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3D_RegStokes_case_1.cpp
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#include <iostream>
#include <vector>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <fstream>
#include <sys/times.h>
// vector researve
using namespace std;
static const int P = 10; // order of Taylor approximation
static const int Pflat = (P + 1)*(P + 1)*(P + 1);
static const int N_cube = 80000; // N_cube points total
static const int N = 80;
static const int N0 = 2000;
static const double sq_theta = 0.25; // theta = 0.5
static const double DEL = 0.02;
const bool UseSleep = false; // for testing memory usage purpose
int max_level = 0;
//**********************************************************//
struct vec_3d
{
double val[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[3][Pflat];
int moment_flag;
double t1[P + 1]; // interpolation points in x direction
double t2[P + 1];
double t3[P + 1];
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[index][kk] = 0;
}
for (int i = 0; i < P + 1; i++)
{
t1[i] = 0.0;
t2[i] = 0.0;
t3[i] = 0.0;
}
}
};
//**************//
vector<panel> tree;
vector<size_t> leaf;
static size_t node_count = 0;
//*****************************************************************************//
long getTickCount()
{
tms tm;
return times(&tm);
}
//*****************************************************************************//
void build_tree_init()
{
panel temp_panel;
// indices of particles belonging to panel
temp_panel.members[0] = 0;
temp_panel.members[1] = N_cube - 1;
temp_panel.xinterval[0] = -5.0; // interval defining the panel
temp_panel.xinterval[1] = 5.0;
temp_panel.yinterval[0] = -5.0;
temp_panel.yinterval[1] = 5.0;
temp_panel.zinterval[0] = 0.0;
temp_panel.zinterval[1] = 10.0;
temp_panel.xc = 0.5 * (temp_panel.xinterval[0] + temp_panel.xinterval[1]);
temp_panel.yc = 0.5 * (temp_panel.yinterval[0] + temp_panel.yinterval[1]);
temp_panel.zc = 0.5 * (temp_panel.zinterval[0] + temp_panel.zinterval[1]);
temp_panel.MAC = (3 * 10 * 10/ 4) / 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 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)
//if (level < fix_level)
{
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);
}
//*****************************************************************************//
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_B(size_t panel_index, double *lambda[3], struct xyz &particles,
double m[][Pflat])
{
// intput : lambda : the RBF coeff
// particles : all particles' coordinate
// panel_index;
// output : m: moments for panel_index^th panel
double t1[P + 1];
double t2[P + 1];
double t3[P + 1];
int i,j,k;
for (i = 0; i < P + 1; i++) {
t1[i] = tree[panel_index].t1[i];
t2[i] = tree[panel_index].t2[i];
t3[i] = tree[panel_index].t3[i];
}
double w1i[P + 1];
double w2j[P + 1];
double w3k[P + 1];
double dj[P + 1];
dj[0] = 0.5;
dj[P] = 0.5;
for (j = 1; j<P; j++)
dj[j] = 1;
for (j = 0; j < P + 1; j++)
w3k[j] = w2j[j] = w1i[j] = ((j % 2 == 0)? 1 : -1) * dj[j];
int tp0 = tree[panel_index].members[0];
int tp1 = tree[panel_index].members[1];
int cluster_size;
cluster_size = tp1 - tp0 + 1;
size_t tp_j;
double **a1i;
double **a2j;
double **a3k;
double *D;
a1i = (double**)calloc(P + 1, sizeof(double*));
a2j = (double**)calloc(P + 1, sizeof(double*));
a3k = (double**)calloc(P + 1, sizeof(double*));
D = (double*)calloc(cluster_size + 1, sizeof(double));
for (i = 0; i < (P + 1); i++)
{
a1i[i] = (double*)calloc(cluster_size + 1, sizeof(double));
a2j[i] = (double*)calloc(cluster_size + 1, sizeof(double));
a3k[i] = (double*)calloc(cluster_size + 1, sizeof(double));
}
double x, y, z;
double SumA1 = 0.0;
double SumA2 = 0.0;
double SumA3 = 0.0;
double temp1,temp2,temp3;
double temp_D;
for (tp_j = tp0; tp_j <= tp1 ; tp_j++) {
x = particles.x[tp_j];
y = particles.y[tp_j];
z = particles.z[tp_j];
for (j = 0; j < P + 1; j++) {
temp1 = w1i[j] / (x - t1[j]);
temp2 = w2j[j] / (y - t2[j]);
temp3 = w3k[j] / (z - t3[j]);
a1i[j][tp_j - tp0] = temp1;
a2j[j][tp_j - tp0] = temp2;
a3k[j][tp_j - tp0] = temp3;
SumA1 += temp1;
SumA2 += temp2;
SumA3 += temp3;
}
D[tp_j - tp0] = 1.0 / (SumA1 * SumA2 * SumA3);
SumA1 = 0.0;
SumA2 = 0.0;
SumA3 = 0.0;
}
double s;
double sum[3] = {0};
int kk = -1;
for (i = 0; i < P + 1; i++) {
for (j = 0; j < P + 1; j++) {
for (k = 0; k < P + 1; k++) {
kk = kk + 1;
sum[0] = 0.0;
sum[1] = 0.0;
sum[2] = 0.0;
for (tp_j = tp0; tp_j <= tp1; tp_j++)
{
s = a1i[i][tp_j - tp0] * a2j[j][tp_j - tp0] * a3k[k][tp_j - tp0] * D[tp_j - tp0];
sum[0] += s * lambda[0][tp_j];
sum[1] += s * lambda[1][tp_j];
sum[2] += s * lambda[2][tp_j];
}
m[0][kk] = sum[0];
m[1][kk] = sum[1];
m[2][kk] = sum[2];
}
}
}
for (i = 0; i < P + 1; i++) {
free(a1i[i]);
free(a2j[i]);
free(a3k[i]);
}
free(a1i);
free(a2j);
free(a3k);
free(D);
}
//*****************************************************************************//
vec_3d Call_Treecode(double x, double y, double z, int panel_index)
{
/* double G[P + 1][P + 1][P + 1] = {{{0.0}}};
double Bxx[P + 1][P + 1][P + 1] = {{{0.0}}};
double Bxy[P + 1][P + 1][P + 1] = {{{0.0}}};
double Bxz[P + 1][P + 1][P + 1] = {{{0.0}}};
double Byy[P + 1][P + 1][P + 1] = {{{0.0}}};
double Bzz[P + 1][P + 1][P + 1] = {{{0.0}}};
double Byz[P + 1][P + 1][P + 1] = {{{0.0}}};
*/
vec_3d velocity;
velocity.val[0] = 0.0;
velocity.val[1] = 0.0;
velocity.val[2] = 0.0;
// Far_Expan_Taylor(a_t, px, py, pz, t1,t2,t3);
double temp_i;
double temp_j;
double temp_k;
double R2, invR, invR3;
double dx[P + 1];
double dy[P + 1];
double dz[P + 1];
double s;
double temp_moments[3];
double G;
double DD;
for (int i = 0; i < P + 1; i++)
{
dx[i] = x - tree[panel_index].t1[i];
dy[i] = y - tree[panel_index].t2[i];
dz[i] = z - tree[panel_index].t3[i];
}
int kk = -1;
for (int i = 0; i < P + 1; i++)
{
temp_i = dx[i] * dx[i];
for (int j = 0; j < P + 1; j++)
{
temp_j = dy[j] * dy[j];
for (int k = 0; k < P + 1; k++)
{
kk = kk + 1;
temp_moments[0] = tree[panel_index].moments[0][kk];
temp_moments[1] = tree[panel_index].moments[1][kk];
temp_moments[2] = tree[panel_index].moments[2][kk];
temp_k = dz[k] * dz[k];
R2 = temp_i + temp_j + temp_k;
invR = 1/ sqrt(R2 + DEL * DEL);
invR3 = invR * invR * invR;
G = -(2 * R2 + 3 * DEL * DEL) * invR3;
velocity.val[0] += temp_moments[0] * (-G - invR);
velocity.val[1] += temp_moments[1] * (-G - invR);
velocity.val[2] += temp_moments[2] * (-G - invR);
DD = temp_moments[0] * dx[i] + temp_moments[1] * dy[j] + temp_moments[2] * dz[k];
DD = DD * invR3;
velocity.val[0] += DD * dx[i]; // part of Bxx + Bxy + Bxz
velocity.val[1] += DD * dy[j];
velocity.val[2] += DD * dz[k];
/*
G[i][j][k] = - (2 * R2 + 3 * DEL * DEL) * invR3;
Bxx[i][j][k] = - (R2 + DEL * DEL - temp_i) * invR3;
Byy[i][j][k] = - (R2 + DEL * DEL - temp_j) * invR3;
Bzz[i][j][k] = - (R2 + DEL * DEL - temp_k) * invR3;
Bxy[i][j][k] = ((x - t1[i]) * (y - t2[j])) * invR3;
Bxz[i][j][k] = ( z - t3[k]) * (x - t1[i]) * invR3;
Byz[i][j][k] = ( z - t3[k]) * (y - t2[j]) * invR3;
*/
}
}
}
/*
int kk = -1;
for (int i = 0; i < P + 1; i++)
{
for (int j = 0; j < P + 1; j++)
{
for (int k = 0; k < P + 1; k++)
{
kk = kk + 1;
temp_moments[0] = tree[panel_index].moments[0][kk];
temp_moments[1] = tree[panel_index].moments[1][kk];
temp_moments[2] = tree[panel_index].moments[2][kk];
velocity.val[0] +=
velocity.val[0] += (-G[i][j][k] + Bxx[i][j][k]) * temp_moments[0] + Bxy[i][j][k] * temp_moments[1] + Bxz[i][j][k] * temp_moments[2];
velocity.val[1] += (-G[i][j][k] + Byy[i][j][k]) * temp_moments[1] + Bxy[i][j][k] * temp_moments[0] + Byz[i][j][k] * temp_moments[2];
velocity.val[2] += (-G[i][j][k] + Bzz[i][j][k]) * temp_moments[2] + Bxz[i][j][k] * temp_moments[0] + Byz[i][j][k] * temp_moments[1];
}
}
}
*/
return velocity;
}
//*****************************************************************************//
vec_3d Call_Ds(int limit_1, int limit_2, int particle_index, double p_x, double p_y, double p_z, struct xyz &particles, double *lambda[3])
{
double x = 0.0;
double y = 0.0;
double z = 0.0;
double a[3][3];
double ff[3];
double x1,y1,z1;
double R,R2,Rinv,Rinv3;
vec_3d velocity;
velocity.val[0] = 0.0;
velocity.val[1] = 0.0;
velocity.val[2] = 0.0;
double G;
double DD;
for (size_t jj = limit_1; jj <= limit_2; jj++)
{
if (jj == particle_index)
continue;
x = p_x - particles.x[jj];
y = p_y - particles.y[jj];
z = p_z - particles.z[jj];
ff[0] = lambda[0][jj];
ff[1] = lambda[1][jj];
ff[2] = lambda[2][jj];
x1 = x * x;
y1 = y * y;
z1 = z * z;
R2 = x1 + y1 + z1;
R = sqrt(R2 + DEL * DEL);
Rinv = 1.0/R;
Rinv3 = Rinv * Rinv * Rinv;
G = -(2 * R2 + 3 * DEL * DEL) * Rinv3;
velocity.val[0] += ff[0] * (-G - Rinv);
velocity.val[1] += ff[1] * (-G - Rinv);
velocity.val[2] += ff[2] * (-G - Rinv);
DD = ff[0] * x + ff[1] * y + ff[2] * z;
DD = DD * Rinv3;
velocity.val[0] += DD * x; // part of Bxx + Bxy + Bxz
velocity.val[1] += DD * y;
velocity.val[2] += DD * z;
/*
a[0][0] = R2 + DEL * DEL + x1;
a[1][1] = R2 + DEL * DEL + y1;
a[2][2] = R2 + DEL * DEL + z1;
a[0][1] = x * y;
a[0][2] = x * z;
a[1][2] = y * z;
a[1][0] = a[0][1];
a[2][0] = a[0][2];
a[2][1] = a[1][2];
velocity.val[0] += (a[0][0] * ff[0] + a[0][1] * ff[1] + a[0][2]* ff[2]) * R3inv;
velocity.val[1] += (a[1][0] * ff[0] + a[1][1] * ff[1] + a[1][2]* ff[2]) * R3inv;
velocity.val[2] += (a[2][0] * ff[0] + a[2][1] * ff[1] + a[2][2]* ff[2]) * R3inv;
*/
}
return velocity;
}
//*****************************************************************************//
vec_3d Comput_RBF(double *lambda[3], struct xyz &particles,size_t particle_index, size_t panel_index)
{
// input :
// lambda : RBF coefficients
// particles : all particles coordinates
// particle_index
// panel_index
// output :
// velocity in 3D
vec_3d velocity;
velocity.val[0] = 0.0;
velocity.val[1] = 0.0;
velocity.val[2] = 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;
size_t limit_1;
size_t limit_2;
double R_sq;
limit_1 = tree[panel_index].members[0];
limit_2 = tree[panel_index].members[1];
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 tpx = p_x - xc;
double tpy = p_y - yc;
double tpz = p_z - zc;
R_sq = tpx * tpx + tpy * tpy + tpz * tpz;
if (tree[panel_index].MAC < R_sq)
{
vec_3d tree_result = Call_Treecode(p_x, p_y, p_z, panel_index);
velocity.val[0] = velocity.val[0] + tree_result.val[0];
velocity.val[1] = velocity.val[1] + tree_result.val[1];
velocity.val[2] = velocity.val[2] + tree_result.val[2];
}
else
{
if (limit_2 - limit_1 < N0) // otherwise, if cluster is a leaf, use direct sum
{
vec_3d DS_result = Call_Ds(limit_1, limit_2, particle_index,p_x, p_y, p_z, particles, lambda);
velocity.val[0] = velocity.val[0] + DS_result.val[0] ;
velocity.val[1] = velocity.val[1] + DS_result.val[1] ;
velocity.val[2] = velocity.val[2] + DS_result.val[2] ;
}//
else // othervise, if cluster is not a leaf, look at children
{
velocity.val[0] = 0.0;
velocity.val[1] = 0.0;
velocity.val[2] = 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];
vec_3d temp_result = Comput_RBF(lambda, particles, particle_index, index);
velocity.val[0] = velocity.val[0] + temp_result.val[0];
velocity.val[1] = velocity.val[1] + temp_result.val[1];
velocity.val[2] = velocity.val[2] + temp_result.val[2];
}
}
}
return velocity;
}
//*****************************************************************************//
void Cluster_Chev_Points(size_t tree_size)
{
double h;
h = 3.14159265358979323846/P;
double t[P + 1] = {0.0};
for (int i = 0; i < P + 1; i++)
t[i] = cos(i * h); //Chebyshev interpolation points [-1,1]
double x1,x2,y1,y2,z1,z2;
size_t tree_index;
for (tree_index = 0; tree_index < tree_size ; tree_index++)
{
x1 = tree[tree_index].xinterval[0];
x2 = tree[tree_index].xinterval[1];
y1 = tree[tree_index].yinterval[0];
y2 = tree[tree_index].yinterval[1];
z1 = tree[tree_index].zinterval[0];
z2 = tree[tree_index].zinterval[1];
for (int i = 0; i < P + 1; i++) // map to the cluster
{
tree[tree_index].t1[i] = x1 + (t[i] + 1)/2 * (x2 - x1);
tree[tree_index].t2[i] = y1 + (t[i] + 1)/2 * (y2 - y1);
tree[tree_index].t3[i] = z1 + (t[i] + 1)/2 * (z2 - z1);
}
}
}
//*****************************************************************************//
int main()
{
tree.reserve(5000);
leaf.reserve(5000);
struct xyz particles(N_cube);
cout << " ===== No box shrink ===========" << endl;
cout << "P is " << P << endl;
cout << "N_cube is " << N_cube << endl;
cout << "theta is " << sqrt(sq_theta) << endl;
cout << "N0 is " << N0 << endl;
FILE * fp;
char S_data_file[64] = {0};
sprintf(S_data_file, "./rand_%d.txt", N);
fp = fopen(S_data_file, "r");
double x1, x2, x3;
int count = -1;
if (fp == NULL)
{
cout << "Cannot open random points file" << endl;
getchar();
exit(0);
}
while (true)
{
count++;
fscanf(fp,"%lf%lf%lf", &x1, &x2, &x3);
if (feof(fp))
break;
if (count >= N_cube)
{
cout << "Out of range" << endl;
exit(0);
}
particles.x[count] = x1;
particles.y[count] = x2;
particles.z[count] = x3;
particles.index[count] = -1;
particles.old_index[count] = count;
}
// ***************** get data *******************************
/*srand(time(NULL));
for (size_t count = 0; count < N_cube; count++)
{
particles.x[count] = L * ((double)rand() / (double)RAND_MAX) ; // [0,L]
particles.y[count] = L * ((double)rand() / (double)RAND_MAX) ; // [0,L]
particles.z[count] = L * ((double)rand() / (double)RAND_MAX) ; // [0,L]
particles.index[count] = -1;
particles.old_index[count] = count;
}*/
double *lambda[3];
lambda[0] = new double[N_cube];
lambda[1] = new double[N_cube];
lambda[2] = new double[N_cube];
char lambda_Str_data_file[64] = {0};
sprintf(lambda_Str_data_file, "./lambda_%d.txt", N);
fp = fopen(lambda_Str_data_file, "r");
count = -1;
if (fp == NULL)
{
cout << "Cannot open lambda file" << endl;
getchar();
exit(0);
}
while (true)
{
count++;
fscanf(fp,"%lf%lf%lf", &x1, &x2, &x3);
if (feof(fp))
break;
if (count >= N_cube)
{
cout << "Out of range" << endl;
exit(0);
}
lambda[0][count] = x1;
lambda[1][count] = x2;
lambda[2][count] = x3;
}
//***************** Set up tree *******************************
long Start_total, Start_btree;
long End_total, End_btree;
Start_total = getTickCount(); // Get currenct CPU time
Start_btree = getTickCount();
build_tree_init();
build_tree_3D_Recursive(0, particles, 0);
End_btree = getTickCount();
//***************** Compute moment for each panel **************
size_t size = tree.size();
Cluster_Chev_Points(size);
for (size_t i = 1; i < size; i++) // skip root
Panel_Moment_B(i, lambda, particles, tree[i].moments);
//***************** Compute Velocity ***************************
vec_3d *velo = new vec_3d[N_cube];
vec_3d *velo_old = new vec_3d[N_cube];
for (int i = 0; i < N_cube; i++)
{
velo[i] = Comput_RBF(lambda, particles, i, 0);
}
End_total = getTickCount(); // Time for all treecode computing
long treecode_cpu_time;
treecode_cpu_time = End_total - Start_total;
// output data to a file
// P12_N40_theta0.2_N0200_time
// P = 12, N = 40, theta = 0.2, N0 = 200, current time
time_t raw_time;
struct tm* time_info;
char time_buffer[80];
time(&raw_time);
time_info = localtime(&raw_time);
strftime(time_buffer, 80, "%Y-%m-%d-%H-%M-%S", time_info);
int N_all = N_cube;
double theta = sqrt(sq_theta);
char file_name[256];
sprintf(file_name, "BR_P%d_N%d_theta%.2f_N0%d_%s", P, N_all, theta, N0, time_buffer);
ofstream output_file(file_name);
output_file << " ===== No box shrink ===========" << endl;
output_file << "P is " << P << endl;
output_file << "N_cube is " << N_cube << endl;
output_file << "theta is " << sqrt(sq_theta) << endl;
output_file << "N0 is " << N0 << endl;
cout << "N_cube is "<< N_cube << endl;
cout << "treecode_cpu_time " << treecode_cpu_time << endl;
cout << "build tree time is " << End_btree - Start_btree << endl;
output_file << "treecode_cpu_time " << treecode_cpu_time << endl;
output_file << "build tree time is " << End_btree - Start_btree << endl;
//***************** Director summation and L_2 Error *****************
vec_3d *v_true = new vec_3d[N_cube];
//***************** compute v_true here ******************************
long Start_ds, End_ds;
Start_ds = getTickCount(); // Get currenct CPU time
// new direct sum
double temp_x, temp_y, temp_z;
double px,py,pz;
double xx,yy,zz;
double xsq,ysq,zsq;
double ff[3];
double sum[3];
double a[3][3];
double R,R2;
double Rinv, Rinv3;
double DD;
double G;
for (size_t i = 0; i < N_cube; i++)
{
temp_x = particles.x[i];
temp_y = particles.y[i];
temp_z = particles.z[i];