/* ************************************************************************* */
int compare_array_3d(N_array_3d * a, N_array_3d * b)
{
int rows, cols, depths, type;
int i, j, k, res = 0;
rows = a->rows;
cols = a->cols;
depths = a->depths;
type = N_get_array_3d_type(a);
#pragma omp parallel for private (i, j, k) shared (depths, rows, cols, type, a, b) reduction(+:res)
for (k = 0; k < depths; k++) {
for (i = 0; i < rows; i++) {
for (j = 0; j < cols; j++) {
if (type == FCELL_TYPE) {
if (N_get_array_3d_f_value(a, i, j, k) !=
N_get_array_3d_f_value(b, i, j, k))
res++;
}
if (type == DCELL_TYPE) {
if (N_get_array_3d_d_value(a, i, j, k) !=
N_get_array_3d_d_value(b, i, j, k))
res++;
}
}
}
}
return res;
}
/* ************************************************************************* */
int fill_array_3d(N_array_3d * a)
{
int rows, cols, depths, type;
int i, j, k, res = 0;
cols = a->cols;
rows = a->rows;
depths = a->depths;
type = N_get_array_3d_type(a);
#pragma omp parallel for private (i, j, k) shared (depths, rows, cols, type, a) reduction(+:res)
for (k = 0; k < depths; k++) {
for (j = 0; j < rows; j++) {
for (i = 0; i < cols; i++) {
if (type == FCELL_TYPE) {
N_put_array_3d_f_value(a, i, j, k,
(float)i * (float)j * (float)k);
if (N_get_array_3d_f_value(a, i, j, k) !=
(float)i * (float)j * (float)k)
res++;
}
if (type == DCELL_TYPE) {
N_put_array_3d_d_value(a, i, j, k,
(double)i * (double)j * (double)k);
if (N_get_array_3d_d_value(a, i, j, k) !=
(double)i * (double)j * (double)k)
res++;
}
}
}
}
return res;
}
/* **************************************************************** */
int make_les_entry_3d(int i, int j, int k, int offset_i, int offset_j,
int offset_k, int count, int pos, N_les * les,
G_math_spvector * spvect, N_array_3d * cell_count,
N_array_3d * status, N_array_3d * start_val,
double entry, int cell_type)
{
int K;
int di = offset_i;
int dj = offset_j;
int dk = offset_k;
K = (int)N_get_array_3d_d_value(cell_count, i + di, j + dj, k + dk) -
(int)N_get_array_3d_d_value(cell_count, i, j, k);
if (cell_type == N_CELL_ACTIVE) {
if ((int)N_get_array_3d_d_value(status, i + di, j + dj, k + dk) >
N_CELL_ACTIVE &&
(int)N_get_array_3d_d_value(status, i + di, j + dj,
k + dk) < N_MAX_CELL_STATE)
les->b[count] -=
N_get_array_3d_d_value(start_val, i + di, j + dj,
k + dk) * entry;
else if ((int)N_get_array_3d_d_value(status, i + di, j + dj, k + dk)
== N_CELL_ACTIVE) {
if ((count + K) >= 0 && (count + K) < les->cols) {
G_debug(5,
" make_les_entry_3d: (N_CELL_ACTIVE) create matrix entry at row[%i] col[%i] value %g\n",
count, count + K, entry);
pos++;
if (les->type == N_SPARSE_LES) {
spvect->index[pos] = count + K;
spvect->values[pos] = entry;
}
else {
les->A[count][count + K] = entry;
}
}
}
}
else if (cell_type == N_CELL_DIRICHLET) {
if ((int)N_get_array_3d_d_value(status, i + di, j + dj, k + dk)
!= N_CELL_INACTIVE) {
if ((count + K) >= 0 && (count + K) < les->cols) {
G_debug(5,
" make_les_entry_3d: (N_CELL_DIRICHLET) create matrix entry at row[%i] col[%i] value %g\n",
count, count + K, entry);
pos++;
if (les->type == N_SPARSE_LES) {
spvect->index[pos] = count + K;
spvect->values[pos] = entry;
}
else {
les->A[count][count + K] = entry;
}
}
}
}
return pos;
}
/*!
* \brief Write info and content of the array data to stdout
*
* Offsets are ignored
*
* \param data N_array_2d *
* \return void
* */
void N_print_array_3d(N_array_3d * data)
{
int i, j, k;
N_print_array_3d_info(data);
for (k = 0; k < data->depths; k++) {
for (j = 0; j < data->rows; j++) {
for (i = 0; i < data->cols; i++) {
if (data->type == FCELL_TYPE)
printf("%6.6f ", N_get_array_3d_f_value(data, i, j, k));
else if (data->type == DCELL_TYPE)
printf("%6.6f ", N_get_array_3d_d_value(data, i, j, k));
}
printf("\n");
}
printf("\n");
}
printf("\n");
return;
}
/*! \brief This is just a placeholder
*
* */
N_data_star *N_callback_solute_transport_3d(void *solutedata,
N_geom_data * geom, int col,
int row, int depth)
{
double Df_e = 0, Df_w = 0, Df_n = 0, Df_s = 0, Df_t = 0, Df_b = 0;
double dx, dy, dz, Az;
double diff_x, diff_y, diff_z;
double diff_xw, diff_yn;
double diff_xe, diff_ys;
double diff_zt, diff_zb;
double cin = 0, cg, cg_start;
double R, nf, cs, q;
double C, W, E, N, S, T, B, V;
double vw = 0, ve = 0, vn = 0, vs = 0, vt = 0, vb = 0;
double Ds_w = 0, Ds_e = 0, Ds_n = 0, Ds_s = 0, Ds_t = 0, Ds_b = 0;
double Dw = 0, De = 0, Dn = 0, Ds = 0, Dt = 0, Db = 0;
double rw = 0.5, re = 0.5, rn = 0.5, rs = 0.5, rt = 0.5, rb = 0.5;
N_solute_transport_data3d *data = NULL;
N_data_star *mat_pos;
N_gradient_3d grad;
/*cast the void pointer to the right data structure */
data = (N_solute_transport_data3d *) solutedata;
N_get_gradient_3d(data->grad, &grad, col, row, depth);
dx = geom->dx;
dy = geom->dy;
dz = geom->dz;
Az = N_get_geom_data_area_of_cell(geom, row);
/*read the data from the arrays */
cg_start = N_get_array_3d_d_value(data->c_start, col, row, depth);
cg = N_get_array_3d_d_value(data->c, col, row, depth);
/*get the surrounding diffusion tensor entries */
diff_x = N_get_array_3d_d_value(data->diff_x, col, row, depth);
diff_y = N_get_array_3d_d_value(data->diff_y, col, row, depth);
diff_z = N_get_array_3d_d_value(data->diff_z, col, row, depth);
diff_xw = N_get_array_3d_d_value(data->diff_x, col - 1, row, depth);
diff_xe = N_get_array_3d_d_value(data->diff_x, col + 1, row, depth);
diff_yn = N_get_array_3d_d_value(data->diff_y, col, row - 1, depth);
diff_ys = N_get_array_3d_d_value(data->diff_y, col, row + 1, depth);
diff_zt = N_get_array_3d_d_value(data->diff_z, col, row, depth + 1);
diff_zb = N_get_array_3d_d_value(data->diff_z, col, row, depth - 1);
/* calculate the diffusion on the cell borders using the harmonical mean */
Df_w = N_calc_harmonic_mean(diff_xw, diff_x);
Df_e = N_calc_harmonic_mean(diff_xe, diff_x);
Df_n = N_calc_harmonic_mean(diff_yn, diff_y);
Df_s = N_calc_harmonic_mean(diff_ys, diff_y);
Df_t = N_calc_harmonic_mean(diff_zt, diff_z);
Df_b = N_calc_harmonic_mean(diff_zb, diff_z);
/* calculate the dispersion */
/*todo */
/* calculate the velocity parts with full upwinding scheme */
vw = grad.WC;
ve = grad.EC;
vn = grad.NC;
vs = grad.SC;
vt = grad.TC;
vb = grad.BC;
/* put the diffusion and dispersion together */
Dw = ((Df_w + Ds_w)) / dx;
De = ((Df_e + Ds_e)) / dx;
Dn = ((Df_n + Ds_n)) / dy;
Ds = ((Df_s + Ds_s)) / dy;
Dt = ((Df_t + Ds_t)) / dz;
Db = ((Df_b + Ds_b)) / dz;
rw = N_exp_upwinding(-1 * vw, dx, Dw);
re = N_exp_upwinding(ve, dx, De);
rs = N_exp_upwinding(-1 * vs, dy, Ds);
rn = N_exp_upwinding(vn, dy, Dn);
rb = N_exp_upwinding(-1 * vb, dz, Dn);
rt = N_exp_upwinding(vt, dz, Dn);
/*mass balance center cell to western cell */
W = -1 * (Dw) * dy * dz - vw * (1 - rw) * dy * dz;
/*mass balance center cell to eastern cell */
E = -1 * (De) * dy * dz + ve * (1 - re) * dy * dz;
/*mass balance center cell to southern cell */
S = -1 * (Ds) * dx * dz - vs * (1 - rs) * dx * dz;
/*mass balance center cell to northern cell */
N = -1 * (Dn) * dx * dz + vn * (1 - rn) * dx * dz;
/*mass balance center cell to bottom cell */
B = -1 * (Db) * Az - vb * (1 - rb) * Az;
/*mass balance center cell to top cell */
T = -1 * (Dt) * Az + vt * (1 - rt) * Az;
/* Retardation */
R = N_get_array_3d_d_value(data->R, col, row, depth);
/* Inner sources */
cs = N_get_array_3d_d_value(data->cs, col, row, depth);
/* effective porosity */
nf = N_get_array_3d_d_value(data->nf, col, row, depth);
/* groundwater sources and sinks */
q = N_get_array_3d_d_value(data->q, col, row, depth);
/* concentration of influent water */
cin = N_get_array_3d_d_value(data->cin, col, row, depth);
/*the diagonal entry of the matrix */
C = ((Dw - vw) * dy * dz +
(De + ve) * dy * dz +
(Ds - vs) * dx * dz +
(Dn + vn) * dx * dz +
(Db - vb) * Az + (Dt + vt) * Az + Az * dz * R / data->dt - q / nf);
/*the entry in the right side b of Ax = b */
V = (cs + cg_start * Az * dz * R / data->dt - q / nf * cin);
/*
* printf("nf %g\n", nf);
* printf("q %g\n", q);
* printf("cs %g\n", cs);
* printf("cin %g\n", cin);
* printf("cg %g\n", cg);
* printf("cg_start %g\n", cg_start);
* printf("Az %g\n", Az);
* printf("z %g\n", z);
* printf("R %g\n", R);
* printf("dt %g\n", data->dt);
*/
G_debug(6, "N_callback_solute_transport_3d: called [%i][%i][%i]", row,
col, depth);
/*create the 7 point star entries */
mat_pos = N_create_7star(C, W, E, N, S, T, B, V);
return mat_pos;
}
/*!
* \brief Integrate Dirichlet or Transmission boundary conditions into the les (3d)
*
* Dirichlet and Transmission boundary conditions will be integrated into
* the provided linear equation system. This is meaningfull if
* the les was created with #N_assemble_les_2d_dirichlet, because in
* this case Dirichlet boundary conditions are not automatically included.
*
* The provided les will be modified:
*
* Ax = b will be splitted into Ax_u + Ax_d = b
*
* x_u - the unknowns
* x_d - the Dirichlet cells
*
* Ax_u = b -Ax_d will be computed. Then the matrix A will be modified to
*
* | A_u 0 | x_u
* | 0 I | x_d
*
* \param les N_les* -- the linear equation system
* \param geom N_geom_data* -- geometrical data information
* \param status N_array_2d* -- the status array containing the cell types
* \param start_val N_array_2d* -- an array with start values
* \return int -- 1 = success, 0 = failure
* */
int N_les_integrate_dirichlet_3d(N_les * les, N_geom_data * geom,
N_array_3d * status, N_array_3d * start_val)
{
int rows, cols, depths;
int count = 0;
int i, j, x, y, z, stat;
double *dvect1;
double *dvect2;
G_debug(2,
"N_les_integrate_dirichlet_3d: integrating the dirichlet boundary condition");
rows = geom->rows;
cols = geom->cols;
depths = geom->depths;
/*we nned to additional vectors */
dvect1 = (double *)G_calloc(les->cols, sizeof(double));
dvect2 = (double *)G_calloc(les->cols, sizeof(double));
/*fill the first one with the x vector data of Dirichlet cells */
count = 0;
for (z = 0; z < depths; z++) {
for (y = 0; y < rows; y++) {
for (x = 0; x < cols; x++) {
stat = (int)N_get_array_3d_d_value(status, x, y, z);
if (stat > N_CELL_ACTIVE && stat < N_MAX_CELL_STATE) {
dvect1[count] =
N_get_array_3d_d_value(start_val, x, y, z);
count++;
}
else if (stat == N_CELL_ACTIVE) {
dvect1[count] = 0.0;
count++;
}
}
}
}
#pragma omp parallel default(shared)
{
/*perform the matrix vector product and */
if (les->type == N_SPARSE_LES)
G_math_Ax_sparse(les->Asp, dvect1, dvect2, les->rows);
else
G_math_d_Ax(les->A, dvect1, dvect2, les->rows, les->cols);
#pragma omp for schedule (static) private(i)
for (i = 0; i < les->cols; i++)
les->b[i] = les->b[i] - dvect2[i];
}
/*now set the Dirichlet cell rows and cols to zero and the
* diagonal entry to 1*/
count = 0;
for (z = 0; z < depths; z++) {
for (y = 0; y < rows; y++) {
for (x = 0; x < cols; x++) {
stat = (int)N_get_array_3d_d_value(status, x, y, z);
if (stat > N_CELL_ACTIVE && stat < N_MAX_CELL_STATE) {
if (les->type == N_SPARSE_LES) {
/*set the rows to zero */
for (i = 0; i < les->Asp[count]->cols; i++)
les->Asp[count]->values[i] = 0.0;
/*set the cols to zero */
for (i = 0; i < les->rows; i++) {
for (j = 0; j < les->Asp[i]->cols; j++) {
if (les->Asp[i]->index[j] == count)
les->Asp[i]->values[j] = 0.0;
}
}
/*entry on the diagonal */
les->Asp[count]->values[0] = 1.0;
}
else {
/*set the rows to zero */
for (i = 0; i < les->cols; i++)
les->A[count][i] = 0.0;
/*set the cols to zero */
for (i = 0; i < les->rows; i++)
les->A[i][count] = 0.0;
/*entry on the diagonal */
les->A[count][count] = 1.0;
}
}
count++;
}
}
}
return 0;
}
/*!
* \brief Assemble a linear equation system (les) based on 3d location data (g3d)
*
* The linear equation system type can be set to N_NORMAL_LES to create a regular
* matrix, or to N_SPARSE_LES to create a sparse matrix. This function returns
* a new created linear equation system which can be solved with
* linear equation solvers. An 3d array with start values and an 3d status array
* must be provided as well as the location geometry and a void pointer to data
* passed to the callback which creates the les row entries. This callback
* must be defined in the N_les_callback_3d structure.
*
* The creation of the les is parallelized with OpenMP.
* If you implement new callbacks, please make sure that the
* function calls are thread safe.
*
* the les can be created in two ways, with dirichlet and similar cells and without them,
* to spare some memory. If the les is created with dirichlet cell, the dirichlet boundary condition
* must be added.
*
* \param les_type int
* \param geom N_geom_data*
* \param status N_array_3d *
* \param start_val N_array_3d *
* \param data void *
* \param call N_les_callback_3d *
* \param cell_type int -- les assemble based on N_CELL_ACTIVE or N_CELL_DIRICHLET
* \return N_les *
* */
N_les *N_assemble_les_3d_param(int les_type, N_geom_data * geom,
N_array_3d * status, N_array_3d * start_val,
void *data, N_les_callback_3d * call,
int cell_type)
{
int i, j, k, count = 0, pos = 0;
int cell_type_count = 0;
N_array_3d *cell_count;
N_les *les = NULL;
int **index_ij;
G_debug(2,
"N_assemble_les_3d: starting to assemble the linear equation system");
cell_count =
N_alloc_array_3d(geom->cols, geom->rows, geom->depths, 1, DCELL_TYPE);
/* First count the number of valid cells and save
* each number in a new 3d array. Those numbers are used
* to create the linear equation system.*/
if (cell_type == N_CELL_DIRICHLET) {
/* include dirichlet cells in the les */
for (k = 0; k < geom->depths; k++) {
for (j = 0; j < geom->rows; j++) {
for (i = 0; i < geom->cols; i++) {
/*use all non-inactive cells for les creation */
if (N_CELL_INACTIVE <
(int)N_get_array_3d_d_value(status, i, j, k) &&
(int)N_get_array_3d_d_value(status, i, j,
k) < N_MAX_CELL_STATE)
cell_type_count++;
}
}
}
}
else {
/*use only active cell in the les */
for (k = 0; k < geom->depths; k++) {
for (j = 0; j < geom->rows; j++) {
for (i = 0; i < geom->cols; i++) {
/*count only active cells */
if (N_CELL_ACTIVE
== (int)N_get_array_3d_d_value(status, i, j, k))
cell_type_count++;
}
}
}
}
G_debug(2,
"N_assemble_les_3d: number of used cells %i\n", cell_type_count);
if (cell_type_count == 0.0)
G_fatal_error
("Not enough active cells [%i] to create the linear equation system. Check the cell status. Only active cells (value = 1) are used to create the equation system.",
cell_type_count);
/* allocate the memory for the linear equation system (les).
* Only valid cells are used to create the les. */
les = N_alloc_les_Ax_b(cell_type_count, les_type);
index_ij = (int **)G_calloc(cell_type_count, sizeof(int *));
for (i = 0; i < cell_type_count; i++)
index_ij[i] = (int *)G_calloc(3, sizeof(int));
count = 0;
/*count the number of cells which should be used to create the linear equation system */
/*save the k, i and j indices and create a ordered numbering */
for (k = 0; k < geom->depths; k++) {
for (j = 0; j < geom->rows; j++) {
for (i = 0; i < geom->cols; i++) {
if (cell_type == N_CELL_DIRICHLET) {
if (N_CELL_INACTIVE <
(int)N_get_array_3d_d_value(status, i, j, k) &&
(int)N_get_array_3d_d_value(status, i, j,
k) < N_MAX_CELL_STATE) {
N_put_array_3d_d_value(cell_count, i, j, k, count);
index_ij[count][0] = i;
index_ij[count][1] = j;
index_ij[count][2] = k;
count++;
G_debug(5,
"N_assemble_les_3d: non-inactive cells count %i at pos x[%i] y[%i] z[%i]\n",
count, i, j, k);
}
}
else if (N_CELL_ACTIVE ==
(int)N_get_array_3d_d_value(status, i, j, k)) {
N_put_array_3d_d_value(cell_count, i, j, k, count);
index_ij[count][0] = i;
index_ij[count][1] = j;
index_ij[count][2] = k;
count++;
G_debug(5,
"N_assemble_les_3d: active cells count %i at pos x[%i] y[%i] z[%i]\n",
count, i, j, k);
}
}
}
}
G_debug(2, "N_assemble_les_3d: starting the parallel assemble loop");
#pragma omp parallel for private(i, j, k, pos, count) schedule(static)
for (count = 0; count < cell_type_count; count++) {
i = index_ij[count][0];
j = index_ij[count][1];
k = index_ij[count][2];
/*create the entries for the */
N_data_star *items = call->callback(data, geom, i, j, k);
G_math_spvector *spvect = NULL;
/*allocate a sprase vector */
if (les_type == N_SPARSE_LES)
spvect = G_math_alloc_spvector(items->count);
/* initial conditions */
les->x[count] = N_get_array_3d_d_value(start_val, i, j, k);
/* the entry in the vector b */
les->b[count] = items->V;
/* pos describes the position in the sparse vector.
* the first entry is always the diagonal entry of the matrix*/
pos = 0;
if (les_type == N_SPARSE_LES) {
spvect->index[pos] = count;
spvect->values[pos] = items->C;
}
else {
les->A[count][count] = items->C;
}
/* western neighbour, entry is col - 1 */
if (i > 0) {
pos =
make_les_entry_3d(i, j, k, -1, 0, 0, count, pos, les, spvect,
cell_count, status, start_val, items->W,
cell_type);
}
/* eastern neighbour, entry col + 1 */
if (i < geom->cols - 1) {
pos = make_les_entry_3d(i, j, k, 1, 0, 0, count, pos, les, spvect,
cell_count, status, start_val, items->E,
cell_type);
}
/* northern neighbour, entry row -1 */
if (j > 0) {
pos =
make_les_entry_3d(i, j, k, 0, -1, 0, count, pos, les, spvect,
cell_count, status, start_val, items->N,
cell_type);
}
/* southern neighbour, entry row +1 */
if (j < geom->rows - 1) {
pos = make_les_entry_3d(i, j, k, 0, 1, 0, count, pos, les, spvect,
cell_count, status, start_val, items->S,
cell_type);
}
/*only for a 7 star entry needed */
if (items->type == N_7_POINT_STAR || items->type == N_27_POINT_STAR) {
/* the upper cell (top), entry depth + 1 */
if (k < geom->depths - 1) {
pos =
make_les_entry_3d(i, j, k, 0, 0, 1, count, pos, les,
spvect, cell_count, status, start_val,
items->T, cell_type);
}
/* the lower cell (bottom), entry depth - 1 */
if (k > 0) {
pos =
make_les_entry_3d(i, j, k, 0, 0, -1, count, pos, les,
spvect, cell_count, status, start_val,
items->B, cell_type);
}
}
/*How many entries in the les */
if (les->type == N_SPARSE_LES) {
spvect->cols = pos + 1;
G_math_add_spvector(les->Asp, spvect, count);
}
if (items)
G_free(items);
}
N_free_array_3d(cell_count);
for (i = 0; i < cell_type_count; i++)
G_free(index_ij[i]);
G_free(index_ij);
return les;
}
