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3D_SingStokes_Taylor_case_2.cpp
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3D_SingStokes_Taylor_case_2.cpp
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#include <iostream>
#include <vector>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <fstream>
#include <sys/times.h>
using namespace std;
static const int N = 81920; // N points in each direction
static const int P = 8; // order of Taylor approximation
static const int Pflat = (P + 1)*(P + 2)*(P + 3)/6;
static const size_t N_cube = N ; // N_cube points total
static const int N0 = 2000;
static const double sq_theta = 0.64; // theta = 0.1
const bool UseSleep = false; // for testing memory usage purpose
int max_level = 0;
//**********************************************************//
struct vec_3d
{
double val_Str[3];
double val_Sto[3];
};
//**************//
struct xyz // particle coordinates (physical)
{
double* x;
double* y;
double* z;
size_t* index;
size_t* old_index;
size_t size;
xyz(size_t N_cube_in)
{
size = N_cube_in;
x = new double[size];
y = new double[size];
z = new double[size];
index = new size_t[size];
old_index = new size_t[size];
}
~xyz()
{
delete[] x;
delete[] y;
delete[] z;
delete[] index;
delete[] old_index;
}
};
//**************//
struct panel
{
size_t members[2];
double xinterval[2];
double yinterval[2];
double zinterval[2];
double xc; // panel center x coordinate
double yc; // panel center y coordinate
double zc; // panel center z coordinate
vector<size_t> children;
double MAC; // r^2 / theta^2
double moments_Sto[3][Pflat];
double moments_Str[3][3][Pflat];
int moment_flag;
panel() // initialization
{
moment_flag = 0;
members[0] = 0;
members[1] = -1;
for(size_t index = 0; index < 3; index ++)
{
for (size_t kk = 0; kk < Pflat + 1; kk++)
moments_Sto[index][kk] = 0.0;
}
for(size_t index1 = 0; index1 < 3; index1 ++)
{
for(size_t index2 = 0; index2 < 3; index2 ++)
{
for (size_t kk = 0; kk < Pflat + 1; kk++)
moments_Str[index1][index2][kk] = 0.0;
}
}
}
};
//**************//
vector<panel> tree;
vector<size_t> leaf;
static size_t node_count = 0;
//*****************************************************************************//
long getTickCount()
{
tms tm;
return times(&tm);
}
//*****************************************************************************//
double delta(int i, int j)
{
double d = 0.0;
if (fabs(i - j) < 1e-5)
d = 1.0;
return d;
}
//*****************************************************************************//
void min_max(struct xyz &s, double min[], double max[])
{
for(int i = 0; i< N_cube; i++)
{
if (s.x[i] < min[0])
min[0] = s.x[i];
if (s.y[i] < min[1])
min[1] = s.y[i];
if (s.z[i] < min[2])
min[2] = s.z[i];
if (s.x[i] > max[0])
max[0] = s.x[i];
if (s.y[i] > max[1])
max[1] = s.y[i];
if (s.z[i] > max[2])
max[2] = s.z[i];
}
}
//*****************************************************************************//
void build_tree_init(struct xyz &s)
{
panel temp_panel;
double min[3] = {10};
double max[3] = {-10};
min_max(s, min,max);
// indices of particles belonging to panel
temp_panel.members[0] = 0;
temp_panel.members[1] = N_cube - 1;
double r2 = (max[0] - min[0])*(max[0] - min[0]) + (max[1] - min[1])*(max[1] - min[1]) + (max[2] - min[2])*(max[2] - min[2]);
temp_panel.xinterval[0] = min[0]; // interval defining the panel
temp_panel.xinterval[1] = max[0];
temp_panel.yinterval[0] = min[1];
temp_panel.yinterval[1] = max[1];
temp_panel.zinterval[0] = min[2];
temp_panel.zinterval[1] = max[2]; // r = sqrt(3) / 2, r^2 = 3 / 4 = 0.75;
temp_panel.xc = 1;
temp_panel.yc = 0;
temp_panel.zc = -2;
temp_panel.MAC = r2 / sq_theta; // MAC = r^2 / theta^2
tree.push_back(temp_panel);
node_count = 1;
}
//*****************************************************************************//
void Swap(size_t i, size_t j, struct xyz &s)
{
if (i == j)
return;
double x = s.x[i];
double y = s.y[i];
double z = s.z[i];
size_t index = s.index[i];
size_t old_index = s.old_index[i];
s.x[i] = s.x[j];
s.y[i] = s.y[j];
s.z[i] = s.z[j];
s.index[i] = s.index[j];
s.old_index[i] = s.old_index[j];
s.x[j] = x;
s.y[j] = y;
s.z[j] = z;
s.index[j] = index;
s.old_index[j] = old_index;
}
//*****************************************************************************//
void split_tree_node(size_t panel_index, struct xyz &particles)
{
panel child[8];
double tp_x0 = tree[panel_index].xinterval[0];
double tp_x1 = tree[panel_index].xinterval[1];
double tp_y0 = tree[panel_index].yinterval[0];
double tp_y1 = tree[panel_index].yinterval[1];
double tp_z0 = tree[panel_index].zinterval[0];
double tp_z1 = tree[panel_index].zinterval[1];
double midpointx = (tp_x0 + tp_x1) / 2.0;
double midpointy = (tp_y0 + tp_y1) / 2.0;
double midpointz = (tp_z0 + tp_z1) / 2.0;
double xc0 = (tp_x0 + midpointx) / 2.0;
double xc1 = (tp_x1 + midpointx) / 2.0;
double yc0 = (tp_y0 + midpointy) / 2.0;
double yc1 = (tp_y1 + midpointy) / 2.0;
double zc0 = (tp_z0 + midpointz) / 2.0;
double zc1 = (tp_z1 + midpointz) / 2.0;
child[0].xinterval[0] = tp_x0;
child[0].xinterval[1] = midpointx;
child[0].yinterval[0] = tp_y0;
child[0].yinterval[1] = midpointy;
child[0].zinterval[0] = tp_z0;
child[0].zinterval[1] = midpointz;
child[0].xc = xc0;
child[0].yc = yc0;
child[0].zc = zc0;
child[0].MAC = ((midpointx - xc0) * (midpointx - xc0) + (midpointy - yc0) * (midpointy - yc0) + (midpointz - zc0) * (midpointz - zc0)) / sq_theta;
child[1].xinterval[0] = midpointx;
child[1].xinterval[1] = tp_x1;
child[1].yinterval[0] = tp_y0;
child[1].yinterval[1] = midpointy;
child[1].zinterval[0] = tp_z0;
child[1].zinterval[1] = midpointz;
child[1].xc = xc1;
child[1].yc = yc0;
child[1].zc = zc0;
child[1].MAC = ((tp_x1 - xc1) * (tp_x1 - xc1) + (midpointy - yc0) * (midpointy - yc0) + (midpointz - zc0) * (midpointz - zc0)) / sq_theta;
child[2].xinterval[0] = tp_x0;
child[2].xinterval[1] = midpointx;
child[2].yinterval[0] = midpointy;
child[2].yinterval[1] = tp_y1;
child[2].zinterval[0] = tp_z0;
child[2].zinterval[1] = midpointz;
child[2].xc = xc0;
child[2].yc = yc1;
child[2].zc = zc0;
child[2].MAC = ((midpointx - xc0) * (midpointx - xc0) + (tp_y1 - yc1) * (tp_y1 - yc1) + (midpointz - zc0) * (midpointz - zc0)) / sq_theta;
child[3].xinterval[0] = midpointx;
child[3].xinterval[1] = tp_x1;
child[3].yinterval[0] = midpointy;
child[3].yinterval[1] = tp_y1;
child[3].zinterval[0] = tp_z0;
child[3].zinterval[1] = midpointz;
child[3].xc = xc1;
child[3].yc = yc1;
child[3].zc = zc0;
child[3].MAC = ((tp_x1 - xc1) * (tp_x1 - xc1) + (tp_y1 - yc1) * (tp_y1 - yc1) + (midpointz - zc0) * (midpointz - zc0)) / sq_theta;
child[4].xinterval[0] = tp_x0;
child[4].xinterval[1] = midpointx;
child[4].yinterval[0] = tp_y0;
child[4].yinterval[1] = midpointy;
child[4].zinterval[0] = midpointz;
child[4].zinterval[1] = tp_z1;
child[4].xc = xc0;
child[4].yc = yc0;
child[4].zc = zc1;
child[4].MAC = ((midpointx - xc0) * (midpointx - xc0) + (midpointy - yc0) * (midpointy - yc0) + (tp_z1 - zc1) * (tp_z1 - zc1)) / sq_theta;
child[5].xinterval[0] = midpointx;
child[5].xinterval[1] = tp_x1;
child[5].yinterval[0] = tp_y0;
child[5].yinterval[1] = midpointy;
child[5].zinterval[0] = midpointz;
child[5].zinterval[1] = tp_z1;
child[5].xc = xc1;
child[5].yc = yc0;
child[5].zc = zc1;
child[5].MAC = ((tp_x1 - xc1) * (tp_x1 - xc1) + (midpointy - yc0) * (midpointy - yc0) + (tp_z1 - zc1) * (tp_z1 - zc1)) / sq_theta;
child[6].xinterval[0] = tp_x0;
child[6].xinterval[1] = midpointx;
child[6].yinterval[0] = midpointy;
child[6].yinterval[1] = tp_y1;
child[6].zinterval[0] = midpointz;
child[6].zinterval[1] = tp_z1;
child[6].xc = xc0;
child[6].yc = yc1;
child[6].zc = zc1;
child[6].MAC = ((midpointx - xc0) * (midpointx - xc0) + (tp_y1 - yc1) * (tp_y1 - yc1) + (tp_z1 - zc1) * (tp_z1 - zc1)) / sq_theta;
child[7].xinterval[0] = midpointx;
child[7].xinterval[1] = tp_x1;
child[7].yinterval[0] = midpointy;
child[7].yinterval[1] = tp_y1;
child[7].zinterval[0] = midpointz;
child[7].zinterval[1] = tp_z1;
child[7].xc = xc1;
child[7].yc = yc1;
child[7].zc = zc1;
child[7].MAC = ((tp_x1 - xc1) * (tp_x1 - xc1) + (tp_y1 - yc1) * (tp_y1 - yc1) + (tp_z1 - zc1) * (tp_z1 - zc1)) / sq_theta;
vector<size_t> v[8];
size_t start = tree[panel_index].members[0];
size_t end = tree[panel_index].members[1];
size_t* addr_table = new size_t[end - start + 1];
size_t index;
for (index = start; index <= end; index++)
{
particles.index[index] = index;
addr_table[index - start] = index;
if (particles.x[index] <= midpointx && particles.y[index] <= midpointy &&
particles.z[index] <= midpointz)
v[0].push_back(index);
else if (particles.x[index] > midpointx && particles.y[index] <= midpointy &&
particles.z[index] <= midpointz )
v[1].push_back(index);
else if (particles.x[index] <= midpointx && particles.y[index] > midpointy &&
particles.z[index]<= midpointz)
v[2].push_back(index);
else if (particles.x[index] > midpointx && particles.y[index] > midpointy &&
particles.z[index] <= midpointz)
v[3].push_back(index);
else if(particles.x[index] <= midpointx && particles.y[index] <= midpointy &&
particles.z[index] > midpointz )
v[4].push_back(index);
else if (particles.x[index] > midpointx && particles.y[index] <= midpointy &&
particles.z[index] > midpointz)
v[5].push_back(index);
else if (particles.x[index] <= midpointx && particles.y[index] > midpointy &&
particles.z[index] > midpointz)
v[6].push_back(index);
else if (particles.x[index] > midpointx && particles.y[index] > midpointy &&
particles.z[index] > midpointz)
v[7].push_back(index);
}
size_t seq = start;
for (size_t j = 0; j < 8; j++)
{
size_t size = v[j].size();
if (size >= 1)
{
for (size_t k = 0; k < size; k++)
{
if (k == 0)
child[j].members[0] = seq;
if (k == size - 1)
child[j].members[1] = seq;
index = v[j][k];
/*
// This is very slow
size_t pos;
for (pos = tree[panel_index].members[0]; pos <= tree[panel_index].members[1]; pos++)
{
if (particles.index[pos] == index)
break;
}
Swap(pos, seq, particles);
*/
// This uses an address table
size_t pos = addr_table[index - start];
size_t out = particles.index[seq];
Swap(pos, seq, particles);
addr_table[index - start] = seq;
addr_table[out - start] = pos;
seq++;
}
node_count++;
tree[panel_index].children.push_back(node_count - 1);
tree.push_back(child[j]);
v[j].clear();
}
}
delete[] addr_table;
}
//*****************************************************************************//
void ShrinkCluster(struct xyz &particles)
{
double min_x = 0.0;;
double max_x = 0.0;
double min_y = 0.0;
double max_y = 0.0;
double min_z = 0.0;
double max_z = 0.0;
double r;
size_t size = tree.size();
int limit_1;
int limit_2;
for (size_t i = 0; i < size; i++)
{
limit_1 = tree[i].members[0];
limit_2 = tree[i].members[1];
min_x = particles.x[limit_1]; // the first point in the current cluster
max_x = particles.x[limit_1];
min_y = particles.y[limit_1];
max_y = particles.y[limit_1];
min_z = particles.z[limit_1];
max_z = particles.z[limit_1];
for (size_t jj = limit_1; jj <= limit_2; jj++)
{
if (particles.x[jj] < min_x)
min_x = particles.x[jj];
if (particles.x[jj] > max_x)
max_x = particles.x[jj];
if (particles.y[jj] < min_y)
min_y = particles.y[jj];
if (particles.y[jj] > max_y)
max_y = particles.y[jj];
if (particles.z[jj] < min_z)
min_z = particles.z[jj];
if (particles.z[jj] > max_z)
max_z = particles.z[jj];
}
tree[i].xc = (min_x + max_x)/2.0;
tree[i].yc = (min_y + max_y)/2.0;
tree[i].zc = (min_z + max_z)/2.0;
r = sqrt ((max_x - min_x) * (max_x - min_x) + (max_y - min_y) * (max_y - min_y) + (max_z - min_z) * (max_z - min_z))/2;
tree[i].MAC = r*r/ sq_theta;
}
}
//*****************************************************************************//
void build_tree_3D_Recursive(size_t panel_index, struct xyz &particles, int level)
{
if (level > max_level)
max_level = level;
size_t n = tree[panel_index].members[1] - tree[panel_index].members[0] + 1;
if (n >= (size_t)N0)
{
split_tree_node(panel_index, particles);
for (size_t i = 0; i < tree[panel_index].children.size(); i++)
{
size_t panel_index_new = tree[panel_index].children[i];
build_tree_3D_Recursive(panel_index_new, particles, level + 1);
}
}
else
leaf.push_back(panel_index);
}
//*****************************************************************************//
// Calculate the far field expansions associated with each panel by recurrence relation
void Far_Expan_Taylor(double a[][P + 4][P + 4], double x, double y, double z,
size_t panel_index)
{
// intput :
// x,y,z is the particle's three coordinates
// panel_index
// output : a[][][] is the coefficients for panel_inde^th panel
double xc = tree[panel_index].xc; // coordernate of the center of panel
double yc = tree[panel_index].yc;
double zc = tree[panel_index].zc;
double tp_x = x - xc;
double tp_y = y - yc;
double tp_z = z - zc;
double R2 = tp_x * tp_x + tp_y * tp_y + tp_z * tp_z; // R2 = R^2
double R = sqrt(R2);
double s, ijk1, ijk2, sum_ijk;
const int Q = P + 2;
// base case
a[0 + 1][0 + 1][0 + 1] = 1.0 / R; // first coefficient is the Greens function itself
// two of the indeces are zero
sum_ijk = 1;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
a[1 + 1][0 + 1][0 + 1] = (ijk2 * tp_x * a[0 + 1][0 + 1][0 + 1]) / s;
a[0 + 1][1 + 1][0 + 1] = (ijk2 * tp_y * a[0 + 1][0 + 1][0 + 1]) / s;
a[0 + 1][0 + 1][1 + 1] = (ijk2 * tp_z * a[0 + 1][0 + 1][0 + 1]) / s;
if (P == 1)
return;
for (int i = 2; i < Q + 1; i++)
{
sum_ijk = i;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[i + 1][0 + 1][0 + 1] = (ijk2 * (tp_x * a[i - 1 + 1][0 + 1][0 + 1]) - ijk1 * (a[i - 2 + 1][0 + 1][0 + 1])) / s;
a[0 + 1][i + 1][0 + 1] = (ijk2 * (tp_y * a[0 + 1][i - 1 + 1][0 + 1]) - ijk1 * (a[0 + 1][i - 2 + 1][0 + 1])) / s;
a[0 + 1][0 + 1][i + 1] = (ijk2 * (tp_z * a[0 + 1][0 + 1][i - 1 + 1]) - ijk1 * (a[0 + 1][0 + 1][i - 2 + 1])) / s;
}
// one index = 0; one index = 1; other index >= 1
sum_ijk = 2;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[1 + 1][1 + 1][0 + 1] = (ijk2 * (tp_x * a[0 + 1][1 + 1][0 + 1] + tp_y * a[1 + 1][0 + 1][0 + 1])) / s ;
a[1 + 1][0 + 1][1 + 1] = (ijk2 * (tp_x * a[0 + 1][0 + 1][1 + 1] + tp_z * a[1 + 1][0 + 1][0 + 1])) / s;
a[0 + 1][1 + 1][1 + 1] = (ijk2 * (tp_y * a[0 + 1][0 + 1][1 + 1] + tp_z * a[0 + 1][1 + 1][0 + 1])) / s;
for (int i = 2; i + 1 <= Q; i++)
{
sum_ijk = i + 1;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[i + 1][1 + 1][0 + 1] = (ijk2 * (tp_x * a[i - 1 + 1][1 + 1][0 + 1] + tp_y * a[i + 1][0 + 1][0 + 1])
- ijk1 * (a[i - 2 + 1][1 + 1][0 + 1])) / s;
a[i + 1][0 + 1][1 + 1] = (ijk2 * (tp_x * a[i - 1 + 1][0 + 1][1 + 1] + tp_z * a[i + 1][0 + 1][0 + 1])
- ijk1 * (a[i - 2 + 1][0 + 1][1 + 1])) / s;
a[1 + 1][i + 1][0 + 1] = (ijk2 * (tp_x * a[0 + 1][i + 1][0 + 1] + tp_y * a[1 + 1][i - 1 + 1][0 + 1])
- ijk1 * (a[1 + 1][i - 2 + 1][0 + 1]))/s;
a[0 + 1][i + 1][1 + 1] = (ijk2 * (tp_y * a[0 + 1][i - 1 + 1][1 + 1] + tp_z * a[0 + 1][i + 1][0 + 1])
- ijk1 * (a[0 + 1][i - 2 + 1][1 + 1])) / s;
a[1 + 1][0 + 1][i + 1] = (ijk2 * (tp_x * a[0 + 1][0 + 1][i + 1] + tp_z * a[1 + 1][0 + 1][i - 1 + 1])
- ijk1 * (a[1 + 1][0 + 1][i - 2 + 1])) / s;
a[0 + 1][1 + 1][i + 1] = (ijk2 * (tp_y * a[0 + 1][0 + 1][i + 1] + tp_z * a[0 + 1][1 + 1][i - 1 + 1])
- ijk1 * (a[0 + 1][1 + 1][i - 2 + 1])) / s;
}
// one index = 0; other indices >= 2
for (int i = 2; i <= Q - 2; i++)
{
for (int j = 2; i + j <= Q; j++)
{
sum_ijk = i + j;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[i + 1][j + 1][0 + 1] = (ijk2 * (tp_x * a[i - 1 + 1][j + 1][0 + 1] + tp_y * a[i + 1][j - 1 + 1][0 + 1])
- ijk1 * (a[i - 2 + 1][j + 1][0 + 1] + a[i + 1][j - 2 + 1][0 + 1])) / s;
a[i + 1][0 + 1][j + 1] = (ijk2 * (tp_x * a[i - 1 + 1][0 + 1][j + 1] + tp_z * a[i + 1][0 + 1][j - 1 + 1])
- ijk1 * (a[i - 2 + 1][0 + 1][j + 1] + a[i + 1][0 + 1][j - 2 + 1])) / s;
a[0 + 1][i + 1][j + 1] = (ijk2 * (tp_y * a[0 + 1][i - 1 + 1][j + 1] + tp_z * a[0 + 1][i + 1][j - 1 + 1])
- ijk1 * (a[0 + 1][i - 2 + 1][j + 1] + a[0 + 1][i + 1][j - 2 + 1])) / s;
}
}
// two indices = 1, other index >= 1
sum_ijk = 3;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[1 + 1][1 + 1][1 + 1] = (ijk2 * (tp_x * a[0 + 1][1 + 1][1 + 1] + tp_y * a[1 + 1][0 + 1][1 + 1] + tp_z * a[1 + 1][1 + 1][0 + 1])) / s;
for (int i = 2; i + 2 <= Q; i++)
{
sum_ijk = i + 2;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[i + 1][1 + 1][1 + 1] = (ijk2 * (tp_x * a[i - 1 + 1][1 + 1][1 + 1] + tp_y * a[i + 1][0 + 1][1 + 1] + tp_z * a[i + 1][1 + 1][0 + 1])
- ijk1 * (a[i - 2 + 1][1 + 1][1 + 1])) / s;
a[1 + 1][i + 1][1 + 1] = (ijk2 * (tp_x * a[0 + 1][i + 1][1 + 1] + tp_y * a[1 + 1][i - 1 + 1][1 + 1] + tp_z * a[1 + 1][i + 1][0 + 1])
- ijk1 * (a[1 + 1][i - 2 + 1][1 + 1])) / s;
a[1 + 1][1 + 1][i + 1] = (ijk2 * (tp_x * a[0 + 1][1 + 1][i + 1] + tp_y * a[1 + 1][0 + 1][i + 1] + tp_z * a[1 + 1][1 + 1][i - 1 + 1])
- ijk1 * (a[1 + 1][1 + 1][i - 2 + 1])) / s;
}
// one index = 1; other indeces >= 2
for (int i = 2; i <= Q - 3; i++)
{
for (int j = 2; i + j < Q; j++)
{
sum_ijk = i + j + 1;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[i + 1][j + 1][1 + 1] = (ijk2 * (tp_x * a[i - 1 + 1][j + 1][1 + 1] + tp_y * a[i + 1][j - 1 + 1][1 + 1] + tp_z * a[i + 1][j + 1][0 + 1])
- ijk1 * (a[i - 2 + 1][j + 1][1 + 1] + a[i + 1][j - 2 + 1][1 + 1])) / s;
a[i + 1][1 + 1][j + 1] = (ijk2 * (tp_x * a[i - 1 + 1][1 + 1][j + 1] + tp_y * a[i + 1][0 + 1][j + 1] + tp_z * a[i + 1][1 + 1][j - 1 + 1])
- ijk1 * (a[i - 2 + 1][1 + 1][j + 1] + a[i + 1][1 + 1][j - 2 + 1])) / s;
a[1 + 1][i + 1][j + 1] = (ijk2 * (tp_x * a[0 + 1][i + 1][j + 1] + tp_y * a[1 + 1][i - 1 + 1][j + 1] + tp_z * a[1 + 1][i + 1][j - 1 + 1])
- ijk1 * (a[1 + 1][i - 2 + 1][j + 1] + a[1 + 1][i + 1][j - 2 + 1])) / s;
}
}
// all indices >= 2
for (int i = 2; i <= Q - 4; i++)
{
for (int j = 2; i + j <= Q - 2; j++)
{
for (int k = 2; i + j + k <= Q; k++)
{
sum_ijk = i + j + k;
s = sum_ijk * R2;
ijk2 = 2.0 * sum_ijk - 1.0;
ijk1 = sum_ijk - 1.0;
a[i + 1][j + 1][k + 1] = (ijk2 * (tp_x * a[i - 1 + 1][j + 1][k + 1] + tp_y * a[i + 1][j - 1 + 1][k + 1] + tp_z * a[i + 1][j + 1][k - 1 + 1])
- ijk1 * (a[i - 2 + 1][j + 1][k + 1] + a[i + 1][j - 2 + 1][k + 1] + a[i + 1][j + 1][k - 2 + 1])) / s;
}
}
}
}
//*****************************************************************************//
double mypow(double x, int n)
{
double result = 1.0;
while (n > 0) {
if (n & 1)
result = result * x;
n = n >> 1;
x = x * x;
}
return result;
}
//*****************************************************************************//
void Panel_Moment_Taylor(size_t panel_index,double *lambda_Sto[3], double *lambda_Str[3], double *normal[3],struct xyz &particles, double m_Sto[][Pflat], double m_Str[][3][Pflat])
{
// intput : lambda : the RBF coeff
// particles : all particles' coordinate
// panel_index;
// output : m: moments for panel_index^th panel
double xc = tree[panel_index].xc;
double yc = tree[panel_index].yc;
double zc = tree[panel_index].zc;
double x, y, z;
size_t tp_j;
double tp0 = tree[panel_index].members[0];
double tp1 = tree[panel_index].members[1];
int kk = -1;
double s;
for (int k1 = 0; k1 < P + 1; k1++)
{
for (int k2 = 0; k1 + k2 < P + 1; k2++)
{
for (int k3 = 0; k1 + k2 + k3 < P + 1; k3++)
{
kk = kk + 1;
for (tp_j = tp0; tp_j <= tp1; tp_j++)
{
x = particles.x[tp_j];
y = particles.y[tp_j];
z = particles.z[tp_j];
s = mypow(x - xc, k1) * mypow(y - yc,k2) * mypow(z - zc, k3);
m_Sto[0][kk] += s * lambda_Sto[0][tp_j];
m_Sto[1][kk] += s * lambda_Sto[1][tp_j];
m_Sto[2][kk] += s * lambda_Sto[2][tp_j];
for (int index1 = 0; index1 < 3; index1++)
{
for (int index2 = 0; index2 < 3; index2++)
{
m_Str[index1][index2][kk] += s * lambda_Str[index1][tp_j] * normal[index2][tp_j];
}
}
}
}
}
}
}
//*****************************************************************************//
vec_3d Comput_RBF(double *lambda_Sto[3], double *lambda_Str[3], double *normal[3], struct xyz &particles, size_t particle_index, size_t panel_index, int dep = 0 )
{
// input :
// lambda : RBF coefficients
// particles : all particles coordinates
// particle_index
// panel_index
// output :
// velocity in 3D
double a_t[P + 4][P + 4][P + 4] = {{{0.0}}};
double C[3][3][3] = {{{0.0}}};
vec_3d velocity;
vec_3d temp_result;
for (int index1 = 0; index1 < 3; index1++)
{
velocity.val_Str[index1] = 0.0;
temp_result.val_Str[index1] = 0.0;
velocity.val_Sto[index1] = 0.0;
temp_result.val_Sto[index1] = 0.0;
}
double dx = 0.0;
double dy = 0.0;
double dz = 0.0;
double p_x = 0.0;
double p_y = 0.0;
double p_z = 0.0;
double xc = 0.0;
double yc = 0.0;
double zc = 0.0;
double R_sq = 0.0;
double R;
double ff_sto[3];
double ff_str[3];
double rnorm[3];
double Rinv, Rinv3, Rinv5;
double DD_sto;
double DD_str;
size_t limit_1;
size_t limit_2;
p_x = particles.x[particle_index];
p_y = particles.y[particle_index];
p_z = particles.z[particle_index];
xc = tree[panel_index].xc;
yc = tree[panel_index].yc;
zc = tree[panel_index].zc;
double tp_x,tp_y,tp_z;
tp_x = p_x - xc;
tp_y = p_y - yc;
tp_z = p_z - zc;
R_sq = tp_x * tp_x + tp_y * tp_y + tp_z * tp_z;
double term2;
int k1p1,k2p1,k3p1;
double moments_sto[3];
double nv1,nv2,nv3;
double MM;
double M1p2,M1p3,M2p3;
double moments_str[3][3];
if (tree[panel_index].MAC < R_sq)
{
// if MAC is satisfied, use Taylor approximation
Far_Expan_Taylor(a_t, p_x, p_y, p_z, panel_index);
double s;
int kk = -1;
for (int k1 = 0; k1 < P + 1; k1++)
{
for (int k2 = 0; k1 + k2 < P + 1; k2++)
{
for (int k3 = 0; k1 + k2 + k3 < P + 1; k3++)
{
kk = kk + 1;
moments_str[0][0] = tree[panel_index].moments_Str[0][0][kk];
moments_str[0][1] = tree[panel_index].moments_Str[0][1][kk];
moments_str[0][2] = tree[panel_index].moments_Str[0][2][kk];
moments_str[1][0] = tree[panel_index].moments_Str[1][0][kk];
moments_str[1][1] = tree[panel_index].moments_Str[1][1][kk];
moments_str[1][2] = tree[panel_index].moments_Str[1][2][kk];
moments_str[2][0] = tree[panel_index].moments_Str[2][0][kk];
moments_str[2][1] = tree[panel_index].moments_Str[2][1][kk];
moments_str[2][2] = tree[panel_index].moments_Str[2][2][kk];
nv1 = tp_x * moments_str[0][0] + tp_y * moments_str[0][1] + tp_z * moments_str[0][2];
nv2 = tp_x * moments_str[1][0] + tp_y * moments_str[1][1] + tp_z * moments_str[1][2];
nv3 = tp_x * moments_str[2][0] + tp_y * moments_str[2][1] + tp_z * moments_str[2][2];
MM = moments_str[0][0] + moments_str[1][1] + moments_str[2][2];
M1p2 = moments_str[0][1] + moments_str[1][0];
M1p3 = moments_str[0][2] + moments_str[2][0];
M2p3 = moments_str[1][2] + moments_str[2][1];
k1p1 = k1 + 1;
k2p1 = k2 + 1;
k3p1 = k3 + 1;
velocity.val_Str[0] += (k1p1 * ((k1 + 2) * a_t[k1p1 + 2][k2p1][k3p1] * nv1 +
k2p1 * a_t[k1p1 + 1][k2p1 + 1][k3p1] * nv2 +
k3p1 * a_t[k1p1 + 1][k2p1][k3p1 + 1] * nv3)
-k1p1 * ((k1 + 2) * (a_t[k1p1 + 1][k2p1][k3p1] * moments_str[0][0]
+ a_t[k1p1 + 2][k2p1 - 1][k3p1] * moments_str[0][1]
+ a_t[k1p1 + 2][k2p1][k3p1 - 1] * moments_str[0][2])
+ k2p1 * (a_t[k1p1][k2p1 + 1][k3p1] * moments_str[1][0]
+ a_t[k1p1 + 1][k2p1][k3p1] * moments_str[1][1]
+ a_t[k1p1 + 1][k2p1 + 1][k3p1 - 1] * moments_str[1][2])
+ k3p1 * (a_t[k1p1][k2p1][k3p1 + 1] * moments_str[2][0]
+ a_t[k1p1 + 1][k2p1 - 1][k3p1 + 1] * moments_str[2][1]
+ a_t[k1p1 + 1][k2p1][k3p1] * moments_str[2][2]))
+ k1p1 * a_t[k1p1 + 1][k2p1][k3p1] * MM +
k1p1 * a_t[k1p1 + 1][k2p1][k3p1] * 2 * moments_str[0][0]
+ k2p1 * a_t[k1p1][k2p1 + 1][k3p1] * M1p2
+ k3p1 * a_t[k1p1][k2p1][k3p1 + 1] * M1p3)/3.0;
velocity.val_Str[1] += (k2p1 * (k1p1 * a_t[k1p1 + 1][k2p1 + 1][k3p1] * nv1 +
(k2 + 2) * a_t[k1p1][k2p1 + 2][k3p1] * nv2 +
k3p1 * a_t[k1p1][k2p1 + 1][k3p1 + 1] * nv3)
-k2p1 * (k1p1 * (a_t[k1p1][k2p1 + 1][k3p1] * moments_str[0][0]
+ a_t[k1p1 + 1][k2p1][k3p1] * moments_str[0][1]
+ a_t[k1p1 + 1][k2p1 + 1][k3p1 - 1] * moments_str[0][2])
+(k2 + 2) * (a_t[k1p1 - 1][k2p1 + 2][k3p1] * moments_str[1][0]
+ a_t[k1p1][k2p1 + 1][k3p1] * moments_str[1][1]
+ a_t[k1p1][k2p1 + 2][k3p1 - 1] * moments_str[1][2])
+k3p1 * (a_t[k1p1 - 1][k2p1 + 1][k3p1 + 1] * moments_str[2][0]
+ a_t[k1p1][k2p1][k3p1 + 1] * moments_str[2][1]
+ a_t[k1p1][k2p1 + 1][k3p1] * moments_str[2][2]))
+k2p1 * a_t[k1p1][k2p1 + 1][k3p1] * MM +
k1p1 * a_t[k1p1 + 1][k2p1][k3p1] * M1p2 +
k2p1 * a_t[k1p1][k2p1 + 1][k3p1] * 2 * moments_str[1][1]
+k3p1 * a_t[k1p1][k2p1][k3p1 + 1] * M2p3)/3.0;
velocity.val_Str[2] += (k3p1 * (k1p1 * a_t[k1p1 + 1][k2p1][k3p1 + 1] * nv1 +
k2p1 * a_t[k1p1][k2p1 + 1][k3p1 + 1] * nv2 +
(k3 + 2) * a_t[k1p1][k2p1][k3p1 + 2] * nv3)
- k3p1 * ( k1p1 * (a_t[k1p1][k2p1][k3p1 + 1] * moments_str[0][0]
+ a_t[k1p1 + 1][k2p1 - 1][k3p1 + 1] * moments_str[0][1]
+ a_t[k1p1 + 1][k2p1][k3p1] * moments_str[0][2])
+ k2p1 * (a_t[k1p1 - 1][k2p1 + 1][k3p1 + 1] * moments_str[1][0]
+ a_t[k1p1][k2p1][k3p1 + 1] * moments_str[1][1]
+ a_t[k1p1][k2p1 + 1][k3p1] * moments_str[1][2])
+ (k3 + 2) * (a_t[k1p1 - 1][k2p1][k3p1 + 2] * moments_str[2][0]
+ a_t[k1p1][k2p1 - 1][k3p1 + 2] * moments_str[2][1]
+ a_t[k1p1][k2p1][k3p1 + 1] * moments_str[2][2]))
+ k3p1 * a_t[k1p1][k2p1][k3p1 + 1] * MM
+k1p1 * a_t[k1p1 + 1][k2p1][k3p1] * M1p3
+ k2p1 * a_t[k1p1][k2p1 + 1][k3p1] * M2p3
+k3p1 * a_t[k1p1][k2p1][k3p1 + 1] * 2 * moments_str[2][2])/3.0;
// stokeslet
moments_sto[0] = tree[panel_index].moments_Sto[0][kk] ;
moments_sto[1] = tree[panel_index].moments_Sto[1][kk] ;
moments_sto[2] = tree[panel_index].moments_Sto[2][kk] ;
term2 = tp_x * moments_sto[0] + tp_y * moments_sto[1] + tp_z * moments_sto[2];
s = a_t[k1p1][k2p1][k3p1];
velocity.val_Sto[0] += (1 - k1) * s * moments_sto[0] + k1p1 * (a_t[k1 + 2][k2p1][k3p1] * term2 - a_t[k1 + 2][k2][k3p1] * moments_sto[1] - a_t[k1 + 2][k2p1][k3] * moments_sto[2]);
velocity.val_Sto[1] += (1 - k2) * s * moments_sto[1] + k2p1 * (a_t[k1p1][k2 + 2][k3p1] * term2 - a_t[k1][k2 + 2][k3p1] * moments_sto[0] - a_t[k1p1][k2 + 2][k3] * moments_sto[2]);
velocity.val_Sto[2] += (1 - k3) * s * moments_sto[2] + k3p1 * (a_t[k1p1][k2p1][k3 + 2] * term2 - a_t[k1][k2p1][k3 + 2] * moments_sto[0] - a_t[k1p1][k2][k3 + 2] * moments_sto[1]);
}
}
}
}
else
{
limit_1 = tree[panel_index].members[0];
limit_2 = tree[panel_index].members[1];
if (limit_2 - limit_1 < N0) // otherwise, if cluster is a leaf, use direct sum
{
for (size_t jj = limit_1; jj <= limit_2; jj++)
{
if (jj == particle_index)
continue;
dx = p_x - particles.x[jj];
dy = p_y - particles.y[jj];
dz = p_z - particles.z[jj];
ff_sto[0] = lambda_Sto[0][jj];
ff_sto[1] = lambda_Sto[1][jj];
ff_sto[2] = lambda_Sto[2][jj];
ff_str[0] = lambda_Str[0][jj];
ff_str[1] = lambda_Str[1][jj];
ff_str[2] = lambda_Str[2][jj];
rnorm[0] = normal[0][jj];
rnorm[1] = normal[1][jj];
rnorm[2] = normal[2][jj];
R = sqrt(dx * dx + dy * dy + dz * dz);
Rinv = 1.0/R;
velocity.val_Sto[0] += ff_sto[0] * Rinv;
velocity.val_Sto[1] += ff_sto[1] * Rinv;
velocity.val_Sto[2] += ff_sto[2] * Rinv;
Rinv3 = Rinv * Rinv * Rinv;
DD_sto = ff_sto[0] * dx + ff_sto[1] * dy + ff_sto[2] * dz;
DD_sto = DD_sto * Rinv3;
velocity.val_Sto[0] += DD_sto * dx;
velocity.val_Sto[1] += DD_sto * dy;
velocity.val_Sto[2] += DD_sto * dz;
DD_str = (ff_str[0] * dx + ff_str[1] * dy + ff_str[2] * dz) *
(rnorm[0] * dx + rnorm[1] * dy + rnorm[2] * dz);
Rinv5 = Rinv3 * Rinv * Rinv;
DD_str = DD_str * Rinv5;
velocity.val_Str[0] += DD_str * dx;
velocity.val_Str[1] += DD_str * dy;
velocity.val_Str[2] += DD_str * dz;
}
}// end if
else // othervise, if cluster is not a leaf, look at children
{
for (int index1 = 0; index1 < 3; index1++)
{
velocity.val_Str[index1] = 0.0;
velocity.val_Sto[index1] = 0.0;
}
size_t length = tree[panel_index].children.size();
for (size_t i = 0; i < length; i++)
{
size_t index = tree[panel_index].children[i];
temp_result = Comput_RBF(lambda_Sto,lambda_Str,normal, particles, particle_index, index, dep + 1);
for(int index_1 = 0; index_1 < 3; index_1++)
{
velocity.val_Str[index_1] = velocity.val_Str[index_1] + temp_result.val_Str[index_1];
velocity.val_Sto[index_1] = velocity.val_Sto[index_1] + temp_result.val_Sto[index_1];
}
}
}
}
/* cout << "velocity.val_Str[0] = "<< velocity.val_Str[0] << endl;
cout << "velocity.val_Str[1] = "<< velocity.val_Str[1] << endl;
cout << "velocity.val_Str[2] = "<< velocity.val_Str[2] << endl;
cout << "velocity.val_Sto[0] = "<< velocity.val_Sto[0] << endl;
cout << "velocity.val_Sto[1] = "<< velocity.val_Sto[1] << endl;
cout << "velocity.val_Sto[2] = "<< velocity.val_Sto[2] << endl;*/
return velocity;
}
//*****************************************************************************//
int main()
{
struct xyz particles(N_cube);
cout << "P is " << P << endl;
cout << "N is " << N << endl;
cout << "theta is " << sqrt(sq_theta) << endl;
cout << "N0 is " << N0 << endl;
// ***************** Generate Random data *******************************
FILE * fp;
double x1, x2, x3,x4,x5,x6,x7,x8,x9;
int count;
char S_data_file[64] = {0};
sprintf(S_data_file, "./data/Points_N%d", N);
fp = fopen(S_data_file, "r");
count = -1;
if (fp == NULL)
{
cout << "Cannot open random points file" << endl;
getchar();
exit(0);
}
while (true)
{
count++;
fscanf(fp,"%lf%lf%lf%lf%lf", &x1, &x2, &x3,&x4,&x5); // x4: area, x5 Farea
if (feof(fp))
break;
if (count >= N_cube)
{
cout << "S Out of range" << endl;
exit(0);
}
particles.x[count] = x1;