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nilsberglund-orleans
2021-11-12 16:22:24 +01:00
committed by GitHub
parent 7c444b3a0b
commit 1f962fc7c8
16 changed files with 4046 additions and 1221 deletions
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246
schrodinger.c
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@@ -39,42 +39,39 @@
/* General geometrical parameters */
// #define WINWIDTH 1280 /* window width */
#define WINWIDTH 720 /* window width */
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
// #define NX 1280 /* number of grid points on x axis */
#define NX 720 /* 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 */
// #define NX 720 /* number of grid points on x 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 */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -2.0
#define YMAX 2.0 /* y interval for 9/16 aspect ratio */
// #define YMIN -1.125
// #define YMAX 1.125 /* y interval for 9/16 aspect ratio */
#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, see list in global_pdes.c */
#define B_DOMAIN 19 /* choice of domain shape */
#define B_DOMAIN 10 /* choice of domain shape */
#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */
#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 RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
#define MU 1.75 /* parameter controlling the dimensions of domain */
#define LAMBDA 0.1 /* parameter controlling the dimensions of domain */
#define MU 0.03 /* 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 */
#define MDEPTH 3 /* depth of computation of Menger gasket */
#define MDEPTH 5 /* 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 */
@@ -98,8 +95,8 @@
/* Physical patameters of wave equation */
// #define DT 0.00000005
#define DT 0.00000001
// #define DT 0.00000001
// #define DT 0.000000005
// #define DT 0.000000005
#define HBAR 1.0
@@ -110,9 +107,9 @@
/* Parameters for length and speed of simulation */
#define NSTEPS 1400 /* number of frames of movie */
#define NVID 2000 /* number of iterations between images displayed on screen */
// #define NVID 1200 /* number of iterations between images displayed on screen */
#define NSTEPS 2500 /* number of frames of movie */
// #define NVID 2000 /* number of iterations between images displayed on screen */
#define NVID 1200 /* number of iterations between images displayed on screen */
#define NSEG 100 /* number of segments of boundary */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
@@ -120,6 +117,7 @@
#define PSLEEP 1 /* sleep time during pause */
#define SLEEP1 1 /* initial sleeping time */
#define SLEEP2 1 /* final sleeping time */
#define END_FRAMES 100 /* still frames at end of movie */
/* For debugging purposes only */
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
@@ -133,22 +131,28 @@
/* Color schemes, see list in global_pdes.c */
#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */
#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */
#define BLACK 1 /* black background */
#define COLOR_SCHEME 1 /* choice of color scheme */
#define COLOR_SCHEME 3 /* choice of color scheme */
#define SCALE 1 /* 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 */
#define E_SCALE 150.0 /* scaling factor for energy representation */
#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 150.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -150.0 /* amplitude of variation of hue for color scheme C_HUE */
#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */
#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 2.0 /* 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 */
#include "global_pdes.c"
#include "sub_wave.c"
@@ -249,7 +253,7 @@ void draw_wave(double *phi[NX], double *psi[NX], short int *xy_in[NX], double sc
glEnd ();
}
void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
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])
// void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
// /* time step of field evolution */
@@ -342,6 +346,168 @@ void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX
// 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],
short int *xy_in[NX])
// void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
// /* time step of field evolution */
// /* phi is real part, psi is imaginary part */
{
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=1; i<NX-1; i++){
for (j=1; j<NY-1; j++){
if (xy_in[i][j]){
x = phi_in[i][j];
y = psi_in[i][j];
delta1 = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
delta2 = psi_in[i+1][j] + psi_in[i-1][j] + psi_in[i][j+1] + psi_in[i][j-1] - 4.0*y;
/* evolve phi and psi */
phi_out[i][j] = x - intstep*delta2;
psi_out[i][j] = y + intstep*delta1;
}
}
}
/* left boundary */
for (j=1; j<NY-1; j++){
if (xy_in[0][j]){
x = phi_in[0][j];
y = psi_in[0][j];
switch (B_COND) {
case (BC_DIRICHLET):
{
delta1 = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
delta2 = psi_in[1][j] + psi_in[0][j+1] + psi_in[0][j-1] - 3.0*y;
phi_out[0][j] = x - intstep*delta2;
psi_out[0][j] = y + intstep*delta1;
break;
}
case (BC_PERIODIC):
{
delta1 = phi_in[1][j] + phi_in[NX-1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 4.0*x;
delta2 = psi_in[1][j] + psi_in[NX-1][j] + psi_in[0][j+1] + psi_in[0][j-1] - 4.0*y;
phi_out[0][j] = x - intstep*delta2;
psi_out[0][j] = y + intstep*delta1;
break;
}
}
}
}
/* right boundary */
for (j=1; j<NY-1; j++){
if (xy_in[0][j]){
x = phi_in[NX-1][j];
y = psi_in[NX-1][j];
switch (B_COND) {
case (BC_DIRICHLET):
{
delta1 = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
delta2 = psi_in[NX-2][j] + psi_in[NX-1][j+1] + psi_in[NX-1][j-1] - 3.0*y;
phi_out[NX-1][j] = x - intstep*delta2;
psi_out[NX-1][j] = y + intstep*delta1;
break;
}
case (BC_PERIODIC):
{
delta1 = phi_in[NX-2][j] + phi_in[0][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 4.0*x;
delta2 = psi_in[NX-2][j] + psi_in[0][j] + psi_in[NX-1][j+1] + psi_in[NX-1][j-1] - 4.0*y;
phi_out[NX-1][j] = x - intstep*delta2;
psi_out[NX-1][j] = y + intstep*delta1;
break;
}
}
}
}
/* top boundary */
for (i=0; i<NX; i++){
if (xy_in[i][NY-1]){
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;
delta1 = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] - 3.0*x;
delta2 = psi_in[iplus][NY-1] + psi_in[iminus][NY-1] + psi_in[i][NY-2] - 3.0*x;
phi_out[i][NY-1] = x - intstep*delta2;
psi_out[i][NY-1] = y + intstep*delta1;
break;
}
case (BC_PERIODIC):
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
delta1 = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] + phi_in[i][0] - 4.0*x;
delta2 = psi_in[iplus][NY-1] + psi_in[iminus][NY-1] + psi_in[i][NY-2] + psi_in[i][0] - 4.0*y;
phi_out[i][NY-1] = x - intstep*delta2;
psi_out[i][NY-1] = y + intstep*delta1;
break;
}
}
}
}
/* bottom boundary */
for (i=0; i<NX; i++){
if (xy_in[i][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;
delta1 = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] - 3.0*x;
delta2 = psi_in[iplus][0] + psi_in[iminus][0] + psi_in[i][1] - 3.0*x;
phi_out[i][0] = x - intstep*delta2;
psi_out[i][0] = y + intstep*delta1;
break;
}
case (BC_PERIODIC):
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
delta1 = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] + phi_in[i][NY-1] - 4.0*x;
delta2 = psi_in[iplus][0] + psi_in[iminus][0] + psi_in[i][1] + psi_in[i][NY-1] - 4.0*y;
phi_out[i][0] = x - intstep*delta2;
psi_out[i][0] = y + intstep*delta1;
break;
}
}
}
}
/* 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;
if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
}
}
}
}
void evolve_wave(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *psi_tmp[NX], short int *xy_in[NX])
/* time step of field evolution */
/* phi is real part, psi is imaginary part */
@@ -392,6 +558,13 @@ void renormalise_field(double *phi[NX], double *psi[NX], short int *xy_in[NX], d
}
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);
}
void animation()
{
double time, scale, dx, var;
@@ -408,6 +581,10 @@ void animation()
psi_tmp[i] = (double *)malloc(NY*sizeof(double));
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
}
/* initialise polyline for von Koch and simular 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);
dx = (XMAX-XMIN)/((double)NX);
intstep = DT/(dx*dx*HBAR);
@@ -416,7 +593,7 @@ void animation()
printf("Integration step %.3lg\n", intstep);
/* initialize wave wave function */
init_coherent_state(0.5, 0.0, 40.0, 0.0, 0.25, phi, psi, xy_in);
init_coherent_state(-0.5, 0.0, 15.0, 0.0, 0.15, phi, psi, xy_in);
// init_coherent_state(0.0, 0.0, 0.0, 5.0, 0.03, phi, psi, xy_in);
// init_coherent_state(-0.5, 0.0, 1.0, 1.0, 0.05, phi, psi, xy_in);
@@ -429,15 +606,14 @@ void animation()
renormalise_field(phi, psi, xy_in, var);
}
blank();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
glColor3f(0.0, 0.0, 0.0);
glutSwapBuffers();
sleep(SLEEP1);
for (i=0; i<=NSTEPS; i++)
@@ -461,6 +637,8 @@ void animation()
draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
glutSwapBuffers();
if (MOVIE)
@@ -476,14 +654,14 @@ void animation()
s = system("mv wave*.tif tif_schrod/");
}
}
}
// if (MOVIE)
// {
// for (i=0; i<20; i++) save_frame();
// s = system("mv wave*.tif tif_schrod/");
// }
if (MOVIE)
{
for (i=0; i<END_FRAMES; i++) save_frame();
s = system("mv wave*.tif tif_schrod/");
}
for (i=0; i<NX; i++)
{
free(phi[i]);