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Nils Berglund
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228
rde.c
228
rde.c
@@ -39,54 +39,66 @@
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#include <omp.h>
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#include <time.h>
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#define MOVIE 0 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
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#define MOVIE 1 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
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/* General geometrical parameters */
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#define WINWIDTH 1920 /* window width */
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#define WINHEIGHT 1000 /* window height */
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#define NX 480 /* number of grid points on x axis */
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#define NY 240 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.041666667
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#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
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// #define WINWIDTH 1280 /* window width */
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// #define WINHEIGHT 720 /* window height */
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//
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// // #define NX 160 /* number of grid points on x axis */
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// // #define NY 90 /* number of grid points on y axis */
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// #define NX 320 /* number of grid points on x axis */
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// #define NY 180 /* number of grid points on y axis */
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//
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// // #define NX 640 /* number of grid points on x axis */
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// // #define NY 360 /* number of grid points on y axis */
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//
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// // #define NX 1280 /* number of grid points on x axis */
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// // #define NY 720 /* number of grid points on y axis */
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// #define NX 600 /* number of grid points on x axis */
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// #define NY 300 /* number of grid points on y axis */
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// // #define NX 480 /* number of grid points on x axis */
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// // #define NY 240 /* number of grid points on y axis */
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// // #define NX 1920 /* number of grid points on x axis */
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// // #define NY 1000 /* number of grid points on y axis */
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//
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// #define XMIN -2.0
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// #define XMAX 2.0 /* x interval */
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// #define YMIN -1.125
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// #define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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// #define YMIN -1.041666667
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// #define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
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// #define WINWIDTH 1280 /* window width */
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// #define WINHEIGHT 720 /* window height */
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// #define NX 200 /* number of grid points on x axis */
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// #define NY 200 /* number of grid points on y axis */
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#define NX 500 /* number of grid points on x axis */
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#define NY 500 /* number of grid points on y axis */
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// #define NX 640 /* number of grid points on x axis */
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// #define NY 360 /* number of grid points on y axis */
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// #define NX 1280 /* number of grid points on x axis */
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// #define NY 720 /* number of grid points on y axis */
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#define XMIN -1.8
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#define XMAX 1.8 /* x interval */
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#define YMIN -1.8
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#define YMAX 1.8 /* y interval for 9/16 aspect ratio */
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/* Choice of simulated equation */
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#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */
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#define NFIELDS 2 /* number of fields in reaction-diffusion equation */
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#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */
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// #define RDE_EQUATION 4 /* choice of reaction term, see list in global_3d.c */
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// #define NFIELDS 3 /* number of fields in reaction-diffusion equation */
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// #define NLAPLACIANS 3 /* number of fields for which to compute Laplacian */
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#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */
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#define POTENTIAL 2 /* type of potential, see list in global_3d.c */
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#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodinger equation) */
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#define POTENTIAL 1 /* type of potential, see list in global_3d.c */
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#define ADD_MAGNETIC_FIELD 1 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
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#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */
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#define JULIA_SCALE 0.5 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */
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#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */
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@@ -96,8 +108,8 @@
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define MU 1.0 /* parameter controlling the dimensions of domain */
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#define NPOLY 6 /* number of sides of polygon */
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#define APOLY 0.333333333 /* angle by which to turn polygon, in units of Pi/2 */
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#define NPOLY 5 /* number of sides of polygon */
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#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 7 /* depth of computation of Menger gasket */
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#define MRATIO 5 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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@@ -111,7 +123,7 @@
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#define X_TARGET 0.4
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#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
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#define ISO_XSHIFT_LEFT -1.65
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#define ISO_XSHIFT_LEFT -1.65
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#define ISO_XSHIFT_RIGHT 0.4
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#define ISO_YSHIFT_LEFT -0.05
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#define ISO_YSHIFT_RIGHT -0.05
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@@ -123,6 +135,9 @@
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/* Physical patameters of wave equation */
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#define DT 0.00000002
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// #define DT 0.00000003
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// #define DT 0.000000011
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// #define DT 0.00000001
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#define VISCOSITY 2.0
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@@ -133,7 +148,7 @@
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#define DELTA 0.1 /* time scale separation */
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#define FHNA 1.0 /* parameter in FHN equation */
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#define FHNC -0.01 /* parameter in FHN equation */
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#define K_HARMONIC 0.2 /* spring constant of harmonic potential */
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#define K_HARMONIC 0.5 /* spring constant of harmonic potential */
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#define K_COULOMB 0.5 /* constant in Coulomb potential */
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#define BZQ 0.0008 /* parameter in BZ equation */
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#define BZF 1.2 /* parameter in BZ equation */
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@@ -167,13 +182,15 @@
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/* Parameters for length and speed of simulation */
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#define NSTEPS 1150 /* number of frames of movie */
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#define NVID 850 /* number of iterations between images displayed on screen */
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// #define NSTEPS 500 /* number of frames of movie */
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#define NSTEPS 1100 /* number of frames of movie */
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#define NVID 500 /* number of iterations between images displayed on screen */
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// #define NVID 1100 /* number of iterations between images displayed on screen */
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#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
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#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */
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#define MAX_DT 0.024 /* maximal value of integration step */
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#define NSEG 100 /* number of segments of boundary */
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#define BOUNDARY_WIDTH 4 /* width of billiard boundary */
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#define BOUNDARY_WIDTH 5 /* width of billiard boundary */
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#define PAUSE 100 /* number of frames after which to pause */
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#define PSLEEP 2 /* sleep time during pause */
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@@ -188,19 +205,19 @@
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#define PLOT_3D 1 /* controls whether plot is 2D or 3D */
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#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */
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#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */
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#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */
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/* Plot type - color scheme */
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#define CPLOT 30
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#define CPLOT 32
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// #define CPLOT 32
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#define CPLOT_B 31
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/* Plot type - height of 3D plot */
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// #define ZPLOT 30 /* z coordinate in 3D plot */
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// #define ZPLOT_B 32 /* z coordinate in second 3D plot */
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#define ZPLOT 30 /* z coordinate in 3D plot */
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#define ZPLOT 32 /* z coordinate in 3D plot */
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// #define ZPLOT 32 /* z coordinate in 3D plot */
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#define ZPLOT_B 30 /* z coordinate in second 3D plot */
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#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
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@@ -209,8 +226,8 @@
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#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
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#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */
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#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */
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#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */
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#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */
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#define ADD_POTENTIAL_TO_Z 0 /* set to 1 to add the external potential to z-coordinate of plot */
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#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */
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#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */
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@@ -237,8 +254,8 @@
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/* Color schemes, see list in global_pdes.c */
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#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */
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#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */
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#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */
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#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* black background */
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@@ -248,12 +265,12 @@
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
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#define VSCALE_AMPLITUDE 7.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */
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#define VSCALE_AMPLITUDE 30.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define CURL_SCALE 0.000015 /* scaling factor for curl representation */
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#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
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#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
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#define MIN_SCHROD_LUM 0.075 /* minimal luminosity in color scheme Z_ARGUMENT*/
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#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
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#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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@@ -263,11 +280,11 @@
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#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */
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#define E_SCALE 100.0 /* scaling factor for energy representation */
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#define LOG_SCALE 1.0 /* scaling factor for energy log representation */
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#define LOG_SHIFT 0.0
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#define LOG_SHIFT 0.0
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#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
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#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */
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#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 2.5 /* scale of color scheme bar for 2nd part */
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#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
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/* only for compatibility with wave_common.c */
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@@ -281,6 +298,13 @@
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#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */
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#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */
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#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
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#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */
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#define AMPLITUDE 0.8 /* amplitude of periodic excitation */
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#define ACHIRP 0.2 /* acceleration coefficient in chirp */
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#define DAMPING 0.0 /* damping of periodic excitation */
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#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */
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#define B_DOMAIN_B 20 /* second domain shape, for comparisons */
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#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */
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/* end of constants added only for compatibility with wave_common.c */
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@@ -288,14 +312,14 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_
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double v_3d[2] = {-0.75, -0.45};
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double w_3d[2] = {0.0, 0.015};
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double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */
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double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */
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double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3D representation */
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int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
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#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */
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#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */
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#define Z_SCALING_FACTOR 1.25 /* overall scaling factor of z axis for REP_PROJ_3D representation */
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#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */
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#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */
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#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */
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#define YSHIFT_3D 0.2 /* overall y shift for REP_PROJ_3D representation */
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#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */
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/* For debugging purposes only */
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@@ -319,7 +343,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO
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double potential(int i, int j)
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/* compute potential (e.g. for Schrödinger equation) */
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{
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double x, y, xy[2], r, small = 2.0e-1, kx, ky;
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double x, y, xy[2], r, small = 2.0e-1, kx, ky, lx = XMAX - XMIN, r1, r2, r3;
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ij_to_xy(i, j, xy);
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x = xy[0];
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@@ -343,12 +367,42 @@ double potential(int i, int j)
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ky = 2.0*DPI/(YMAX - YMIN);
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return(-K_HARMONIC*cos(kx*x)*cos(ky*y));
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}
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case (POT_FERMIONS):
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{
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r = sqrt((x-y)*(x-y) + small*small);
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return (-K_COULOMB/r);
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}
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case (POT_FERMIONS_PERIODIC):
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{
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r1 = sqrt((x-y)*(x-y) + small*small);
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r2 = sqrt((x-lx-y)*(x-lx-y) + small*small);
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r3 = sqrt((x+lx-y)*(x+lx-y) + small*small);
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// r = r/3.0;
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return (-0.5*K_COULOMB*(1.0/r1 + 1.0/r2 + 1.0/r3));
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}
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default:
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{
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return(0.0);
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}
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}
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}
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}
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void compute_vector_potential(int i, int j, double *ax, double *ay)
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/* initialize the vector potential, for Schrodinger equation in a magnetic field */
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{
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double x, y, xy[2], b;
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ij_to_xy(i, j, xy);
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x = xy[0];
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y = xy[1];
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b = sqrt(K_HARMONIC);
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/* magnetic field strength b is chosen such that b^2/4 = K_HARMONIC */
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*ax = b*y;
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*ay = -b*x;
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}
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void initialize_potential(double potential_field[NX*NY])
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@@ -364,18 +418,40 @@ void initialize_potential(double potential_field[NX*NY])
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}
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}
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void evolve_wave_half(double *phi_in[NFIELDS], double *phi_out[NFIELDS], short int xy_in[NX*NY], double potential_field[NX*NY])
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void initialize_vector_potential(double vpotential_field[2*NX*NY])
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/* initialize the potential field, e.g. for the Schrödinger equation */
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{
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int i, j;
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#pragma omp parallel for private(i,j)
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for (i=0; i<NX; i++){
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for (j=0; j<NY; j++){
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compute_vector_potential(i, j, &vpotential_field[i*NY+j], &vpotential_field[NX*NY+i*NY+j]);
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}
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}
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}
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void evolve_wave_half(double *phi_in[NFIELDS], double *phi_out[NFIELDS], short int xy_in[NX*NY], double potential_field[NX*NY], double vector_potential_field[2*NX*NY])
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/* time step of field evolution */
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{
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int i, j, k, iplus, iminus, jplus, jminus;
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double x, y, z, deltax, deltay, deltaz, rho, pot;
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double *delta_phi[NLAPLACIANS];
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double x, y, z, deltax, deltay, deltaz, rho, pot, vx, vy;
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double *delta_phi[NLAPLACIANS], *nabla_phi, *nabla_psi;
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static double invsqr3 = 0.577350269; /* 1/sqrt(3) */
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for (i=0; i<NLAPLACIANS; i++) delta_phi[i] = (double *)malloc(NX*NY*sizeof(double));
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/* compute the Laplacian of phi */
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for (i=0; i<NLAPLACIANS; i++) compute_laplacian(phi_in[i], delta_phi[i], xy_in);
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for (i=0; i<NLAPLACIANS; i++) compute_laplacian_rde(phi_in[i], delta_phi[i], xy_in);
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/* compute the gradient of phi if there is a magnetic field */
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if (ADD_MAGNETIC_FIELD)
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{
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nabla_phi = (double *)malloc(2*NX*NY*sizeof(double));
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nabla_psi = (double *)malloc(2*NX*NY*sizeof(double));
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compute_gradient_xy(phi_in[0], nabla_phi);
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compute_gradient_xy(phi_in[1], nabla_psi);
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}
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#pragma omp parallel for private(i,j,k,x,y,z,deltax,deltay,deltaz,rho)
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for (i=0; i<NX; i++){
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@@ -447,6 +523,13 @@ void evolve_wave_half(double *phi_in[NFIELDS], double *phi_out[NFIELDS], short i
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phi_out[0][i*NY+j] += intstep*pot*phi_in[1][i*NY+j];
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phi_out[1][i*NY+j] -= intstep*pot*phi_in[0][i*NY+j];
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}
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if (ADD_MAGNETIC_FIELD)
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{
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vx = vector_potential_field[i*NY+j];
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vy = vector_potential_field[NX*NY+i*NY+j];
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phi_out[0][i*NY+j] -= 2.0*intstep*(vx*nabla_phi[i*NY+j] + vy*nabla_phi[NX*NY+i*NY+j]);
|
||||
phi_out[1][i*NY+j] -= 2.0*intstep*(vx*nabla_psi[i*NY+j] + vy*nabla_psi[NX*NY+i*NY+j]);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -463,13 +546,19 @@ void evolve_wave_half(double *phi_in[NFIELDS], double *phi_out[NFIELDS], short i
|
||||
}
|
||||
|
||||
for (i=0; i<NLAPLACIANS; i++) free(delta_phi[i]);
|
||||
|
||||
if (ADD_MAGNETIC_FIELD)
|
||||
{
|
||||
free(nabla_phi);
|
||||
free(nabla_psi);
|
||||
}
|
||||
}
|
||||
|
||||
void evolve_wave(double *phi[NFIELDS], double *phi_tmp[NFIELDS], short int xy_in[NX*NY], double potential_field[NX*NY])
|
||||
void evolve_wave(double *phi[NFIELDS], double *phi_tmp[NFIELDS], short int xy_in[NX*NY], double potential_field[NX*NY], double vector_potential_field[2*NX*NY])
|
||||
/* time step of field evolution */
|
||||
{
|
||||
evolve_wave_half(phi, phi_tmp, xy_in, potential_field);
|
||||
evolve_wave_half(phi_tmp, phi, xy_in, potential_field);
|
||||
evolve_wave_half(phi, phi_tmp, xy_in, potential_field, vector_potential_field);
|
||||
evolve_wave_half(phi_tmp, phi, xy_in, potential_field, vector_potential_field);
|
||||
}
|
||||
|
||||
|
||||
@@ -643,7 +732,7 @@ void animation()
|
||||
{
|
||||
double time = 0.0, scale, dx, var, jangle, cosj, sinj, sqrintstep,
|
||||
intstep0, viscosity_printed, fade_value, noise = NOISE_INTENSITY;
|
||||
double *phi[NFIELDS], *phi_tmp[NFIELDS], *potential_field;
|
||||
double *phi[NFIELDS], *phi_tmp[NFIELDS], *potential_field, *vector_potential_field;
|
||||
short int *xy_in;
|
||||
int i, j, k, s, nvid, field;
|
||||
static int counter = 0;
|
||||
@@ -664,6 +753,12 @@ void animation()
|
||||
potential_field = (double *)malloc(NX*NY*sizeof(double));
|
||||
initialize_potential(potential_field);
|
||||
}
|
||||
|
||||
if (ADD_MAGNETIC_FIELD)
|
||||
{
|
||||
vector_potential_field = (double *)malloc(2*NX*NY*sizeof(double));
|
||||
initialize_vector_potential(vector_potential_field);
|
||||
}
|
||||
|
||||
npolyline = init_polyline(MDEPTH, polyline);
|
||||
for (i=0; i<npolyline; i++) printf("vertex %i: (%.3f, %.3f)\n", i, polyline[i].x, polyline[i].y);
|
||||
@@ -684,7 +779,9 @@ void animation()
|
||||
// init_random(0.5, 0.4, phi, xy_in);
|
||||
// init_random(0.0, 0.4, phi, xy_in);
|
||||
// init_gaussian(x, y, mean, amplitude, scalex, phi, xy_in)
|
||||
init_coherent_state(-0.7, 0.0, 3.5, 0.0, 0.15, phi, xy_in);
|
||||
init_coherent_state(1.0, 0.0, 0.0, 5.0, 0.1, phi, xy_in);
|
||||
// init_fermion_state(-0.5, 0.5, 2.0, 0.0, 0.1, phi, xy_in);
|
||||
// init_boson_state(-0.5, 0.5, 2.0, 0.0, 0.1, phi, xy_in);
|
||||
|
||||
init_cfield_rde(phi, xy_in, CPLOT, rde, 0);
|
||||
if (PLOT_3D) init_zfield_rde(phi, xy_in, ZPLOT, rde, 0);
|
||||
@@ -752,7 +849,9 @@ void animation()
|
||||
// printf("Integration step %.5lg\n", intstep);
|
||||
|
||||
printf("Evolving wave\n");
|
||||
for (j=0; j<nvid; j++) evolve_wave(phi, phi_tmp, xy_in, potential_field);
|
||||
for (j=0; j<nvid; j++) evolve_wave(phi, phi_tmp, xy_in, potential_field, vector_potential_field);
|
||||
|
||||
if (ANTISYMMETRIZE_WAVE_FCT) antisymmetrize_wave_function(phi, xy_in);
|
||||
|
||||
for (j=0; j<NFIELDS; j++) printf("field[%i] = %.3lg\t", j, phi[j][0]);
|
||||
printf("\n");
|
||||
@@ -886,6 +985,7 @@ void animation()
|
||||
}
|
||||
free(xy_in);
|
||||
if (ADD_POTENTIAL) free(potential_field);
|
||||
if (ADD_MAGNETIC_FIELD) free(vector_potential_field);
|
||||
|
||||
printf("Time %.5lg\n", time);
|
||||
|
||||
|
||||
Reference in New Issue
Block a user