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张壹
2022-02-16 11:57:36 +08:00
parent f11958464f
commit 93a0a173c6
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.gitignore vendored
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*.exe *.exe
*.out *.out
*.app *.app
.DS_Store

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fmm_2d_grid/fmm_2d_grid.cpp Normal file
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#include "iostream"
#include "cmath"
#include "vector"
using namespace std;
struct point_2d
{
double x, y;
};
struct source : point_2d
{
double rad;
double slow;
};
struct grid_point : point_2d
{
int tag = 0; //0 = far away, 1 = close, 2 = active
double time = 1e+30;
double syn_time = 1e+30; //synthetic direct arrive time (only for error test)
double slow;
grid_point* neighbor[4] = {NULL,NULL,NULL,NULL}; //up down left right
};
typedef vector<grid_point> grid_point_array;
typedef vector<grid_point*> ptr_grid_point_array;
void update_heap(ptr_grid_point_array& a, int i, int n)
{
int iMax = i,
iLeft = 2 * i + 1,
iRight = 2 * (i + 1);
if (iLeft < n && a[iMax]->time < a[iLeft]->time) {
iMax = iLeft;
}
if (iRight < n && a[iMax]->time < a[iRight]->time) {
iMax = iRight;
}
if (iMax != i) {
grid_point* tmp = a[iMax];
a[iMax] = a[i];
a[i] = tmp;
update_heap(a, iMax, n);
}
return;
}
void heap_sort(ptr_grid_point_array& a, int n)
{
for (int i = (n - 1) / 2; i >= 0; i--) {
update_heap(a, i, n);
}
for (int i = n - 1; i > 0; --i) {
grid_point* tmp = a[i];
a[i] = a[0];
a[0] = tmp;
update_heap(a, 0, i);
}
return;
}
double dis_point_2d(point_2d a, point_2d b)
{
return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
}
void local_update(grid_point* point_ptr, double delta_h)
{
//solve a quadratic equation to get the trial time
/*
double a = 0, b = 0, c = -1.0 * pow(delta_h,2) * pow(point_ptr->slow,2);
for (int i = 0; i < 4; i++)
{
if (point_ptr->neighbor[i] != NULL && point_ptr->neighbor[i]->tag == 2)
{
a += 1.0;
b += -2.0*point_ptr->neighbor[i]->time;
c += pow(point_ptr->neighbor[i]->time,2);
}
}
*/
// a second order upwind difference scheme
double a = 0, b = 0, c = -4.0 * pow(delta_h,2) * pow(point_ptr->slow,2);
for (int i = 0; i < 4; i++)
{
if (point_ptr->neighbor[i] != NULL && point_ptr->neighbor[i]->tag == 2)
{
a += 4.0;
b += -8.0*point_ptr->neighbor[i]->time;
c += 4.0*pow(point_ptr->neighbor[i]->time,2);
if (point_ptr->neighbor[i]->neighbor[i] != NULL && point_ptr->neighbor[i]->neighbor[i]->tag == 2)
{
a += 5.0;
b += -16.0*point_ptr->neighbor[i]->time + 6.0*point_ptr->neighbor[i]->neighbor[i]->time;
c += 12.0*pow(point_ptr->neighbor[i]->time,2) - 8.0*point_ptr->neighbor[i]->time*point_ptr->neighbor[i]->neighbor[i]->time
+ pow(point_ptr->neighbor[i]->neighbor[i]->time,2);
}
}
}
double delta = b*b - 4.0*a*c; //in a upwind scheme, delta is always bigger than zero
point_ptr->time = min(point_ptr->time, 0.5*(sqrt(delta) - b)/a);
return;
}
void abnormal_slowness(grid_point_array& grid_recall, double ab_slow,double xmin, double xmax, double ymin, double ymax)
{
for (int i = 0; i < grid_recall.size(); i++)
{
if (grid_recall[i].x >= xmin && grid_recall[i].x <= xmax && grid_recall[i].y >= ymin && grid_recall[i].y <= ymax)
{
grid_recall[i].slow = ab_slow;
}
}
return;
}
int main(int argc, char const *argv[])
{
//set grid parameters
int xnum = 201;
int ynum = 101;
double xmin = 0;
double ymin = 0;
double dh = 5;
//set source parameters
source init_source;
init_source.x = 50;
init_source.y = 250;
init_source.rad = 25;
init_source.slow = 1.0;
//initialize grid
grid_point_array grid_2d;
grid_2d.resize(xnum*ynum);
//down-left corner to up-right corner
for (int i = 0; i < ynum; i++)
{
for (int j = 0; j < xnum; j++)
{
grid_2d[i*xnum+j].x = xmin + dh*j;
grid_2d[i*xnum+j].y = ymin + dh*i;
grid_2d[i*xnum+j].slow = init_source.slow;
if (i <= ynum-2) grid_2d[i*xnum+j].neighbor[0] = &grid_2d[(i+1)*xnum+j]; //up
if (i >= 1) grid_2d[i*xnum+j].neighbor[1] = &grid_2d[(i-1)*xnum+j]; //down
if (j >= 1) grid_2d[i*xnum+j].neighbor[2] = &grid_2d[i*xnum+j-1]; //left
if (j <= xnum-2) grid_2d[i*xnum+j].neighbor[3] = &grid_2d[i*xnum+j+1]; //right
//calculate synthetic direct arrive time
grid_2d[i*xnum+j].syn_time = dis_point_2d(grid_2d[i*xnum+j], init_source) * init_source.slow;
}
}
//add abnormal slowness here
//abnormal_slowness(grid_2d,2.0,250,500,0,500);
//abnormal_slowness(grid_2d,4.0,800,1000,0,500);
//abnormal_slowness(grid_2d,1e+30,200,250,0,250);
//abnormal_slowness(grid_2d,1e+30,500,550,250,500);
//abnormal_slowness(grid_2d,1e+30,800,850,0,250);
ptr_grid_point_array close_node_ptr;
//initialize source nodes and close nodes;
for (int i = 0; i < xnum*ynum; i++)
{
if (dis_point_2d(grid_2d[i],init_source) <= init_source.rad)
{
grid_2d[i].tag = 2;
grid_2d[i].time = dis_point_2d(grid_2d[i],init_source) * init_source.slow;
}
}
for (int i = 0; i < xnum*ynum; i++)
{
if (grid_2d[i].tag == 2)
{
for (int j = 0; j < 4; j++)
{
if (grid_2d[i].neighbor[j] != NULL && grid_2d[i].neighbor[j]->tag == 0)
{
grid_2d[i].neighbor[j]->tag = 1;
close_node_ptr.push_back(grid_2d[i].neighbor[j]);
}
}
}
}
//calculate trial time for all close nodes
for (int i = 0; i < close_node_ptr.size(); i++)
{
local_update(close_node_ptr[i], dh);
}
//marching forward and updating the close nodes set
while (!close_node_ptr.empty())
{
// heap sort close nodes pointers to put the node first that has smallest time
heap_sort(close_node_ptr,close_node_ptr.size());
//change the first node's tag to 2 and update it's neighbor's time if it is not active
close_node_ptr[0]->tag = 2;
for (int i = 0; i < 4; i++)
{
if (close_node_ptr[0]->neighbor[i] != NULL && close_node_ptr[0]->neighbor[i]->tag == 0)
{
close_node_ptr[0]->neighbor[i]->tag = 1;
local_update(close_node_ptr[0]->neighbor[i], dh);
close_node_ptr.push_back(close_node_ptr[0]->neighbor[i]);
}
else if (close_node_ptr[0]->neighbor[i] != NULL && close_node_ptr[0]->neighbor[i]->tag == 1)
{
local_update(close_node_ptr[0]->neighbor[i], dh);
}
}
close_node_ptr.erase(close_node_ptr.begin());
}
for (int i = 0; i < xnum*ynum; i++)
{
if (grid_2d[i].time > 1e+10)
{
cout << grid_2d[i].x << " " << grid_2d[i].y << " " << grid_2d[i].tag << " " << grid_2d[i].syn_time << " nan " << grid_2d[i].time - grid_2d[i].syn_time << endl;
}
else cout << grid_2d[i].x << " " << grid_2d[i].y << " " << grid_2d[i].tag << " " << grid_2d[i].syn_time << " " << grid_2d[i].time << " " << grid_2d[i].time - grid_2d[i].syn_time << endl;
}
return 0;
}

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fmm_2d_grid/run.sh Executable file
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#!/bin/bash
g++-9 fmm_2d_grid.cpp -o fmm_2d_grid -O2
./fmm_2d_grid > out.txt
xyz2grd out.txt -Gout.nc -R0/1000/0/500 -I5/5 -i0,1,5
ncview out.nc

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0
# Generated by triangle -pq30a20 cube_mesh.poly

141161
fmm_2d_triangle/cube_mesh.1_linear.msh Normal file
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File diff suppressed because it is too large Load Diff

35
fmm_2d_triangle/cube_mesh.poly Normal file
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@@ -0,0 +1,35 @@
16 2 0 1
0 0 0 1
1 200 0 1
2 200 400 1
3 250 400 1
4 250 0 1
5 800 0 1
6 800 400 1
7 850 400 1
8 850 0 1
9 1000 0 1
10 1000 500 1
11 550 500 1
12 550 100 1
13 500 100 1
14 500 500 1
15 0 500 1
16 0 1
0 0 1 1
1 1 2 1
2 2 3 1
3 3 4 1
4 4 5 1
5 5 6 1
6 6 7 1
7 7 8 1
8 8 9 1
9 9 10 1
10 10 11 1
11 11 12 1
12 12 13 1
13 13 14 1
14 14 15 1
15 15 0 1
0

580
fmm_2d_triangle/fmm_2d_triangle.cpp Normal file
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@@ -0,0 +1,580 @@
#include "iostream"
#include "fstream"
#include "sstream"
#include "string.h"
#include "cmath"
#include "vector"
#include "iomanip"
#include "algorithm"
#include "ctime"
#include "gctl/gctl_stream.h"
#include "gctl/gctl_heapsort.h"
#include "gctl/gctl_geometry2d.h"
#include "gctl/gctl_triangle_io.h"
using namespace std;
struct vertex;
struct ele;
struct source : public gctl::point2d_c
{
double rad;
double slow;
};
struct vertex : public gctl::vertex2d_c
{
int tag = 0; //0 = far away, 1 = close, 2 = active
double slow; // slow are constant within a element. a mean value must be set in local update
double time = 1e+30;
double syn_time = 1e+30; //synthetic direct arrive time (only for error test)
vector<vertex*> v_neigh; //neighbor vertex unknown amount
vector<ele*> e_neigh; //neighbor element unknown amount
vector<int> ve_order; // 此顶点在相接三角形中的顶点序号(0、1或者2)，与e_neigh中的三角形一一对应，应该能提高计算效率
};
struct ele
{
int id, tag = 0; //0 = not calculated, 1 = already calculated
vertex* vec_ptr[3];
double slow;
double area;
double edge_l[3];
};
double local_update_triangle(double area, double length_ab, double length_ac,
double length_bc, double a_time, double b_time, double slow)
{
///< 沿边ac或bc传播的走时值
double direct_time = GCTL_MIN(a_time + slow*length_ac,
b_time + slow*length_bc);
double u = b_time - a_time;
double w = slow*slow*length_ab*length_ab - u*u;
if (w < 0) return direct_time;
w = sqrt(w);
double rho0 = 2.0*area/length_ab;
double ksi0 = sqrt(length_ac*length_ac - rho0*rho0)/length_ab;
double ksi = ksi0 - u*rho0/(length_ab*w);
if (ksi >= 1 || ksi <= 0) return direct_time;
else
{
double trial_time = a_time + u*ksi0 + w*rho0/length_ab;
if (trial_time > a_time && trial_time > b_time)
return GCTL_MIN(trial_time, direct_time);
else return direct_time;
}
}
void local_update(vertex* vert_ptr)
{
int j;
double time1, time2;
// loop over all neighboring triangles. If any one have two known vertice, update time
for (int i = 0; i < vert_ptr->e_neigh.size(); i++)
{
if (vert_ptr->e_neigh[i]->tag == 0)
{
j = vert_ptr->ve_order[i];
if (vert_ptr->e_neigh[i]->vec_ptr[(j+1)%3]->tag == 2 &&
vert_ptr->e_neigh[i]->vec_ptr[(j+2)%3]->tag == 2)
{
time1 = vert_ptr->e_neigh[i]->vec_ptr[(j+1)%3]->time;
time2 = vert_ptr->e_neigh[i]->vec_ptr[(j+2)%3]->time;
if (time1 <= time2)
vert_ptr->time = GCTL_MIN(vert_ptr->time, local_update_triangle(
vert_ptr->e_neigh[i]->area, vert_ptr->e_neigh[i]->edge_l[j],
vert_ptr->e_neigh[i]->edge_l[(j+2)%3], vert_ptr->e_neigh[i]->edge_l[(j+1)%3],
time1, time2, vert_ptr->e_neigh[i]->slow));
else
vert_ptr->time = GCTL_MIN(vert_ptr->time, local_update_triangle(
vert_ptr->e_neigh[i]->area, vert_ptr->e_neigh[i]->edge_l[j],
vert_ptr->e_neigh[i]->edge_l[(j+1)%3], vert_ptr->e_neigh[i]->edge_l[(j+2)%3],
time2, time1, vert_ptr->e_neigh[i]->slow));
vert_ptr->e_neigh[i]->tag = 1;
}
}
}
return;
}
class FMM_2D_TRIANGLE
{
public:
FMM_2D_TRIANGLE(){}
~FMM_2D_TRIANGLE(){}
// read mesh files generated by triangle
int ReadFiles(char* filename);
// output a Gmsh (.msh) file
int OutMsh(char* filename, bool tag);
// initialize node slowness. slowness of the source will be used if default slowness is zero.
void InitNodeSlowness(double default_slow = 0.0);
// add abnormal slowness
void SetRectangeSlowness(double ab_slow,double xmin,double xmax,double ymin,double ymax);
// initialize triangle's slowness
void InitEleSlowness();
// calculate synthetic direct arrive time and fmm time
void CalculateSolution();
// set source parameters
int set_init_source(double x,double y,double r,double s);
private:
int node_num_, ele_num_;
vector<vertex> nodes_;
vector<ele> elements_;
vector<vertex*> nodes_ptr_;
source init_source_;
};
int FMM_2D_TRIANGLE::ReadFiles(char* filename)
{
ifstream infile;
string temp_str;
stringstream temp_ss;
char full_name[1024];
//read node file first
strcpy(full_name,filename);
strcat(full_name,".node");
infile.open(full_name);
if (!infile)
{
cerr << "file open error: " << full_name << endl;
return -1;
}
else
{
clog << "reading node file:\t" << full_name;
getline(infile,temp_str);
temp_ss = gctl::str2ss(temp_str);
temp_ss >> node_num_;
nodes_.resize(node_num_);
for (int i = 0; i < node_num_; i++)
{
getline(infile,temp_str);
temp_ss = gctl::str2ss(temp_str);
temp_ss >> nodes_[i].id >> nodes_[i].x >> nodes_[i].y;
}
infile.close();
clog << " ... done!" << endl;
}
//read element file
int tmp_ids[3];
strcpy(full_name,filename);
strcat(full_name,".ele");
infile.open(full_name);
if (!infile)
{
cerr << "file open error: " << full_name << endl;
return -1;
}
else
{
clog << "reading element file:\t" << full_name;
getline(infile,temp_str);
temp_ss = gctl::str2ss(temp_str);
temp_ss >> ele_num_;
elements_.resize(ele_num_);
for (int i = 0; i < ele_num_; i++)
{
getline(infile,temp_str);
temp_ss = gctl::str2ss(temp_str);
temp_ss >> elements_[i].id >> tmp_ids[0] >> tmp_ids[1] >> tmp_ids[2];
elements_[i].vec_ptr[0] = &nodes_[tmp_ids[0]];
elements_[i].vec_ptr[1] = &nodes_[tmp_ids[1]];
elements_[i].vec_ptr[2] = &nodes_[tmp_ids[2]];
}
infile.close();
clog << " ... done!" << endl;
}
// reorder the vertice sequence to anti-clockwise
gctl::point2d_c v01, v02;
vertex *tmp_ptr;
for (int i = 0; i < ele_num_; i++)
{
v01.x = elements_[i].vec_ptr[1]->x - elements_[i].vec_ptr[0]->x;
v01.y = elements_[i].vec_ptr[1]->y - elements_[i].vec_ptr[0]->y;
v02.x = elements_[i].vec_ptr[2]->x - elements_[i].vec_ptr[0]->x;
v02.y = elements_[i].vec_ptr[2]->y - elements_[i].vec_ptr[0]->y;
if (v01.x*v02.y - v01.y*v02.x < 0)
{
tmp_ptr = elements_[i].vec_ptr[1];
elements_[i].vec_ptr[1] = elements_[i].vec_ptr[2];
elements_[i].vec_ptr[2] = tmp_ptr;
}
}
//sort neighboring vertice and triangles for a vertex
double p;
for (int i = 0; i < ele_num_; i++)
{
for (int j = 0; j < 3; j++)
{
// opposite edge length of vertex j
elements_[i].edge_l[j] = gctl::geometry2d::distance(elements_[i].vec_ptr[(j+1)%3], elements_[i].vec_ptr[(j+2)%3]);
}
// calculate triangle's area
p = 0.5*(elements_[i].edge_l[0] + elements_[i].edge_l[1] + elements_[i].edge_l[2]);
elements_[i].area = sqrt(p*(p-elements_[i].edge_l[0])*(p-elements_[i].edge_l[1])*(p-elements_[i].edge_l[2]));
for (int j = 0; j < 3; j++)
{
// add current element to each vertex element's neighboring list
elements_[i].vec_ptr[j]->e_neigh.push_back(&elements_[i]);
elements_[i].vec_ptr[j]->ve_order.push_back(j);
// add the other two vertice to current vertex's node neighboring list
// this operation will create duplicate enters for nodes's neighbors
elements_[i].vec_ptr[j]->v_neigh.push_back(elements_[i].vec_ptr[(j+1)%3]);
elements_[i].vec_ptr[j]->v_neigh.push_back(elements_[i].vec_ptr[(j+2)%3]);
}
}
// remove duplicate enters for neighboring vertice
vector<vertex*>::iterator pos;
for (int i = 0; i < node_num_; i++)
{
sort(nodes_[i].v_neigh.begin(),nodes_[i].v_neigh.end()); //对顶点序列由小到大排序
pos = unique(nodes_[i].v_neigh.begin(),nodes_[i].v_neigh.end()); //获取重复序列开始的位置
nodes_[i].v_neigh.erase(pos,nodes_[i].v_neigh.end()); //删除重复点
}
//output statistics to screen
clog << "node number:\t" << node_num_ << endl;
clog << "element number:\t" << ele_num_ << endl;
return 0;
}
int FMM_2D_TRIANGLE::OutMsh(char* filename, bool tag)
{
ofstream outfile;
if (tag)
strcat(filename,"_linear.msh");
else
strcat(filename,".msh");
outfile.open(filename);
if (!outfile)
{
cerr << "file open error: " << filename << endl;
return -1;
}
else clog << "writing .msh file:\t" << filename << endl;
outfile<<"$MeshFormat"<<endl<<"2.2 0 8"<<endl<<"$EndMeshFormat"<<endl<<"$Nodes"<<endl<<node_num_<<endl;
// set the first vertex index to 1 to avoid a display bug in Gmsh
for (int i = 0; i < node_num_; i++)
{
outfile << nodes_[i].id + 1 << " " << setprecision(16) << nodes_[i].x << " " << nodes_[i].y << " 0" << endl;
}
outfile<<"$EndNodes"<<endl;
outfile<<"$Elements"<<endl<<ele_num_<<endl;
for (int i = 0; i < ele_num_; i++)
{
outfile << elements_[i].id + 1 <<" 2 1 0";
for (int j = 0; j < 3; j++)
outfile << " " << elements_[i].vec_ptr[j]->id + 1;
outfile << endl;
}
outfile << "$EndElements"<< endl;
if (tag)
{
int tmp_node_num = 0;
for (int i = 0; i < node_num_; i++)
{
if (nodes_[i].time < 1e+10)
tmp_node_num++;
}
outfile <<"$NodeData"<< endl;
outfile<<1<<endl<<"\"fmm arrive time (ms)\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<tmp_node_num<<endl;
for (int i = 0; i < node_num_; i++)
{
if (nodes_[i].time < 1e+10)
{
outfile << nodes_[i].id + 1 << " " << setprecision(16) << nodes_[i].time << endl;
}
}
outfile<<"$EndNodeData"<< endl;
outfile <<"$NodeData"<< endl;
outfile<<1<<endl<<"\"synthetic time (ms)\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<tmp_node_num<<endl;
for (int i = 0; i < node_num_; i++)
{
if (nodes_[i].time < 1e+10) // this condition seems unnecessary, we will keep it here until we know better
{
outfile << nodes_[i].id + 1 << " " << setprecision(16) << nodes_[i].syn_time << endl;
}
}
outfile<<"$EndNodeData"<< endl;
// 这里我们顺带统计一下误差的平均值和标准差
vector<double> tmp_err(tmp_node_num, 0.0);
double mean_err = 0.0;
outfile <<"$NodeData"<< endl;
outfile<<1<<endl<<"\"fmm - synthetic time (ms)\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<tmp_node_num<<endl;
for (int i = 0; i < node_num_; i++)
{
if (nodes_[i].time < 1e+10)
{
tmp_err[i] = nodes_[i].time - nodes_[i].syn_time;
mean_err += tmp_err[i];
outfile << nodes_[i].id + 1 << " " << setprecision(16) << tmp_err[i] << endl;
}
}
outfile<<"$EndNodeData"<< endl;
mean_err /= 1.0*tmp_node_num;
double rms_err = 0.0;
for (int i = 0; i < tmp_node_num; i++)
{
rms_err += pow(tmp_err[i] - mean_err,2);
}
clog << "mean error = " << mean_err << endl;
clog << "rms of error= " << sqrt(rms_err/tmp_node_num) << endl;
outfile <<"$ElementData"<< endl;
outfile<<1<<endl<<"\"model slowness (s/m)\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<ele_num_<<endl;
for (int i = 0; i < ele_num_; i++)
{
outfile << elements_[i].id + 1 << " " << setprecision(16) << elements_[i].slow << endl;
}
outfile<<"$EndElementData"<< endl;
}
outfile.close();
return 0;
}
void FMM_2D_TRIANGLE::InitNodeSlowness(double default_slow)
{
// if no background slowness is given.
// set all node's slowness as the same as source's slowness.
if (default_slow == 0.0)
{
for (int i = 0; i < node_num_; i++)
{
nodes_[i].slow = init_source_.slow;
}
}
else
{
for (int i = 0; i < node_num_; i++)
{
nodes_[i].slow = default_slow;
}
}
return;
}
// set slowness within a rectangular area.
void FMM_2D_TRIANGLE::SetRectangeSlowness(double ab_slow,double xmin,double xmax,double ymin,double ymax)
{
for (int i = 0; i < node_num_; i++)
{
if (nodes_[i].x >= xmin && nodes_[i].x <= xmax &&
nodes_[i].y >= ymin && nodes_[i].y <= ymax)
{
nodes_[i].slow = ab_slow;
}
}
return;
}
// set element's slowness as the mean value of three vertice's slowness.
void FMM_2D_TRIANGLE::InitEleSlowness()
{
for (int i = 0; i < ele_num_; i++)
{
elements_[i].slow = (elements_[i].vec_ptr[0]->slow + elements_[i].vec_ptr[1]->slow + elements_[i].vec_ptr[2]->slow)/3.0;
}
return;
}
void FMM_2D_TRIANGLE::CalculateSolution()
{
time_t start_time, stop_time;
start_time = time(NULL);
clog << "calculating first arrive time ... ";
//calculate synthetic direct arrival time for all nodes
//this calculation is only valid for testing when there is no abnormal slowness or obstacles.
for (int i = 0; i < node_num_; i++)
{
nodes_[i].syn_time = gctl::geometry2d::distance(&nodes_[i], &init_source_) * init_source_.slow;
}
//initialize source nodes and close nodes
//set a vertex's tag as 'active' if it is inside the initial radius
//and calculate node's time as direct arrival time
for (int i = 0; i < node_num_; i++)
{
if (gctl::geometry2d::distance(&nodes_[i], &init_source_) <= init_source_.rad)
{
nodes_[i].tag = 2;
nodes_[i].time = gctl::geometry2d::distance(&nodes_[i], &init_source_) * init_source_.slow;
}
}
//set all close vertice's tag to 'close' and add them to wave front list
for (int i = 0; i < node_num_; i++)
{
if (nodes_[i].tag == 2)
{
for (int j = 0; j < nodes_[i].v_neigh.size(); j++)
{
if (nodes_[i].v_neigh[j]->tag == 0)
{
nodes_[i].v_neigh[j]->tag = 1;
nodes_ptr_.push_back(nodes_[i].v_neigh[j]);
}
}
}
}
//assign initial tags for elements
//set an element as calculated only if all its three vectice are activated.
for (int i = 0; i < ele_num_; i++)
{
if (elements_[i].vec_ptr[0]->tag == 2 &&
elements_[i].vec_ptr[1]->tag == 2 &&
elements_[i].vec_ptr[2]->tag == 2)
{
elements_[i].tag = 1;
}
}
//calculate trial time for all close nodes
for (int i = 0; i < nodes_ptr_.size(); i++)
{
local_update(nodes_ptr_[i]);
}
gctl::heap_sort<vertex*> time_sorter;
//marching forward and updating the close nodes set
while (!nodes_ptr_.empty())
{
// heap sort close nodes pointers to put a node at the first place if it has the smallest time
time_sorter.execute(&nodes_ptr_, [](vector<vertex*> *a, int l_id, int r_id)->bool{
if (a->at(l_id)->time < a->at(r_id)->time) return true;
else return false;
});
//change the first node's tag to 2 and update it's neighbor's time if it is not active (tag != 2)
//this step is needed as a vertex may possess smaller time once it's neighbor time is updated.
nodes_ptr_[0]->tag = 2;
for (int i = 0; i < nodes_ptr_[0]->v_neigh.size(); i++)
{
// if a neighboring node is not added to the wave front list.
// Add it to the list and update it's time
if (nodes_ptr_[0]->v_neigh[i]->tag == 0)
{
nodes_ptr_[0]->v_neigh[i]->tag = 1;
local_update(nodes_ptr_[0]->v_neigh[i]);
nodes_ptr_.push_back(nodes_ptr_[0]->v_neigh[i]);
}
// already in the wave front list, update it's time
else if (nodes_ptr_[0]->v_neigh[i]->tag == 1)
{
local_update(nodes_ptr_[0]->v_neigh[i]);
}
}
// remove the first node from the wave front list
nodes_ptr_.erase(nodes_ptr_.begin());
}
stop_time = time(NULL);
clog << stop_time - start_time << " s" << endl;
return;
}
int FMM_2D_TRIANGLE::set_init_source(double x, double y, double r, double s)
{
if (s <=0 || r <= 0)
{
cerr << "source initialization error!" << endl;
return -1;
}
else
{
init_source_.x = x; init_source_.y = y;
init_source_.slow = s; init_source_.rad = r;
return 0;
}
}
/*******************************************main function here*****************************/
// argv[1] -> running mode
// argv[2] -> name of the input triangle file
// argv[3] -> source parameter
// argv[4] -> abnormal slownesses separated by commas
int main(int argc, char* argv[])
{
FMM_2D_TRIANGLE instance;
if (!strcmp(argv[1],"convert"))
{
if(!instance.ReadFiles(argv[2]))
instance.OutMsh(argv[2],false);
}
else if (!strcmp(argv[1],"calculate"))
{
double s_x, s_y, s_rad, s_slow;
if (4 != sscanf(argv[3], "%lf/%lf/%lf/%lf", &s_x, &s_y, &s_rad, &s_slow))
{
cerr << "wrong source parameter." << endl;
return 0;
}
if(instance.set_init_source(s_x, s_y, s_rad, s_slow)) return 0;
if(instance.ReadFiles(argv[2])) return 0;
//set node slowness here
instance.InitNodeSlowness();
//add abnormal slowness
double ab_slow, ab_xmin, ab_xmax, ab_ymin, ab_ymax;
string all_ab_para, old_ab_para;
string tmp_str;
if (argc >= 5)
{
old_ab_para = argv[4];
gctl::replace_all(all_ab_para, old_ab_para, ",", " ");
stringstream tmp_ss = gctl::str2ss(all_ab_para);
while (tmp_ss >> tmp_str)
{
if (5 != sscanf(tmp_str.c_str(), "%lf/%lf/%lf/%lf/%lf",
&ab_slow, &ab_xmin, &ab_xmax, &ab_ymin, &ab_ymax))
{
cerr << "wrong source parameter." << endl;
return 0;
}
instance.SetRectangeSlowness(ab_slow, ab_xmin, ab_xmax, ab_ymin, ab_ymax);
}
}
// set element slowness here
instance.InitEleSlowness();
instance.CalculateSolution();
if(instance.OutMsh(argv[2],true)) return 0;
}
return 0;
}

10
fmm_2d_triangle/get_mesh.sh Executable file
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#!/bin/bash
# get triangular mesh with the minimal internal angle set to 30 degrees and the maximal area equals 50
#triangle -pq30a50 cube_mesh.poly
triangle -pq30a20 cube_mesh.poly
# display the mesh using showme (the native triangle software visualization tool)
#triangle-showme -b cube_mesh.1
# convert to Gmsh (.msh) file and display
#./fmm_2d_triangle convert cube_mesh.1 && open -a Gmsh cube_mesh.1.msh
./fmm_2d_triangle convert cube_mesh.1 && open -a Gmsh cube_mesh.1.msh

11
fmm_2d_triangle/routine1.sh Executable file
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#!/bin/bash
# compile
# g++-9 fmm_2d_triangle.cpp -o fmm_2d_triangle -I/usr/local/include -L/usr/local/lib -lgctl
# get triangular mesh with the minimal internal angle set to 30 degrees and the maximal area equals 50
#triangle -pq30a50 simple_mesh.poly
# convert to Gmsh (.msh) file and display
#./fmm_2d_triangle convert simple_mesh.1 && open -a Gmsh simple_mesh.1.msh
# calculate fmm time
./fmm_2d_triangle calculate cube_mesh.1 50/50/30/1.0 && open -a Gmsh cube_mesh.1_linear.msh

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fmm_2d_triangle/simple_mesh.1.msh Normal file
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fmm_2d_triangle/simple_mesh.1.node Normal file
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360
fmm_2d_triangle/simple_mesh.1.poly Normal file
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@@ -0,0 +1,360 @@
0 2 0 1
356 1
0 1 5015 1
1 2 4780 1
2 3 6485 1
3 0 8090 1
4 4 1943 1
5 5 4119 1
6 7 7782 1
7 10 4359 1
8 12 736 1
9 28 7799 1
10 81 8083 1
11 203 642 1
12 215 483 1
13 251 7 1
14 436 803 1
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16 441 733 1
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215 5325 5705 1
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245 6434 6437 1
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247 6435 6432 1
248 6439 6402 1
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252 6452 6481 1
253 6457 6462 1
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255 6462 6447 1
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260 6485 6457 1
261 6486 3 1
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266 6518 6369 1
267 6521 6370 1
268 6525 6670 1
269 6528 8036 1
270 6474 6434 1
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273 6594 6564 1
274 6595 6406 1
275 6600 6569 1
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277 6674 6675 1
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282 6831 7042 1
283 6791 7491 1
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285 6972 6328 1
286 6979 7044 1
287 7042 6953 1
288 7044 6831 1
289 7046 6979 1
290 6879 7406 1
291 7218 7239 1
292 7232 7243 1
293 7239 7232 1
294 7243 6879 1
295 7225 7402 1
296 7247 7673 1
297 7249 8070 1
298 7331 7564 1
299 7336 7553 1
300 7402 7218 1
301 7406 7249 1
302 7491 7225 1
303 7549 7550 1
304 7550 6791 1
305 7553 7549 1
306 7557 7607 1
307 7559 8067 1
308 7564 7557 1
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310 7607 7336 1
311 7615 7675 1
312 7627 7637 1
313 7636 7627 1
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355 8090 7316 1
0
# Generated by triangle -pq30a50 simple_mesh.poly

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11
fmm_2d_triangle/simple_mesh.poly Normal file
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@@ -0,0 +1,11 @@
4 2 0 1
0 0 0 1
1 1000 0 1
2 1000 500 1
3 0 500 1
4 0 1
0 0 1 1
1 1 2 1
2 2 3 1
3 3 0 1
0

317
fmm_3d_block/fmm_3d_block.cpp Normal file
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#include "iostream"
#include "cmath"
#include "vector"
#include "fstream"
#include "iomanip"
using namespace std;
struct point_3d
{
double x, y, z;
};
struct source : point_3d
{
double rad;
double slow;
};
struct grid_point : point_3d
{
int tag = 0; //0 = far away, 1 = close, 2 = active
double time = 1e+30;
double syn_time = 1e+30; //synthetic direct arrive time (only for error test)
double slow;
grid_point* neighbor[6] = {NULL,NULL,NULL,NULL,NULL,NULL}; //up down left right in out
};
typedef vector<grid_point> grid_point_array;
typedef vector<grid_point*> ptr_grid_point_array;
void update_heap(ptr_grid_point_array& a, int i, int n)
{
int iMax = i,
iLeft = 2 * i + 1,
iRight = 2 * (i + 1);
if (iLeft < n && a[iMax]->time < a[iLeft]->time) {
iMax = iLeft;
}
if (iRight < n && a[iMax]->time < a[iRight]->time) {
iMax = iRight;
}
if (iMax != i) {
grid_point* tmp = a[iMax];
a[iMax] = a[i];
a[i] = tmp;
update_heap(a, iMax, n);
}
return;
}
void heap_sort(ptr_grid_point_array& a, int n)
{
for (int i = (n - 1) / 2; i >= 0; i--) {
update_heap(a, i, n);
}
for (int i = n - 1; i > 0; --i) {
grid_point* tmp = a[i];
a[i] = a[0];
a[0] = tmp;
update_heap(a, 0, i);
}
return;
}
double dis_point_3d(point_3d a, point_3d b)
{
return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y) + (a.z-b.z)*(a.z-b.z));
}
void local_update(grid_point* point_ptr, double delta_h)
{
//solve a quadratic equation to get the trial time
/*
double a = 0, b = 0, c = -1.0 * pow(delta_h,2) * pow(point_ptr->slow,2);
for (int i = 0; i < 6; i++)
{
if (point_ptr->neighbor[i] != NULL && point_ptr->neighbor[i]->tag == 2)
{
a += 1.0;
b += -2.0*point_ptr->neighbor[i]->time;
c += pow(point_ptr->neighbor[i]->time,2);
}
}
*/
// a second order upwind difference scheme
double a = 0, b = 0, c = -4.0 * pow(delta_h,2) * pow(point_ptr->slow,2);
for (int i = 0; i < 6; i++)
{
if (point_ptr->neighbor[i] != NULL && point_ptr->neighbor[i]->tag == 2)
{
a += 4.0;
b += -8.0*point_ptr->neighbor[i]->time;
c += 4.0*pow(point_ptr->neighbor[i]->time,2);
if (point_ptr->neighbor[i]->neighbor[i] != NULL && point_ptr->neighbor[i]->neighbor[i]->tag == 2)
{
a += 5.0;
b += -16.0*point_ptr->neighbor[i]->time + 6.0*point_ptr->neighbor[i]->neighbor[i]->time;
c += 12.0*pow(point_ptr->neighbor[i]->time,2) - 8.0*point_ptr->neighbor[i]->time*point_ptr->neighbor[i]->neighbor[i]->time
+ pow(point_ptr->neighbor[i]->neighbor[i]->time,2);
}
}
}
double delta = b*b - 4.0*a*c; //in a upwind scheme, delta is always bigger than zero
point_ptr->time = min(point_ptr->time, 0.5*(sqrt(delta) - b)/a);
return;
}
void abnormal_slowness(grid_point_array& grid_recall, double ab_slow,double xmin, double xmax, double ymin, double ymax, double zmin, double zmax)
{
for (int i = 0; i < grid_recall.size(); i++)
{
if (grid_recall[i].x >= xmin && grid_recall[i].x <= xmax &&
grid_recall[i].y >= ymin && grid_recall[i].y <= ymax &&
grid_recall[i].z >= zmin && grid_recall[i].z <= zmax)
{
grid_recall[i].slow = ab_slow;
}
}
return;
}
int main(int argc, char const *argv[])
{
//set grid parameters
int xnum = 101;
int ynum = 51;
int znum = 51;
double xmin = 0;
double ymin = 0;
double zmin = 0;
double dh = 10;
//set source parameters
source init_source;
init_source.x = 50;
init_source.y = 250;
init_source.z = 250;
init_source.rad = 30;
init_source.slow = 1.0;
//output name
char ofilename[1024] = "out.msh";
//initialize grid
grid_point_array grid_3d;
grid_3d.resize(xnum*ynum*znum);
//down-left corner to up-right corner
for (int k = 0; k < znum; k++)
{
for (int i = 0; i < ynum; i++)
{
for (int j = 0; j < xnum; j++)
{
grid_3d[i*xnum+j+k*xnum*ynum].x = xmin + dh*j;
grid_3d[i*xnum+j+k*xnum*ynum].y = ymin + dh*i;
grid_3d[i*xnum+j+k*xnum*ynum].z = zmin + dh*k;
grid_3d[i*xnum+j+k*xnum*ynum].slow = init_source.slow;
if (k <= znum-2) grid_3d[i*xnum+j+k*xnum*ynum].neighbor[0] = &grid_3d[i*xnum+j+(k+1)*xnum*ynum];
if (k >= 1) grid_3d[i*xnum+j+k*xnum*ynum].neighbor[1] = &grid_3d[i*xnum+j+(k-1)*xnum*ynum];
if (j >= 1) grid_3d[i*xnum+j+k*xnum*ynum].neighbor[2] = &grid_3d[i*xnum+j-1+k*xnum*ynum]; //left
if (j <= xnum-2) grid_3d[i*xnum+j+k*xnum*ynum].neighbor[3] = &grid_3d[i*xnum+j+1+k*xnum*ynum]; //right
if (i <= ynum-2) grid_3d[i*xnum+j+k*xnum*ynum].neighbor[4] = &grid_3d[(i+1)*xnum+j+k*xnum*ynum]; //up
if (i >= 1) grid_3d[i*xnum+j+k*xnum*ynum].neighbor[5] = &grid_3d[(i-1)*xnum+j+k*xnum*ynum]; //down
//calculate synthetic direct arrive time
grid_3d[i*xnum+j+k*xnum*ynum].syn_time = dis_point_3d(grid_3d[i*xnum+j+k*xnum*ynum], init_source) * init_source.slow;
}
}
}
//add abnormal slowness here
//abnormal_slowness(grid_3d,1e+30,200,250,0,500,0,250);
//abnormal_slowness(grid_3d,1e+30,500,550,0,500,250,500);
//abnormal_slowness(grid_3d,1e+30,800,850,0,500,0,250);
ptr_grid_point_array close_node_ptr;
//initialize source nodes and close nodes;
for (int i = 0; i < xnum*ynum*znum; i++)
{
if (dis_point_3d(grid_3d[i],init_source) <= init_source.rad)
{
grid_3d[i].tag = 2;
grid_3d[i].time = dis_point_3d(grid_3d[i],init_source) * init_source.slow;
}
}
for (int i = 0; i < xnum*ynum*znum; i++)
{
if (grid_3d[i].tag == 2)
{
for (int j = 0; j < 6; j++)
{
if (grid_3d[i].neighbor[j] != NULL && grid_3d[i].neighbor[j]->tag == 0)
{
grid_3d[i].neighbor[j]->tag = 1;
close_node_ptr.push_back(grid_3d[i].neighbor[j]);
}
}
}
}
//calculate trial time for all close nodes
for (int i = 0; i < close_node_ptr.size(); i++)
{
local_update(close_node_ptr[i], dh);
}
//marching forward and updating the close nodes set
while (!close_node_ptr.empty())
{
// heap sort close nodes pointers to put the node first that has smallest time
heap_sort(close_node_ptr,close_node_ptr.size());
//change the first node's tag to 2 and update it's neighbor's time if it is not active
close_node_ptr[0]->tag = 2;
for (int i = 0; i < 6; i++)
{
if (close_node_ptr[0]->neighbor[i] != NULL && close_node_ptr[0]->neighbor[i]->tag == 0)
{
close_node_ptr[0]->neighbor[i]->tag = 1;
local_update(close_node_ptr[0]->neighbor[i], dh);
close_node_ptr.push_back(close_node_ptr[0]->neighbor[i]);
}
else if (close_node_ptr[0]->neighbor[i] != NULL && close_node_ptr[0]->neighbor[i]->tag == 1)
{
local_update(close_node_ptr[0]->neighbor[i], dh);
}
}
close_node_ptr.erase(close_node_ptr.begin());
}
//output Gmsh(.msh) file
ofstream outfile;
outfile.open(ofilename);
if (!outfile)
{
cerr << "file open error: " << ofilename << endl;
return -1;
}
outfile<<"$MeshFormat"<<endl<<"2.2 0 8"<<endl<<"$EndMeshFormat"<<endl<<"$Nodes"<<endl<<xnum*ynum*znum<<endl;
// set the first vertex index to 1 to avoid a display bug in Gmsh
for (int i = 0; i < xnum*ynum*znum; i++)
{
outfile << i + 1 << " " << setprecision(16) << grid_3d[i].x << " " << grid_3d[i].y << " " << grid_3d[i].z << endl;
}
outfile<<"$EndNodes"<<endl;
outfile<<"$Elements"<<endl<< (xnum-1)*(ynum-1)*(znum-1) <<endl;
for (int k = 0; k < znum-1; k++)
{
for (int i = 0; i < ynum-1; i++)
{
for (int j = 0; j < xnum-1; j++)
{
outfile << 1 + j + i*(xnum-1) + k*(xnum-1)*(ynum-1) <<" 5 1 0 ";
outfile << 1 + j + i*xnum + k*xnum*ynum << " "
<< 1 + j + i*xnum + k*xnum*ynum + 1 << " "
<< 1 + j + (i+1)*xnum + k*xnum*ynum + 1 << " "
<< 1 + j + (i+1)*xnum + k*xnum*ynum << " "
<< 1 + j + i*xnum + (k+1)*xnum*ynum << " "
<< 1 + j + i*xnum + (k+1)*xnum*ynum + 1 << " "
<< 1 + j + (i+1)*xnum + (k+1)*xnum*ynum + 1 << " "
<< 1 + j + (i+1)*xnum + (k+1)*xnum*ynum << endl;
}
}
}
outfile << "$EndElements"<< endl;
int tmp_node_num = 0;
for (int i = 0; i < xnum*ynum*znum; i++)
{
if (grid_3d[i].time < 1e+10)
tmp_node_num++;
}
outfile <<"$NodeData"<< endl;
outfile<<1<<endl<<"\"fmm arrive time (ms)\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<tmp_node_num<<endl;
for (int i = 0; i < xnum*ynum*znum; i++)
{
if (grid_3d[i].time < 1e+10)
{
outfile << i + 1 << " " << setprecision(16) << grid_3d[i].time << endl;
}
}
outfile<<"$EndNodeData"<< endl;
outfile <<"$NodeData"<< endl;
outfile<<1<<endl<<"\"fmm - synthetic time (ms)\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<tmp_node_num<<endl;
for (int i = 0; i < xnum*ynum*znum; i++)
{
if (grid_3d[i].time < 1e+10)
{
outfile << i + 1 << " " << setprecision(16) << grid_3d[i].time - grid_3d[i].syn_time << endl;
}
}
outfile<<"$EndNodeData"<< endl;
outfile <<"$NodeData"<< endl;
outfile<<1<<endl<<"\"node tag\""<<endl<<1<<endl<<0.0<<endl
<<3<<endl<<0<<endl<<1<<endl<<xnum*ynum*znum<<endl;
for (int i = 0; i < xnum*ynum*znum; i++)
{
outfile << i + 1 << " " << setprecision(16) << grid_3d[i].tag << endl;
}
outfile<<"$EndNodeData"<< endl;
outfile.close();
return 0;
}

1300843
fmm_3d_block/out.msh Normal file
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7
fmm_3d_block/run.sh Executable file
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@@ -0,0 +1,7 @@
#!/bin/bash
g++-9 fmm_3d_block.cpp -o fmm_3d_block -O2
./fmm_3d_block
open -a Gmsh out.msh