1]);
}
}
if (FLOOR)
{
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(phi, phi_tmp, xy_in)
/* time step of field evolution */
double *phi[NX], *phi_tmp[NX]; short int *xy_in[NX];
{
evolve_wave_half(phi, phi_tmp, xy_in);
evolve_wave_half(phi_tmp, phi, xy_in);
}
void old_evolve_wave(phi, xy_in)
/* time step of field evolution */
double *phi[NX]; short int *xy_in[NX];
{
int i, j, iplus, iminus, jplus, jminus;
double delta1, delta2, x, y, *newphi[NX];;
double delta1, delta2, x, y, *newphi[NX];
for (i=0; i<NX; i++) newphi[i] = (double *)malloc(NY*sizeof(double));
@@ -552,9 +595,6 @@ void evolve_wave(phi, xy_in)
// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
}
double compute_variance(phi, xy_in)
/* compute the variance (total probability) of the field */
double *phi[NX]; short int * xy_in[NX];
@@ -658,7 +698,6 @@ short int *xy_in[NX];
sinj = sin(jangle);
julia_x = 0.5*(cosj*(1.0 - 0.5*cosj) + 0.5*sinj*sinj);
julia_y = 0.5*sinj*(1.0-cosj) + yshift;
/* need to decrease 0.05 for i > 2000 */
// julia_x = 0.5*(cosj*(1.0 - 0.5*cosj) + 0.5*sinj*sinj);
// julia_y = 0.5*sinj*(1.0-cosj);
init_julia_set(phi, xy_in);
@@ -669,7 +708,7 @@ short int *xy_in[NX];
void animation()
{
double time, scale, dx, var, jangle, cosj, sinj;
double *phi[NX];
double *phi[NX], *phi_tmp[NX];
short int *xy_in[NX];
int i, j, s;
@@ -677,6 +716,7 @@ void animation()
for (i=0; i<NX; i++)
{
phi[i] = (double *)malloc(NY*sizeof(double));
phi_tmp[i] = (double *)malloc(NY*sizeof(double));
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
}
@@ -687,7 +727,7 @@ void animation()
// julia_x = 0.1;
// julia_y = 0.6;
set_Julia_parameters(0, phi, xy_in);
// set_Julia_parameters(0, phi, xy_in);
printf("Integration step %.3lg\n", intstep);
@@ -710,7 +750,7 @@ void animation()
draw_wave(phi, xy_in, 1.0, 0);
draw_billiard();
print_Julia_parameters(i);
// print_Julia_parameters(i);
// print_level(MDEPTH);
@@ -734,17 +774,17 @@ void animation()
draw_wave(phi, xy_in, scale, i);
for (j=0; j<NVID; j++) evolve_wave(phi, xy_in);
for (j=0; j<NVID; j++) evolve_wave(phi, phi_tmp, xy_in);
draw_billiard();
// print_level(MDEPTH);
print_Julia_parameters(i);
// print_Julia_parameters(i);
glutSwapBuffers();
/* modify Julia set */
set_Julia_parameters(i, phi, xy_in);
// set_Julia_parameters(i, phi, xy_in);
if (MOVIE)
{
@@ -770,6 +810,7 @@ void animation()
for (i=0; i<NX; i++)
{
free(phi[i]);
free(phi_tmp[i]);
}
}