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@ -2038,21 +2038,245 @@ updated gradually. Some constants have been moved to global files in later versi
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### 10 May 21 - A perfect wave front in the Bermuda triangle billiard ###
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**Program:** `xxx.c`
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**Program:** `drop_billiard.c`
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**Initial condition in function `animation()`:** `xxx`
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**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs);`
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```
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#define MOVIE 0 /* set to 1 to generate movie */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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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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/* Choice of the billiard table */
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#define B_DOMAIN 8 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define LAMBDA 1.0 /* parameter controlling shape of billiard */
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#define MU 0.1 /* second parameter controlling shape of billiard */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define NPART 10000 /* number of particles */
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#define NPARTMAX 20000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define LPERIODIC 0.01 /* lines longer than this are not drawn (useful for Sinai billiard) */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define MARGIN 0.02 /* distance above which points of curve are not drawn */
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#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 5000 /* number of frames of movie */
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#define TIME 150 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.0001 /* integration step */
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#define NVID 25 /* number of iterations between images displayed on screen */
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#define NCOLORS 10 /* number of colors */
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#define COLORSHIFT 60 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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#define BLACK 1 /* set to 1 for black background */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 9 May 21 - Waves around a conical singularity ###
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**Program:** `xxx.c`
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**Program:** Special code `wave_conical.c`, not yet incorporated
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**Initial condition in function `animation()`:** `xxx`
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Main changes:
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```
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#define D_CONICAL 999 /* L-shape with conical singularity */
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#define LAMBDA 0.3 /* parameter controlling the dimensions of domain */
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#define NPOLY 6 /* number of sides of polygon */
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical patameters of wave equation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define KAPPA 5.0e-7 /* "elasticity" term enforcing oscillations */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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/* Parameters for length and speed of simulation */
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#define NSTEPS 7500 //7500 /* number of frames of movie */
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#define NVID 50 /* number of iterations between images displayed on screen */
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#define NSEG 100 /* number of segments of boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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/* Color schemes */
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#define COLOR_SCHEME 1 /* choice of color scheme */
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#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
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#define C_HUE 1 /* color scheme modifies hue */
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#define SCALE 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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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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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 120.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP 120.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* Basic math */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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int xy_in_billiard(x, y)
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/* returns 1 if (x,y) represents a point in the billiard */
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double x, y;
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{
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double l2, r2, omega, c, angle;
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int k, condition;
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switch (B_DOMAIN) {
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case D_CONICAL:
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{
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if ((vabs(x) < 1.0)&&(y > -1.0)&&(y < 0.0)) return(1);
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else if ((vabs(y) < 1.0)&&(x > -1.0)&&(x < 0.0)) return(1);
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else return(0);
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}
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}
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void draw_billiard() /* draws the billiard boundary */
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{
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double x0, x, y, phi, r = 0.01, pos[2], pos1[2], alpha, dphi, omega, rgb[3];
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int i;
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glColor3f(0.0, 0.0, 0.0);
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glLineWidth(5);
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glEnable(GL_LINE_SMOOTH);
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switch (B_DOMAIN) {
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case (D_CONICAL):
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{
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draw_segment(-1.0, -1.0, 0.0, -1.0, 0.0, 1.0, 0.5);
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draw_segment(-1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.5);
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draw_segment(-1.0, -1.0, -1.0, 0.0, 220.0, 1.0, 0.5);
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draw_segment(1.0, -1.0, 1.0, 0.0, 220.0, 1.0, 0.5);
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draw_segment(0.0, -1.0, 1.0, -1.0, 60.0, 1.0, 0.5);
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draw_segment(0.0, 0.0, 1.0, 0.0, 60.0, 1.0, 0.5);
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draw_segment(-1.0, 0.0, -1.0, 1.0, 180.0, 1.0, 0.5);
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draw_segment(0.0, 0.0, 0.0, 1.0, 180.0, 1.0, 0.5);
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break;
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}
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}
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}
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void evolve_wave(phi, psi, xy_in)
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/* time step of field evolution */
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/* phi is value of field at time t, psi at time t-1 */
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double *phi[NX], *psi[NX]; short int *xy_in[NX];
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{
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int i, j, iplus, iminus, jplus, jminus, i1, i2, i3, j1, j2, j3, ij[2];
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double delta, x, y;
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/* boundaries */
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xy_to_ij(-1.0, -1.0, ij);
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i1 = ij[0]; j1 = ij[1];
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xy_to_ij(0.0, 0.0, ij);
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i2 = ij[0]; j2 = ij[1];
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xy_to_ij(1.0, 1.0, ij);
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i3 = ij[0]; j3 = ij[1];
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#pragma omp parallel for private(i,j,iplus,iminus,delta,x,y)
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for (i=0; i<NX; i++){
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for (j=0; j<NY; j++){
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if (xy_in[i][j]){
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/* boundary conditions */
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iplus = i+1;
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if ((iplus == i2)&&(j > j2)) iplus = i1+1;
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else if ((iplus == i3)&&(j <= j2)) iplus = i1+1;
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iminus = i-1;
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if ((iminus == i1)&&(j > j2)) iminus = i2-1;
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else if ((iminus == i1)&&(j <= j2)) iminus = i3-1;
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jplus = j+1;
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if ((jplus == j2)&&(i > i2)) jplus = j1+1;
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else if ((jplus == j3)&&(i <= i2)) jplus = j1+1;
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jminus = j-1;
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if ((jminus == j1)&&(i > i2)) jminus = j2-1;
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else if ((jminus == j1)&&(i <= i2)) jminus = j3-1;
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/* discretized Laplacian */
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delta = phi[iplus][j] + phi[iminus][j] + phi[i][jplus] + phi[i][jminus] - 4.0*phi[i][j];
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x = phi[i][j];
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y = psi[i][j];
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/* evolve phi */
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phi[i][j] = -y + 2*x + courant2*delta - KAPPA*x - GAMMA*(x-y);
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psi[i][j] = x;
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if (FLOOR)
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{
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if (phi[i][j] > VMAX) phi[i][j] = VMAX;
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if (phi[i][j] < -VMAX) phi[i][j] = -VMAX;
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if (psi[i][j] > VMAX) psi[i][j] = VMAX;
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if (psi[i][j] < -VMAX) psi[i][j] = -VMAX;
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}
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}
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}
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}
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}
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```
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