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27898d890ff83b1341c3d1cc4654a89d96720523
LBPM/analysis/eikonal.cpp
Mark Berrill 27898d890f Fixing bug in Domain
2018-05-16 14:00:35 -04:00

385 lines
15 KiB
C++
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#include "analysis/eikonal.h"
#include "analysis/imfilter.h"
static inline float minmod(float &a, float &b)
{
float value = a;
if ( a*b < 0.0)
value=0.0;
else if (fabs(a) > fabs(b))
value = b;
return value;
}
static inline double minmod(double &a, double &b){
double value;
value = a;
if ( a*b < 0.0) value=0.0;
else if (fabs(a) > fabs(b)) value = b;
return value;
}
template<class TYPE>
static inline MPI_Datatype getType( );
template<> inline MPI_Datatype getType<float>() { return MPI_FLOAT; }
template<> inline MPI_Datatype getType<double>() { return MPI_DOUBLE; }
/******************************************************************
* Solve the eikonal equation *
******************************************************************/
template<class TYPE>
TYPE Eikonal( Array<TYPE> &Distance, const Array<char> &ID, const Domain &Dm, const int timesteps)
{
/*
* This routine converts the data in the Distance array to a signed distance
* by solving the equation df/dt = sign(1-|grad f|), where Distance provides
* the values of f on the mesh associated with domain Dm
* It has been tested with segmented data initialized to values [-1,1]
* and will converge toward the signed distance to the surface bounding the associated phases
*
* Reference:
* Min C (2010) On reinitializing level set functions, Journal of Computational Physics 229
*/
int xdim = Dm.Nx-2;
int ydim = Dm.Ny-2;
int zdim = Dm.Nz-2;
fillHalo<TYPE> fillData(Dm.Comm, Dm.rank_info,xdim,ydim,zdim,1,1,1,0,1);
// Arrays to store the second derivatives
Array<TYPE> Dxx(Dm.Nx,Dm.Ny,Dm.Nz);
Array<TYPE> Dyy(Dm.Nx,Dm.Ny,Dm.Nz);
Array<TYPE> Dzz(Dm.Nx,Dm.Ny,Dm.Nz);
Array<int8_t> sign(ID.size());
for (size_t i=0; i<sign.length(); i++)
sign(i) = ID(i) == 0 ? -1:1;
int count = 0;
double dt = 0.1;
double GlobalVar = 0.0;
while (count < timesteps){
// Communicate the halo of values
fillData.fill(Distance);
// Compute second order derivatives
for (int k=1;k<Dm.Nz-1;k++){
for (int j=1;j<Dm.Ny-1;j++){
for (int i=1;i<Dm.Nx-1;i++){
Dxx(i,j,k) = Distance(i+1,j,k) + Distance(i-1,j,k) - 2*Distance(i,j,k);
Dyy(i,j,k) = Distance(i,j+1,k) + Distance(i,j-1,k) - 2*Distance(i,j,k);
Dzz(i,j,k) = Distance(i,j,k+1) + Distance(i,j,k-1) - 2*Distance(i,j,k);
}
}
}
fillData.fill(Dxx);
fillData.fill(Dyy);
fillData.fill(Dzz);
double LocalMax = 0.0;
double LocalVar = 0.0;
// Execute the next timestep
for (int k=1;k<Dm.Nz-1;k++){
for (int j=1;j<Dm.Ny-1;j++){
for (int i=1;i<Dm.Nx-1;i++){
double s = sign(i,j,k);
// local second derivative terms
double Dxxp = minmod(Dxx(i,j,k),Dxx(i+1,j,k));
double Dyyp = minmod(Dyy(i,j,k),Dyy(i,j+1,k));
double Dzzp = minmod(Dzz(i,j,k),Dzz(i,j,k+1));
double Dxxm = minmod(Dxx(i,j,k),Dxx(i-1,j,k));
double Dyym = minmod(Dyy(i,j,k),Dyy(i,j-1,k));
double Dzzm = minmod(Dzz(i,j,k),Dzz(i,j,k-1));
/* //............Compute upwind derivatives ...................
Dxp = Distance(i+1,j,k) - Distance(i,j,k) + 0.5*Dxxp;
Dyp = Distance(i,j+1,k) - Distance(i,j,k) + 0.5*Dyyp;
Dzp = Distance(i,j,k+1) - Distance(i,j,k) + 0.5*Dzzp;
Dxm = Distance(i,j,k) - Distance(i-1,j,k) + 0.5*Dxxm;
Dym = Distance(i,j,k) - Distance(i,j-1,k) + 0.5*Dyym;
Dzm = Distance(i,j,k) - Distance(i,j,k-1) + 0.5*Dzzm;
*/
double Dxp = Distance(i+1,j,k)- Distance(i,j,k) - 0.5*Dxxp;
double Dyp = Distance(i,j+1,k)- Distance(i,j,k) - 0.5*Dyyp;
double Dzp = Distance(i,j,k+1)- Distance(i,j,k) - 0.5*Dzzp;
double Dxm = Distance(i,j,k) - Distance(i-1,j,k) + 0.5*Dxxm;
double Dym = Distance(i,j,k) - Distance(i,j-1,k) + 0.5*Dyym;
double Dzm = Distance(i,j,k) - Distance(i,j,k-1) + 0.5*Dzzm;
// Compute upwind derivatives for Godunov Hamiltonian
double Dx, Dy, Dz;
if ( s < 0.0){
if (Dxp + Dxm > 0.f)
Dx = Dxp*Dxp;
else
Dx = Dxm*Dxm;
if (Dyp + Dym > 0.f)
Dy = Dyp*Dyp;
else
Dy = Dym*Dym;
if (Dzp + Dzm > 0.f)
Dz = Dzp*Dzp;
else
Dz = Dzm*Dzm;
}
else{
if (Dxp + Dxm < 0.f)
Dx = Dxp*Dxp;
else
Dx = Dxm*Dxm;
if (Dyp + Dym < 0.f)
Dy = Dyp*Dyp;
else
Dy = Dym*Dym;
if (Dzp + Dzm < 0.f)
Dz = Dzp*Dzp;
else
Dz = Dzm*Dzm;
}
//Dx = max(Dxp*Dxp,Dxm*Dxm);
//Dy = max(Dyp*Dyp,Dym*Dym);
//Dz = max(Dzp*Dzp,Dzm*Dzm);
double norm = sqrt(Dx + Dy + Dz);
if (norm > 1.0)
norm = 1.0;
Distance(i,j,k) += dt*s*(1.0 - norm);
LocalVar += dt*s*(1.0 - norm);
if (fabs(dt*s*(1.0 - norm)) > LocalMax)
LocalMax = fabs(dt*s*(1.0 - norm));
}
}
}
double GlobalMax;
MPI_Allreduce(&LocalVar,&GlobalVar,1,MPI_DOUBLE,MPI_SUM,Dm.Comm);
MPI_Allreduce(&LocalMax,&GlobalMax,1,MPI_DOUBLE,MPI_MAX,Dm.Comm);
GlobalVar /= (Dm.Nx-2)*(Dm.Ny-2)*(Dm.Nz-2)*Dm.nprocx()*Dm.nprocy()*Dm.nprocz();
count++;
if (count%50 == 0 && Dm.rank()==0 ){
printf("Time=%i, Max variation=%f, Global variation=%f \n",count,GlobalMax,GlobalVar);
fflush(stdout);
}
if (fabs(GlobalMax) < 1e-5){
if (Dm.rank()==0)
printf("Exiting with max tolerance of 1e-5 \n");
count=timesteps;
}
}
return GlobalVar;
}
template float Eikonal<float>( Array<float>&, const Array<char>&, const Domain&, int );
template double Eikonal<double>( Array<double>&, const Array<char>&, const Domain&, int );
/******************************************************************
* A fast distance calculation *
******************************************************************/
bool CalcDist3DIteration( Array<float> &Distance, const Domain & )
{
const float sq2 = sqrt(2.0f);
const float sq3 = sqrt(3.0f);
float dist0[27];
dist0[0] = sq3; dist0[1] = sq2; dist0[2] = sq3;
dist0[3] = sq2; dist0[4] = 1; dist0[5] = sq2;
dist0[6] = sq3; dist0[7] = sq2; dist0[8] = sq3;
dist0[9] = sq2; dist0[10] = 1; dist0[11] = sq2;
dist0[12] = 1; dist0[13] = 0; dist0[14] = 1;
dist0[15] = sq2; dist0[16] = 1; dist0[17] = sq2;
dist0[18] = sq3; dist0[19] = sq2; dist0[20] = sq3;
dist0[21] = sq2; dist0[22] = 1; dist0[23] = sq2;
dist0[24] = sq3; dist0[25] = sq2; dist0[26] = sq3;
bool changed = false;
for (size_t k=1; k<Distance.size(2)-1; k++) {
for (size_t j=1; j<Distance.size(1)-1; j++) {
for (size_t i=1; i<Distance.size(0)-1; i++) {
float dist[27];
dist[0] = Distance(i-1,j-1,k-1); dist[1] = Distance(i,j-1,k-1); dist[2] = Distance(i+1,j-1,k-1);
dist[3] = Distance(i-1,j,k-1); dist[4] = Distance(i,j,k-1); dist[5] = Distance(i+1,j,k-1);
dist[6] = Distance(i-1,j+1,k-1); dist[7] = Distance(i,j+1,k-1); dist[8] = Distance(i+1,j+1,k-1);
dist[9] = Distance(i-1,j-1,k); dist[10] = Distance(i,j-1,k); dist[11] = Distance(i+1,j-1,k);
dist[12] = Distance(i-1,j,k); dist[13] = Distance(i,j,k); dist[14] = Distance(i+1,j,k);
dist[15] = Distance(i-1,j+1,k); dist[16] = Distance(i,j+1,k); dist[17] = Distance(i+1,j+1,k);
dist[18] = Distance(i-1,j-1,k+1); dist[19] = Distance(i,j-1,k+1); dist[20] = Distance(i+1,j-1,k+1);
dist[21] = Distance(i-1,j,k+1); dist[22] = Distance(i,j,k+1); dist[23] = Distance(i+1,j,k+1);
dist[24] = Distance(i-1,j+1,k+1); dist[25] = Distance(i,j+1,k+1); dist[26] = Distance(i+1,j+1,k+1);
float tmp = 1e100;
for (int k=0; k<27; k++)
tmp = std::min(tmp,dist[k]+dist0[k]);
if ( tmp < Distance(i,j,k) ) {
Distance(i,j,k) = tmp;
changed = true;
}
}
}
}
return changed;
}
void CalcDist3D( Array<float> &Distance, const Array<char> &ID, const Domain &Dm )
{
PROFILE_START("Calc Distance");
// Initialize the distance to be 0 fore the cells adjacent to the interface
Distance.fill(1e100);
for (size_t k=1; k<ID.size(2)-1; k++) {
for (size_t j=1; j<ID.size(1)-1; j++) {
for (size_t i=1; i<ID.size(0)-1; i++) {
char id = ID(i,j,k);
if ( id!=ID(i-1,j,k) || id!=ID(i+1,j,k) || id!=ID(i,j-1,k) || id!=ID(i,j+1,k) || id!=ID(i,j,k-1) || id!=ID(i,j,k+1) )
Distance(i,j,k) = 0.5;
}
}
}
// Compute the distance everywhere
fillHalo<float> fillData(Dm.Comm, Dm.rank_info,Dm.Nx,Dm.Ny,Dm.Nz,1,1,1,0,1);
while ( true ) {
// Communicate the halo of values
fillData.fill(Distance);
// The distance of the cell is the minimum of the distance of the neighbors plus the distance to that node
bool changed = CalcDist3DIteration( Distance, Dm );
changed = sumReduce(Dm.Comm,changed);
if ( !changed )
break;
}
// Update the sign of the distance
for (size_t i=0; i<ID.length(); i++)
Distance(i) *= ID(i)>0 ? 1:-1;
PROFILE_STOP("Calc Distance");
}
/******************************************************************
* A fast distance calculation *
******************************************************************/
void CalcDistMultiLevelHelper( Array<float> &Distance, const Domain &Dm )
{
size_t ratio = 4;
std::function<float(const Array<float>&)> coarsen = [ratio]( const Array<float>& data )
{
float tmp = 1e100;
int nx = data.size(0);
int ny = data.size(1);
int nz = data.size(2);
for (int k=0; k<nz; k++) {
float z = k-0.5*(nz-1);
for (int j=0; j<ny; j++) {
float y = j-0.5*(ny-1);
for (int i=0; i<nx; i++) {
float x = i-0.5*(nx-1);
tmp = std::min(data(i,j,k)+sqrt(x*x+y*y+z*z),tmp);
}
}
}
return tmp/ratio;
};
int Nx = Dm.Nx-2;
int Ny = Dm.Ny-2;
int Nz = Dm.Nz-2;
ASSERT(int(Distance.size(0))==Nx+2&&int(Distance.size(1))==Ny+2&&int(Distance.size(2))==Nz+2);
fillHalo<float> fillData(Dm.Comm,Dm.rank_info,Nx,Ny,Nz,1,1,1,0,1);
if ( Nx%ratio==0 && Nx>8 && Ny%ratio==0 && Ny>8 && Nz%ratio==0 && Nz>8 ) {
// Use recursive version
int Nr = std::max(std::max(ratio,ratio),ratio);
// Run Nr iterations, communicate, run Nr iterations
for (int i=0; i<Nr; i++)
CalcDist3DIteration( Distance, Dm );
/*fillData.fill(Distance);
for (int i=0; i<Nr; i++)
CalcDist3DIteration( Distance, Dm );*/
// Coarsen
Array<float> dist(Nx,Ny,Nz);
fillData.copy(Distance,dist);
auto db = Dm.getDatabase()->cloneDatabase();
auto n = db->getVector<int>( "n" );
db->putVector<int>( "n", { n[0]/ratio, n[1]/ratio, n[2]/ratio } );
Domain Dm2(db);
Dm2.CommInit(Dm.Comm);
fillHalo<float> fillData2(Dm2.Comm,Dm2.rank_info,Nx/ratio,Ny/ratio,Nz/ratio,1,1,1,0,1);
auto dist2 = dist.coarsen( {ratio,ratio,ratio}, coarsen );
Array<float> Distance2(Nx/ratio+2,Ny/ratio+2,Nz/ratio+2);
fillData2.copy(dist2,Distance2);
// Solve
CalcDistMultiLevelHelper( Distance2, Dm2 );
// Interpolate the coarse grid to the fine grid
fillData2.copy(Distance2,dist2);
for (int k=0; k<Nz; k++) {
int k2 = k/ratio;
float z = (k-k2*ratio)-0.5*(ratio-1);
for (int j=0; j<Ny; j++) {
int j2 = j/ratio;
float y = (j-j2*ratio)-0.5*(ratio-1);
for (int i=0; i<Nx; i++) {
int i2 = i/ratio;
float x = (i-i2*ratio)-0.5*(ratio-1);
dist(i,j,k) = std::min(dist(i,j,k),ratio*dist2(i2,j2,k2)+sqrt(x*x+y*y+z*z));
}
}
}
fillData.copy(dist,Distance);
// Run Nr iterations, communicate, run Nr iterations
for (int i=0; i<Nr; i++)
CalcDist3DIteration( Distance, Dm );
fillData.fill(Distance);
for (int i=0; i<Nr; i++)
CalcDist3DIteration( Distance, Dm );
} else {
// Use coarse-grid version
while ( true ) {
// Communicate the halo of values
fillData.fill(Distance);
// The distance of the cell is the minimum of the distance of the neighbors plus the distance to that node
bool changed = CalcDist3DIteration( Distance, Dm );
changed = sumReduce(Dm.Comm,changed);
if ( !changed )
break;
}
}
}
void CalcDistMultiLevel( Array<float> &Distance, const Array<char> &ID, const Domain &Dm )
{
PROFILE_START("Calc Distance Multilevel");
int Nx = Dm.Nx-2;
int Ny = Dm.Ny-2;
int Nz = Dm.Nz-2;
ASSERT(int(Distance.size(0))==Nx+2&&int(Distance.size(1))==Ny+2&&int(Distance.size(2))==Nz+2);
fillHalo<float> fillData(Dm.Comm,Dm.rank_info,Nx,Ny,Nz,1,1,1,0,1);
// Initialize the distance to be 0 fore the cells adjacent to the interface
Distance.fill(1e100);
for (size_t k=1; k<ID.size(2)-1; k++) {
for (size_t j=1; j<ID.size(1)-1; j++) {
for (size_t i=1; i<ID.size(0)-1; i++) {
char id = ID(i,j,k);
if ( id!=ID(i-1,j,k) || id!=ID(i+1,j,k) || id!=ID(i,j-1,k) || id!=ID(i,j+1,k) || id!=ID(i,j,k-1) || id!=ID(i,j,k+1) )
Distance(i,j,k) = 0.5;
}
}
}
// Solve the for the distance using a recursive method
CalcDistMultiLevelHelper( Distance, Dm );
// Update the sign of the distance
for (size_t i=0; i<ID.length(); i++)
Distance(i) *= ID(i)>0 ? 1:-1;
fillData.fill(Distance);
// Run a quick filter to smooth the data
float sigma = 0.6;
Array<float> H = imfilter::create_filter<float>( { 1 }, "gaussian", &sigma );
std::vector<imfilter::BC> BC(3,imfilter::BC::replicate);
Distance = imfilter::imfilter_separable<float>( Distance, {H,H,H}, BC );
PROFILE_STOP("Calc Distance Multilevel");
}
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