inline static double analytical_solution_circle(double t, double x, double y) {
double x0 = get_center_x() + t * func_u(t, x, y);
double y0 = get_center_y() + t * func_v(t, x, y);
double value = (x - x0) * (x - x0) + (y - y0) * (y - y0);
if (value <= R_SQ) return INN_DENSITY;
return OUT_DENSITY;
}
inline void print_data_to_files(double *phi, double *density, double *residual, int tl) {
double x0 = get_center_x() + tl*TAU * func_u(tl*TAU, get_center_x(), get_center_y());
double y0 = get_center_y() + tl*TAU* func_v(tl*TAU, get_center_x(), get_center_y());
print_surface("phi", NX, NY, HX, HY, tl, A, C, x0, y0, TAU, U, V, phi);
print_surface("rho", NX, NY, HX, HY, tl, A, C, x0, y0, TAU, U, V, density);
// print_surface("res", NX, NY, HX, HY, tl, A, C, get_center_x_2(), get_center_y_2(), TAU,
// U, V, residual);
double *err_lock = calc_error_2(HX, HY, tl * TAU, density);
print_surface("err-l", NX, NY, HX, HY, tl, A, C, x0, y0, TAU, U, V, err_lock);
delete[] err_lock;
}
__pure inline static double func_f(double b, double time, double ub, double bb, double lb, double rb, double x, double y)
{
double arg_v = 0.1 * (x - lb) * (x - rb) * (1 + time) * (y - ub) * (y - bb);
double rho = analytical_solution(time, x, y);
double drho_dt = x * y * cos(time * x * y);
double drho_dx = time * y * cos(time * x * y);
double dtho_dy = time * x * cos(time * x * y);
double u = func_u(b, x, y);
double v = func_v(ub, bb, lb, rb, time, x, y);
double du_dx = -b * y * (1 - y) / (1 + sqr(x));
double dv_dx = 0.1 * (x - lb) * (x - rb) * (1 + time) * (y - bb + y - ub);
dv_dx /= (1 + arg_v * arg_v);
return drho_dt + rho * du_dx + u * drho_dx + rho * dv_dx + v * dtho_dy;
}
static double integrate(int i, int j)
{
dp_t left(OX[i-1], OY[j]);
dp_t right(OX[i+1], OY[j]);
dp_t up(OX[i], OY[j+1]);
dp_t bottom(OX[i], OY[j-1]);
dp_t center(OX[i], OY[j]);
double u = func_u(B, center.x, center.y);
double v = func_v(UB, BB, LB, RB, TIME, center.x, center.y);
center.x = center.x - TAU * u;
center.y = center.y - TAU * v;
// проверим случай вылета точки за левую границу
if (center.x <= 0) // вылет за левую границу
{
dp_t center_tk(OX[i], OY[j]);
// найдем точку (t, y) пересечения траектории и оси ординат
double y_ = 0;
double t_ = 0;
if ( center_tk.x - center.x < FLT_MIN )
{
y_ = 0.5 * (center_tk.y + center_tk.y);
}
else
{
y_ = center_tk.y - center.x
* ((center_tk.y - center.y) / (center_tk.x - center.x));
}
// найдем время t* в точке перечесения
// уравнение прямой для точки (y, t)
// t - t1 / t2-t1 = y-y1/y2-y1
// => t = t1 + (y-y1)*(t2-t1)/y2-y1
// здесь center_tk = первая точка
// center = вторая
// TAU = t2 - t1
// TIME = время на K слое по времени
t_ = TIME - TAU * ((y_-center_tk.y)/(center.y - center_tk.y));
// посчитаем TAU*
double tau_ = TIME - t_;
double u = func_u(B, left.x, left.y);
double v = func_v(UB, BB, LB, RB, t_, left.x, left.y);
left.x = left.x - tau_ * u;
left.y = left.y - tau_ * v;
u = func_u(B, right.x, right.y);
v = func_v(UB, BB, LB, RB, t_, right.x, right.y);
right.x = right.x - tau_ * u;
right.y = right.y - tau_ * v;
u = func_u(B, up.x, up.y);
v = func_v(UB, BB, LB, RB, t_, up.x, up.y);
up.x = up.x - tau_ * u;
up.y = up.y - tau_ * v;
u = func_u(B, bottom.x, bottom.y);
v = func_v(UB, BB, LB, RB, t_, bottom.x, bottom.y);
bottom.x = bottom.x - tau_ * u;
bottom.y = bottom.y - tau_ * v;
u = func_u(B, center.x, center.y);
v = func_v(UB, BB, LB, RB, t_, center.x, center.y);
center.x = center_tk.x - tau_ * u;
center.y = center_tk.y - tau_ * v;
double w_x_ksi = 0.5 * ((right.x-center.x)/HX + (center.x - left.x)/HX);
double w_y_ksi = 0.5 * ((right.y-center.y)/HX + (center.y - left.y)/HX);
double w_x_the = 0.5 * ((up.x-center.x)/HY + (center.x - bottom.x)/HY);
double w_y_the = 0.5 * ((up.y-center.y)/HY + (center.y - bottom.y)/HY);
double det = w_x_ksi*w_y_the - w_x_the *w_y_ksi;
double rho = analytical_solution(t_, 0, y_);
//printf("%s\n", "WALL COLLISION");
//return det * rho * INVERTED_HX_HY;
return det * rho;
}
u = func_u(B, left.x, left.y);
v = func_v(UB, BB, LB, RB, TIME, left.x, left.y);
left.x = left.x - TAU * u;
left.y = left.y - TAU * v;
u = func_u(B, right.x, right.y);
v = func_v(UB, BB, LB, RB, TIME, right.x, right.y);
right.x = right.x - TAU * u;
right.y = right.y - TAU * v;
u = func_u(B, up.x, up.y);
v = func_v(UB, BB, LB, RB, TIME, up.x, up.y);
up.x = up.x - TAU * u;
up.y = up.y - TAU * v;
u = func_u(B, bottom.x, bottom.y);
v = func_v(UB, BB, LB, RB, TIME, bottom.x, bottom.y);
bottom.x = bottom.x - TAU * u;
bottom.y = bottom.y - TAU * v;
double w_x_ksi = 0.5 * ((right.x-center.x)/HX + (center.x - left.x)/HX);
double w_y_ksi = 0.5 * ((right.y-center.y)/HX + (center.y - left.y)/HX);
double w_x_the = 0.5 * ((up.x-center.x)/HY + (center.x - bottom.x)/HY);
double w_y_the = 0.5 * ((up.y-center.y)/HY + (center.y - bottom.y)/HY);
double det = w_x_ksi*w_y_the - w_x_the *w_y_ksi;
int x = floor(center.x / HX);
int y = floor(center.y / HY);
double rho = PREV_DENSITY[y * OX_LEN_1 + x] * (center.x - OX[x + 1]) * (center.y - OY[y + 1]);
rho -= PREV_DENSITY[y * OX_LEN_1 + x + 1] * (center.x - OX[x]) * (center.y - OY[y + 1]);
rho += PREV_DENSITY[(y + 1) * OX_LEN_1 + x + 1] * (center.x - OX[x]) * (center.y - OY[y]);
rho -= PREV_DENSITY[(y + 1) * OX_LEN_1 + x] * (center.x - OX[x + 1]) * (center.y - OY[y]);
return det * rho * INVERTED_HX_HY;
}
static double get_phi(int i, int j)
{
dp_t u_left(OX[i-1], OY[j+1]); // left upper
dp_t u_right(OX[i+1], OY[j+1]); // right upper
dp_t b_left(OX[i-1], OY[j-1]); // left bottom
dp_t b_right(OX[i+1], OY[j-1]); // right bottom
dp_t center(OX[i], OY[j]);
double u = func_u();
double v = func_v();
center.x = center.x - TAU * u;
center.y = center.y - TAU * v;
u = func_u();
v = func_v();
u_left.x = u_left.x - TAU * u;
u_left.y = u_left.y - TAU * v;
u = func_u();
v = func_v();
u_right.x = u_right.x - TAU * u;
u_right.y = u_right.y - TAU * v;
u = func_u();
v = func_v();
b_left.x = b_left.x - TAU * u;
b_left.y = b_left.y - TAU * v;
u = func_u();
v = func_v();
b_right.x = b_right.x - TAU * u;
b_right.y = b_right.y - TAU * v;
int nx = 10;
int ny = 10;
double x_step = 1.0/nx;
double y_step = 1.0/ny;
double* x_mesh = create_mesh_vector(nx);
double* y_mesh = create_mesh_vector(ny);
if (i == 1 && j == 1 && f == 0)
{
// __print_vector(x_mesh, nx);
// __print_vector(y_mesh, ny);
f = 1;
}
// get right part for jakoby
double phi = 0;
for(int i = 0; i < nx; ++i)
{
for(int j = 0; j < ny; ++j)
{
dp_t ideal;
ideal.x = x_mesh[i] + x_step/2.;
ideal.y = y_mesh[j] + y_step/2.;
dp_t real = get_point_real_pt_by_ideal_pt(b_left, b_right, u_right, u_left,
ideal);
double dens = get_density_in_real_pt(b_left, b_right, u_right, u_left,
real);
double jakob = jakobian(b_left, b_right, u_right, u_left, ideal);
phi += dens * jakob;
}
}
phi = (16*phi/9*x_step*y_step);
delete[] x_mesh;
delete[] y_mesh;
return phi;
}
double *solve_2(double &tme) {
fflush(stdout);
int ic = 0;
double *phi = new double[XY];
double *prev_density = new double[XY];
double *density = new double[XY];
double *residual = new double[XY];
//<editor-fold desc="Fill initial data">
for (int i = 0; i < NX_1; ++i) {
for (int j = 0; j < NY_1; ++j) {
density[NY_1 * i + j] = 0.;
prev_density[NY_1 * i + j] = 0.;
residual[NY_1 * i + j] = 0.;
phi[NY_1 * i + j] = 0.;
}
}
// G1 -- (x_i, 0=C) -- bottom boundary
for (int i = 0; i < NX_1; ++i) {
prev_density[NY_1 * i] = analytical_solution_circle(0., A + HX * i, C);
if (fabs(prev_density[NY_1 * i]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * i] = 0;
}
// G2 -- (NX=B, y_j) -- right boundary
for (int j = 1; j < NY; ++j) {
prev_density[NY_1 * NX + j] = analytical_solution_circle(0., A + HX * NX, C + HY * j);
if (fabs(prev_density[NY_1 * NX + j]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * NX + j] = 0;
}
// G3 -- (x_i, NY=D) -- top boundary
for (int i = 0; i < NX_1; ++i) {
prev_density[NY_1 * i + NY] = analytical_solution_circle(0., A + HX * i, C + HY * NY);
if (fabs(prev_density[NY_1 * i + NY]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * i + NY] = 0;
}
// G4 -- (0=A, y_j) -- left boundary
for (int j = 1; j < NY; ++j) {
prev_density[j] = analytical_solution_circle(0., A, C + HY * j);
if (fabs(prev_density[j]) < fabs(DBL_MIN_TRIM)) prev_density[j] = 0;
}
memcpy(density, prev_density, XY * sizeof(double));
// inner points
for (int i = 1; i < NX; ++i) {
for (int j = 1; j < NY; ++j) {
prev_density[NY_1 * i + j] = analytical_solution_circle(0., A + HX * i, C + HY * j);
//if (fabs(prev_density[NY_1 * i + j]) < fabs(DBL_MIN_TRIM)) prev_density[NY_1 * i + j] = 0;
}
}
//</editor-fold>
double sum_rho = calc_array_sum(prev_density, NX_1, NY_1, 0);
double sum_abs_rho = calc_array_sum(prev_density, NX_1, NY_1, 1);
printf("SUM RHO INIT = %le\n", sum_rho);
printf("SUM ABS RHO INIT= %le\n", sum_abs_rho);
fflush(stdout);
double maxRes = FLT_MAX;
double *extrems = new double[2];
double *extrems_err = new double[2];
for (int tl = 1; tl <= TIME_STEP_CNT; tl++) {
//<editor-fold desc="Calculate phi">
// with usage of prev_density we calculate phi function values
// G3 -- (x_i, NY=D) -- top boundary
for (int i = 1; i < NX; ++i) {
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(i, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(i, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(i, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(i, NY, prev_density, TAU * tl);
}
phi[NY_1 * i + NY] = integ;
}
// G2 -- (NX=B, y_j) -- right boundary
for (int j = 1; j < NY; ++j) {
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(NX, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(NX, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(NX, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(NX, j, prev_density, TAU * tl);
}
phi[NY_1 * NX + j] = integ;
}
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(NX, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(NX, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(NX, NY, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(NX, NY, prev_density, TAU * tl);
}
// point (1,1)
phi[NY_1 * NX + NY] = integ;
// inner points
for (int i = 1; i < NX; ++i)
for (int j = 1; j < NY; ++j) {
double integ = 0.;
if (INTEGR_TYPE == 1) {
integ = get_phi_integ_midpoint(i, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 2) {
integ = get_phi_integ_trapezium(i, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 3) {
integ = get_phi_integ_exact(i, j, prev_density, TAU * tl);
}
else if (INTEGR_TYPE == 4) {
integ = get_phi_integ_b_control_midpoint(i, j, prev_density, TAU * tl);
}
phi[NY_1 * i + j] = integ;
}
//</editor-fold>
ic = 0;
double maxErr = FLT_MAX;
while (((maxErr > EPS) || (maxRes > RES_EPS)) && (ic < NX_1 * NY_1)) {
//<editor-fold desc="Calculate density">
// point 1,1
double rpCoef = 64. / (9. * HX * HY);
density[NY_1 * NX + NY] = -1. / 3. * (prev_density[NY_1 * NX + NY - 1]
+ prev_density[NY_1 * (NX - 1) + NY])
- 1. / 9. * prev_density[NY_1 * (NX - 1) + NY - 1]
+ rpCoef * phi[NY_1 * NX + NY];
if (fabs(density[NY_1 * NX + NY]) < fabs(DBL_MIN_TRIM)) density[NY_1 * NX + NY] = 0;
// G3 -- (x_i, NY=D) -- top boundary
rpCoef = 32. / (9. * HX * HY);
for (int i = 1; i < NX; ++i) {
density[NY_1 * i + NY] = -1. / 3. * prev_density[NY_1 * i + NY - 1]
- 1. / 6. * (prev_density[NY_1 * (i + 1) + NY] +
prev_density[NY_1 * (i - 1) + NY])
- 1. / 18. * (prev_density[NY_1 * (i + 1) + NY - 1] +
prev_density[NY_1 * (i - 1) + NY - 1])
+ rpCoef * phi[NY_1 * i + NY];
if (fabs(density[NY_1 * i + NY]) < fabs(DBL_MIN_TRIM)) density[NY_1 * i + NY] = 0;
}
// G2 -- (NX=B, y_j) -- right boundary
rpCoef = 32. / (9. * HX * HY);
for (int j = 1; j < NY; ++j) {
density[NY_1 * NX + j] = -1. / 3. * prev_density[NY_1 * (NX - 1) + j]
- 1. / 6. * (prev_density[NY_1 * NX + j - 1] +
prev_density[NY_1 * NX + j + 1])
- 1. / 18. * (prev_density[NY_1 * (NX - 1) + j - 1] +
prev_density[NY_1 * (NX - 1) + j + 1])
+ rpCoef * phi[NY_1 * NX + j];
if (fabs(density[NY_1 * NX + j]) < fabs(DBL_MIN_TRIM)) density[NY_1 * NX + j] = 0;
}
rpCoef = 16. / (9. * HX * HY);
for (int i = 1; i < NX; ++i) {
for (int j = 1; j < NY; ++j) {
density[NY_1 * i + j] = -1. / 6. * (
prev_density[NY_1 * i + j - 1] + // left
prev_density[NY_1 * (i - 1) + j] + // upper
prev_density[NY_1 * i + j + 1] + // right
prev_density[NY_1 * (i + 1) + j] // bottom
) - 1. / 36. * (
prev_density[NY_1 * (i + 1) + j + 1] + // bottom right
prev_density[NY_1 * (i + 1) + j - 1] + // bottom left
prev_density[NY_1 * (i - 1) + j + 1] + // upper right
prev_density[NY_1 * (i - 1) + j - 1] // upper left
) + rpCoef * phi[NY_1 * i + j];
if (fabs(density[NY_1 * i + j]) < fabs(DBL_MIN_TRIM)) density[NY_1 * i + j] = 0;
}
}
++ic;
maxErr = FLT_MIN;
for (int i = 0; i < NX_1; ++i)
for (int j = 0; j < NY_1; ++j) {
double val = fabs(density[i * NY_1 + j] - prev_density[i * NY_1 + j]);
if (val > maxErr) maxErr = val;
}
//</editor-fold>
//<editor-fold desc="Calculate residual">
// point 1,1
rpCoef = HX * HY / 64.;
residual[NY_1 * NX + NY] = rpCoef * (
9. * density[NY_1 * NX + NY] +
3. * (
density[NY_1 * NX + NY - 1] +
density[NY_1 * (NX - 1) + NY]
) +
density[NY_1 * (NX - 1) + NY - 1]
) - phi[NY_1 * NX + NY];
// G3 -- (x_i, NY=D) -- top boundary
for (int i = 1; i < NX; ++i)
residual[NY_1 * i + NY] = rpCoef * (
18. * density[NY_1 * i + NY] +
6. * density[NY_1 * i + NY - 1] +
3. * (
density[NY_1 * (i + 1) + NY] +
density[NY_1 * (i - 1) + NY]
) +
density[NY_1 * (i + 1) + NY - 1] +
density[NY_1 * (i - 1) + NY - 1]
) - phi[NY_1 * i + NY];
// G2 -- (NX=B, y_j) -- right boundary
for (int j = 1; j < NY; ++j)
residual[NY_1 * NX + j] = rpCoef * (
18. * density[NY_1 * NX + j] +
6. * density[NY_1 * (NX - 1) + j] +
3. * (
density[NY_1 * NX + j - 1] +
density[NY_1 * NX + j + 1]
) +
density[NY_1 * (NX - 1) + j - 1] +
density[NY_1 * (NX - 1) + j + 1]
) - phi[NY_1 * NX + j];
// inner points
for (int i = 1; i < NX; ++i) {
for (int j = 1; j < NY; ++j) {
residual[NY_1 * i + j] = rpCoef * (
36. * density[NY_1 * i + j] +
6. * (
density[NY_1 * i + j - 1] + // left
density[NY_1 * (i - 1) + j] + // upper
density[NY_1 * i + j + 1] + // right
density[NY_1 * (i + 1) + j] // bottom
) +
prev_density[NY_1 * (i + 1) + j + 1] + // bottom right
prev_density[NY_1 * (i + 1) + j - 1] + // bottom left
prev_density[NY_1 * (i - 1) + j + 1] + // upper right
prev_density[NY_1 * (i - 1) + j - 1] // upper left
) - phi[NY_1 * i + j];
}
}
maxRes = FLT_MIN;
for (int i = 0; i < NX_1; ++i) {
for (int j = 0; j < NY_1; ++j) {
double val = fabs(residual[i * NY_1 + j]);
if (val > maxRes) maxRes = val;
}
}
//</editor-fold>
memcpy(prev_density, density, XY * sizeof(double));
}
sum_rho = calc_array_sum(density, NX_1, NY_1, 0);
sum_abs_rho = calc_array_sum(density, NX_1, NY_1, 1);
extrems = calc_array_extrems(density, NX_1, NY_1);
printf("tl = %d IterCount = %d Max(Residual) = %le Sum(Rho) = %le Sum(absRho) = %le "
"Min(Rho) = %le Max(Rho) = %le\n",
tl, ic, maxRes, sum_rho, sum_abs_rho, extrems[0], extrems[1]);
fflush(stdout);
if (tl % 1 == 0) {
print_data_to_files(phi, density, residual, tl);
double x_0 = get_center_x() + tl * TAU * func_u(0, 0, 0);
double y_0 = get_center_y() + tl * TAU * func_v(0, 0, 0);
int fixed_x = (int) (x_0 / HX);
int fixed_y = (int) (y_0 / HY);
print_line_along_x("rho", NX, NY, HX, HY, tl, A, C, x_0, y_0, TAU,
U, V, density, fixed_y);
print_line_along_y("rho", NX, NY, HX, HY, tl, A, C, x_0, y_0, TAU,
U, V, density, fixed_x);
}
}
double x_0 = get_center_x() + TIME_STEP_CNT * TAU * func_u(0, 0, 0);
double y_0 = get_center_y() + TIME_STEP_CNT * TAU * func_v(0, 0, 0);
int fixed_x = (int) (x_0 / HX);
int fixed_y = (int) (y_0 / HY);
/* print_line_along_x("rho", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, density, fixed_y);
print_line_along_y("rho", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, density, fixed_x);
*/
double *err = calc_error_22(HX, HY, TAU * TIME_STEP_CNT, density);
print_line_along_x("err", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, err, fixed_y);
print_line_along_y("err", NX, NY, HX, HY, TIME_STEP_CNT, A, C, x_0, y_0, TAU,
U, V, err, fixed_x);
extrems_err = calc_array_extrems(err, NX_1, NY_1);
err = calc_error_2(HX, HY, TAU * TIME_STEP_CNT, density);
double l1_err_vec = get_l1_norm_vec(NX_1, NY_1, err);
double l1_err_tr = get_l1_norm_int_trapezoidal(HX, HY, NX, NY, err); // note! a loop boundary
extrems = calc_array_extrems(density, NX_1, NY_1);
append_statistics(NX_1, NY_1, TAU, ic, l1_err_vec, l1_err_tr, maxRes, extrems, extrems_err, TIME_STEP_CNT);
delete[] prev_density;
delete[] phi;
delete[] err;
delete[] residual;
delete[] extrems;
delete[] extrems_err;
return density;
}
static double get_phi_integ_exact(int ii, int jj, double *density, double time_value) {
double x1 = 0.;
double y1 = 0.;
double x2 = 0.;
double y2 = 0.;
double x3 = 0.;
double y3 = 0.;
double x4 = 0.;
double y4 = 0.;
if (ii > 0 && ii < NX && jj > 0 && jj < NY) {
// p1 (x_{i-1/2}, y_{j-1/2})
x1 = A + ii * HX - HX / 2.;
y1 = C + jj * HY - HY / 2.;
// p2 (x_{i+1/2}, y_{j-1/2})
x2 = A + ii * HX + HX / 2.;
y2 = C + jj * HY - HY / 2.;
// p3 (x_{i+1/2}, y_{j+1/2})
x3 = A + ii * HX + HX / 2.;
y3 = C + jj * HY + HY / 2.;
// p4 (x_{i-1/2}, y_{j+1/2})
x4 = A + ii * HX - HX / 2.;
y4 = C + jj * HY + HY / 2.;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (ii == NX && jj == NY) { // point (1,1) omega_{i-1,j-1}
// p1 (x_{NX-1/2}, y_{NY-1/2})
x1 = B - HX / 2.;
y1 = D - HY / 2.;
// p2 (B, y_{NY-1/2})
x2 = B;
y2 = D - HY / 2.;
// p3 (B, D)
x3 = B;
y3 = D;
// p4 (x_{NX-1/2}, D)
x4 = B - HX / 2.;
y4 = D;
if (x1 <= A || x1 > B || x2 <= A || x2 > B || x3 <= A || x3 > B || x4 <= A || x4 > B
|| y1 <= C || y1 > D || y2 <= C || y2 > D || y3 <= C || y3 > D || y4 <= C || y4 > D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (jj == NY && ii > 0 && ii < NX) { // G3 -- top boundary
// p1 (x_{i-1/2}, y_{NY-1/2})
x1 = A + ii * HX - HX / 2.;
y1 = D - HY / 2.;
// p2 (x_{i+1/2}, y_{NY-1/2})
x2 = A + ii * HX + HX / 2.;
y2 = D - HY / 2.;
//p3 (x_{i+1/2}, D)
x3 = A + ii * HX + HX / 2.;
y3 = D;
//p4 (x_{i-1/2}, D)
x4 = A + ii * HX - HX / 2.;
y4 = D;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 > D || y2 <= C || y2 > D || y3 <= C || y3 > D || y4 <= C || y4 > D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (ii == NX && jj > 0 && jj < NY) { // G2 -- right boundary
// p1 (x_{NX-1/2}, y_{j-1/2})
x1 = B - HX / 2.;
y1 = C + jj * HY - HY / 2.;
// p2 (B, y_{j-1/2})
x2 = B;
y2 = C + jj * HY - HY / 2.;
// p3 (B, y_{j+1/2})
x3 = B;
y3 = C + jj * HY + HY / 2.;
// p4 (x_{NX-1/2}, y_{j+1/2})
x4 = B - HX / 2.;
y4 = C + jj * HY + HY / 2.;
if (x1 <= A || x1 > B || x2 <= A || x2 > B || x3 <= A || x3 > B || x4 <= A || x4 > B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else printf("ERROR! INDEX (K LEVEL) i=%d j=%d ", ii, jj);
double u = func_u(time_value, x1, y1);
double v = func_v(time_value, x1, y1);
x1 = x1 - TAU * u;
y1 = y1 - TAU * v;
u = func_u(time_value, x2, y2);
v = func_v(time_value, x2, y2);
x2 = x2 - TAU * u;
y2 = y2 - TAU * v;
u = func_u(time_value, x3, y3);
v = func_v(time_value, x3, y3);
x3 = x3 - TAU * u;
y3 = y3 - TAU * v;
u = func_u(time_value, x4, y4);
v = func_v(time_value, x4, y4);
x4 = x4 - TAU * u;
y4 = y4 - TAU * v;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D) {
printf("Time level %.8le! ERROR INDEX (K-1 LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4=%.8le\n ", time_value, ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
return 0.;// на всякий случай
}
int sq_i = (int) ((x1 - A) / HX);
int sq_j = (int) ((y1 - C) / HY);
// get right part for jakoby
int ip = ii - 1;
int jp = jj - 1;
// if (ip != sq_i || jp != sq_j) {
// printf("ALARM! (%d %d) != (%d %d)\n", ip, jp, sq_i, sq_j);
// }
double mes = HX * HY;
double dens = density[ip * NY_1 + jp]
+ density[(ip + 1) * NY_1 + jp]
+ density[(ip + 1) * NY_1 + jp + 1]
+ density[ip * NY_1 + jp + 1];
dens = dens / 4.;
double phi = dens * mes;
if (fabs(phi) < fabs(DBL_MIN_TRIM)) phi = 0;
return phi;
}
static double get_phi_integ_b_control_midpoint(int ii, int jj, double *density, double time_value) {
double x1 = 0.;
double y1 = 0.;
double x2 = 0.;
double y2 = 0.;
double x3 = 0.;
double y3 = 0.;
double x4 = 0.;
double y4 = 0.;
double phi = 0.;
if (ii > 0 && ii < NX && jj > 0 && jj < NY) {
// p1 (x_{i-1/2}, y_{j-1/2})
x1 = A + ii * HX - HX / 2.;
y1 = C + jj * HY - HY / 2.;
// p2 (x_{i+1/2}, y_{j-1/2})
x2 = A + ii * HX + HX / 2.;
y2 = C + jj * HY - HY / 2.;
// p3 (x_{i+1/2}, y_{j+1/2})
x3 = A + ii * HX + HX / 2.;
y3 = C + jj * HY + HY / 2.;
// p4 (x_{i-1/2}, y_{j+1/2})
x4 = A + ii * HX - HX / 2.;
y4 = C + jj * HY + HY / 2.;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (ii == NX && jj == NY) { // point (1,1) omega_{i-1,j-1}
// p1 (x_{NX-1/2}, y_{NY-1/2})
x1 = B - HX / 2.;
y1 = D - HY / 2.;
// p2 (B, y_{NY-1/2})
x2 = B;
y2 = D - HY / 2.;
// p3 (B, D)
x3 = B;
y3 = D;
// p4 (x_{NX-1/2}, D)
x4 = B - HX / 2.;
y4 = D;
if (x1 <= A || x1 > B || x2 <= A || x2 > B || x3 <= A || x3 > B || x4 <= A || x4 > B
|| y1 <= C || y1 > D || y2 <= C || y2 > D || y3 <= C || y3 > D || y4 <= C || y4 > D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (jj == NY && ii > 0 && ii < NX) { // G3 -- top boundary
// p1 (x_{i-1/2}, y_{NY-1/2})
x1 = A + ii * HX - HX / 2.;
y1 = D - HY / 2.;
// p2 (x_{i+1/2}, y_{NY-1/2})
x2 = A + ii * HX + HX / 2.;
y2 = D - HY / 2.;
//p3 (x_{i+1/2}, D)
x3 = A + ii * HX + HX / 2.;
y3 = D;
//p4 (x_{i-1/2}, D)
x4 = A + ii * HX - HX / 2.;
y4 = D;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 > D || y2 <= C || y2 > D || y3 <= C || y3 > D || y4 <= C || y4 > D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (ii == NX && jj > 0 && jj < NY) { // G2 -- right boundary
// p1 (x_{NX-1/2}, y_{j-1/2})
x1 = B - HX / 2.;
y1 = C + jj * HY - HY / 2.;
// p2 (B, y_{j-1/2})
x2 = B;
y2 = C + jj * HY - HY / 2.;
// p3 (B, y_{j+1/2})
x3 = B;
y3 = C + jj * HY + HY / 2.;
// p4 (x_{NX-1/2}, y_{j+1/2})
x4 = B - HX / 2.;
y4 = C + jj * HY + HY / 2.;
if (x1 <= A || x1 > B || x2 <= A || x2 > B || x3 <= A || x3 > B || x4 <= A || x4 > B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("ERROR INDEX (K LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else printf("ERROR! INDEX (K LEVEL) i=%d j=%d ", ii, jj);
double u = func_u(time_value, x1, y1);
double v = func_v(time_value, x1, y1);
x1 = x1 - TAU * u;
y1 = y1 - TAU * v;
u = func_u(time_value, x2, y2);
v = func_v(time_value, x2, y2);
x2 = x2 - TAU * u;
y2 = y2 - TAU * v;
u = func_u(time_value, x3, y3);
v = func_v(time_value, x3, y3);
x3 = x3 - TAU * u;
y3 = y3 - TAU * v;
u = func_u(time_value, x4, y4);
v = func_v(time_value, x4, y4);
x4 = x4 - TAU * u;
y4 = y4 - TAU * v;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D) {
//printf("Time level %.8le! ERROR INDEX (K-1 LEVEL) i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
// "x4=%.8le * y4=%.8le\n ", time_value, ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
phi = OUT_DENSITY;
return phi; //!!!!
}
int nx = IDEAL_SQ_SIZE_X;
int ny = IDEAL_SQ_SIZE_Y;
double x_step = 1. / nx;
double y_step = 1. / ny;
// get right part for jakoby
double mes = x_step * y_step;
for (int i = 0; i < nx; ++i) {
for (int j = 0; j < ny; ++j) {
double ideal_x = i * x_step + x_step / 2.;
double ideal_y = j * y_step + y_step / 2.;
double real_x = x1 + (x2 - x1) * ideal_x + (x4 - x1) * ideal_y
+ (x1 + x3 - x2 - x4) * ideal_x * ideal_y;
double real_y = y1 + (y2 - y1) * ideal_x + (y4 - y1) * ideal_y
+ (y1 + y3 - y2 - y4) * ideal_x * ideal_y;
// find out in which square real point was placed
int sq_i = (int) ((real_x - A) / HX);
int sq_j = (int) ((real_y - C) / HY);
double x = A + sq_i * HX;
double y = C + sq_j * HY;
double a11 = (x2 - x1) + (x1 + x3 - x2 - x4) * ideal_y;
double a12 = (x4 - x1) + (x1 + x3 - x2 - x4) * ideal_x;
double a21 = (y2 - y1) + (y1 + y3 - y2 - y4) * ideal_y;
double a22 = (y4 - y1) + (y1 + y3 - y2 - y4) * ideal_x;
double jakob = a11 * a22 - a21 * a12;
// formula 4
double dens = density[sq_i * NY_1 + sq_j] * (1 - (real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j] * ((real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j + 1] * ((real_x - x) / HX) * ((real_y - y) / HY)
+ density[sq_i * NY_1 + sq_j + 1] * (1 - (real_x - x) / HX) * ((real_y - y) / HY);
phi += mes * dens * jakob;
}
}
if (fabs(phi) < fabs(DBL_MIN_TRIM)) phi = 0;
return phi;
}
static double get_phi_integ_trapezium(int ii, int jj, double *density, double time_value) {
double x1 = 0.;
double y1 = 0.;
double x2 = 0.;
double y2 = 0.;
double x3 = 0.;
double y3 = 0.;
double x4 = 0.;
double y4 = 0.;
if (ii > 0 && ii < NX && jj > 0 && jj < NY) {
// p1 (x_{i-1/2}, y_{j-1/2})
x1 = A + ii * HX - HX / 2.;
y1 = C + jj * HY - HY / 2.;
// p2 (x_{i+1/2}, y_{j-1/2})
x2 = A + ii * HX + HX / 2.;
y2 = C + jj * HY - HY / 2.;
// p3 (x_{i+1/2}, y_{j+1/2})
x3 = A + ii * HX + HX / 2.;
y3 = C + jj * HY + HY / 2.;
// p4 (x_{i-1/2}, y_{j+1/2})
x4 = A + ii * HX - HX / 2.;
y4 = C + jj * HY + HY / 2.;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("ERROR INDEX i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (ii == NX && jj == NY) { // point (1,1) omega_{i-1,j-1}
// p1 (x_{NX-1/2}, y_{NY-1/2})
x1 = B - HX / 2.;
y1 = D - HY / 2.;
// p2 (B, y_{NY-1/2})
x2 = B;
y2 = D - HY / 2.;
// p3 (B, D)
x3 = B;
y3 = D;
// p4 (x_{NX-1/2}, D)
x4 = B - HX / 2.;
y4 = D;
if (x1 <= A || x1 > B || x2 <= A || x2 > B || x3 <= A || x3 > B || x4 <= A || x4 > B
|| y1 <= C || y1 > D || y2 <= C || y2 > D || y3 <= C || y3 > D || y4 <= C || y4 > D)
printf("ERROR INDEX i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (jj == NY && ii > 0 && ii < NX) { // G3 -- top boundary
// p1 (x_{i-1/2}, y_{NY-1/2})
x1 = A + ii * HX - HX / 2.;
y1 = D - HY / 2.;
// p2 (x_{i+1/2}, y_{NY-1/2})
x2 = A + ii * HX + HX / 2.;
y2 = D - HY / 2.;
//p3 (x_{i+1/2}, D)
x3 = A + ii * HX + HX / 2.;
y3 = D;
//p4 (x_{i-1/2}, D)
x4 = A + ii * HX - HX / 2.;
y4 = D;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 > D || y2 <= C || y2 > D || y3 <= C || y3 > D || y4 <= C || y4 > D)
printf("ERROR INDEX i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else if (ii == NX && jj > 0 && jj < NY) { // G2 -- right boundary
// p1 (x_{NX-1/2}, y_{j-1/2})
x1 = B - HX / 2.;
y1 = C + jj * HY - HY / 2.;
// p2 (B, y_{j-1/2})
x2 = B;
y2 = C + jj * HY - HY / 2.;
// p3 (B, y_{j+1/2})
x3 = B;
y3 = C + jj * HY + HY / 2.;
// p4 (x_{NX-1/2}, y_{j+1/2})
x4 = B - HX / 2.;
y4 = C + jj * HY + HY / 2.;
if (x1 <= A || x1 > B || x2 <= A || x2 > B || x3 <= A || x3 > B || x4 <= A || x4 > B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("ERROR INDEX i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4%.8le\n ", ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
}
else
printf("ERROR! INDEX i=%d j=%d ", ii, jj);
double u = func_u(time_value, x1, y1);
double v = func_v(time_value, x1, y1);
x1 = x1 - TAU * u;
y1 = y1 - TAU * v;
u = func_u(time_value, x2, y2);
v = func_v(time_value, x2, y2);
x2 = x2 - TAU * u;
y2 = y2 - TAU * v;
u = func_u(time_value, x3, y3);
v = func_v(time_value, x3, y3);
x3 = x3 - TAU * u;
y3 = y3 - TAU * v;
u = func_u(time_value, x4, y4);
v = func_v(time_value, x4, y4);
x4 = x4 - TAU * u;
y4 = y4 - TAU * v;
if (x1 <= A || x1 >= B || x2 <= A || x2 >= B || x3 <= A || x3 >= B || x4 <= A || x4 >= B
|| y1 <= C || y1 >= D || y2 <= C || y2 >= D || y3 <= C || y3 >= D || y4 <= C || y4 >= D)
printf("Time level %.8le! ERROR INDEX i=%d j=%d : x1=%.8le * y1=%.8le ** x2=%.8le * y2=%.8le ** x3=%.8le * y3=%.8le ** "
"x4=%.8le * y4=%.8le\n ", time_value, ii, jj, x1, y1, x2, y2, x3, y3, x4, y4);
int nx = IDEAL_SQ_SIZE_X;
int ny = IDEAL_SQ_SIZE_Y;
double x_step = 1. / nx;
double y_step = 1. / ny;
// get right part for jakoby
double phi = 0.;
double mes = x_step * y_step;
for (int i = 0; i < nx; ++i) {
for (int j = 0; j < ny; ++j) {
double ideal_x = i * x_step + x_step / 2.;
double ideal_y = j * y_step + y_step / 2.;
double a11 = (x2 - x1) + (x1 + x3 - x2 - x4) * ideal_y;
double a12 = (x4 - x1) + (x1 + x3 - x2 - x4) * ideal_x;
double a21 = (y2 - y1) + (y1 + y3 - y2 - y4) * ideal_y;
double a22 = (y4 - y1) + (y1 + y3 - y2 - y4) * ideal_x;
double jakob = a11 * a22 - a21 * a12;
// point (x_i,y_j)
ideal_x = i * x_step;
ideal_y = j * y_step;
double real_x = x1 + (x2 - x1) * ideal_x + (x4 - x1) * ideal_y
+ (x1 + x3 - x2 - x4) * ideal_x * ideal_y;
double real_y = y1 + (y2 - y1) * ideal_x + (y4 - y1) * ideal_y
+ (y1 + y3 - y2 - y4) * ideal_x * ideal_y;
if (real_x < A || real_y < C || real_x > B || real_y > D) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : REAL x=%.8le * y=%.8le ** IDEAL x=%.8le * y=%.8le \n",
time_value, ii, jj, real_x, real_y, ideal_x, ideal_y);
printf("1: %.8le * %.8le ** 2: %.8le * %.8le ** 3: %.8le * %.8le ** 4: %.8le * %.8le\n",
x1, y1, x2, y2, x3, y3, x4, y4);
}
// find out in which square real point was placed
int sq_i = (int) ((real_x - A) / HX);
int sq_j = (int) ((real_y - C) / HY);
if (sq_i < 0 || sq_j < 0 || sq_i > NX - 1 || sq_j > NY - 1) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : i*=%d j*=%d\n", time_value,
ii, jj, sq_i, sq_j);
}
double x = A + sq_i * HX;
double y = C + sq_j * HY;
// formula 4
double dens_1 = density[sq_i * NY_1 + sq_j] * (1 - (real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j] * ((real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j + 1] * ((real_x - x) / HX) * ((real_y - y) / HY)
+ density[sq_i * NY_1 + sq_j + 1] * (1 - (real_x - x) / HX) * ((real_y - y) / HY);
// point (x_{i+1},y_j)
ideal_x = (i + 1) * x_step;
ideal_y = j * y_step;
real_x = x1 + (x2 - x1) * ideal_x + (x4 - x1) * ideal_y
+ (x1 + x3 - x2 - x4) * ideal_x * ideal_y;
real_y = y1 + (y2 - y1) * ideal_x + (y4 - y1) * ideal_y
+ (y1 + y3 - y2 - y4) * ideal_x * ideal_y;
if (real_x < A || real_y < C || real_x > B || real_y > D) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : REAL x=%.8le * y=%.8le ** IDEAL x=%.8le * y=%.8le \n",
time_value, ii, jj, real_x, real_y, ideal_x, ideal_y);
printf("1: %.8le * %.8le ** 2: %.8le * %.8le ** 3: %.8le * %.8le ** 4: %.8le * %.8le\n",
x1, y1, x2, y2, x3, y3, x4, y4);
}
// find out in which square real point was placed
sq_i = (int) ((real_x - A) / HX);
sq_j = (int) ((real_y - C) / HY);
if (sq_i < 0 || sq_j < 0 || sq_i > NX - 1 || sq_j > NY - 1) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : i*=%d j*=%d\n", time_value,
ii, jj, sq_i, sq_j);
}
x = A + sq_i * HX;
y = C + sq_j * HY;
// formula 4
double dens_2 = density[sq_i * NY_1 + sq_j] * (1 - (real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j] * ((real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j + 1] * ((real_x - x) / HX) * ((real_y - y) / HY)
+ density[sq_i * NY_1 + sq_j + 1] * (1 - (real_x - x) / HX) * ((real_y - y) / HY);
// point (x_{i+1},y_{j+1})
ideal_x = (i + 1) * x_step;
ideal_y = (j + 1) * y_step;
real_x = x1 + (x2 - x1) * ideal_x + (x4 - x1) * ideal_y
+ (x1 + x3 - x2 - x4) * ideal_x * ideal_y;
real_y = y1 + (y2 - y1) * ideal_x + (y4 - y1) * ideal_y
+ (y1 + y3 - y2 - y4) * ideal_x * ideal_y;
if (real_x < A || real_y < C || real_x > B || real_y > D) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : REAL x=%.8le * y=%.8le ** IDEAL x=%.8le * y=%.8le \n",
time_value, ii, jj, real_x, real_y, ideal_x, ideal_y);
printf("1: %.8le * %.8le ** 2: %.8le * %.8le ** 3: %.8le * %.8le ** 4: %.8le * %.8le\n",
x1, y1, x2, y2, x3, y3, x4, y4);
}
// find out in which square real point was placed
sq_i = (int) ((real_x - A) / HX);
sq_j = (int) ((real_y - C) / HY);
if (sq_i < 0 || sq_j < 0 || sq_i > NX - 1 || sq_j > NY - 1) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : i*=%d j*=%d\n", time_value,
ii, jj, sq_i, sq_j);
}
x = A + sq_i * HX;
y = C + sq_j * HY;
// formula 4
double dens_3 = density[sq_i * NY_1 + sq_j] * (1 - (real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j] * ((real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j + 1] * ((real_x - x) / HX) * ((real_y - y) / HY)
+ density[sq_i * NY_1 + sq_j + 1] * (1 - (real_x - x) / HX) * ((real_y - y) / HY);
// point (x_i,y_{j+1})
ideal_x = i * x_step;
ideal_y = (j + 1) * y_step;
real_x = x1 + (x2 - x1) * ideal_x + (x4 - x1) * ideal_y
+ (x1 + x3 - x2 - x4) * ideal_x * ideal_y;
real_y = y1 + (y2 - y1) * ideal_x + (y4 - y1) * ideal_y
+ (y1 + y3 - y2 - y4) * ideal_x * ideal_y;
if (real_x < A || real_y < C || real_x > B || real_y > D) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : REAL x=%.8le * y=%.8le ** IDEAL x=%.8le * y=%.8le \n",
time_value, ii, jj, real_x, real_y, ideal_x, ideal_y);
printf("1: %.8le * %.8le ** 2: %.8le * %.8le ** 3: %.8le * %.8le ** 4: %.8le * %.8le\n",
x1, y1, x2, y2, x3, y3, x4, y4);
}
// find out in which square real point was placed
sq_i = (int) ((real_x - A) / HX);
sq_j = (int) ((real_y - C) / HY);
if (sq_i < 0 || sq_j < 0 || sq_i > NX - 1 || sq_j > NY - 1) {
printf("Time level %.8le! ERROR INDEX i=%d j=%d : i*=%d j*=%d\n", time_value,
ii, jj, sq_i, sq_j);
}
x = A + sq_i * HX;
y = C + sq_j * HY;
// formula 4
double dens_4 = density[sq_i * NY_1 + sq_j] * (1 - (real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j] * ((real_x - x) / HX) * (1 - (real_y - y) / HY)
+ density[(sq_i + 1) * NY_1 + sq_j + 1] * ((real_x - x) / HX) * ((real_y - y) / HY)
+ density[sq_i * NY_1 + sq_j + 1] * (1 - (real_x - x) / HX) * ((real_y - y) / HY);
phi += (dens_1 + dens_2 + dens_3 + dens_4) * jakob;
}
}
phi = 0.25 * phi * mes;
if (fabs(phi) < fabs(DBL_MIN_TRIM)) phi = 0;
return phi;
}
static void
func_f(FLOAT x, FLOAT y, FLOAT z, FLOAT *value)
{
func_u(x, y, z, value);
*value = 12. * M_PI * M_PI * *value + a * *value;
}
