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// ATC headers
#include "ATC_TransferPartitionOfUnity.h"
#include "ATC_Error.h"
#include "FE_Engine.h"
#include "LammpsInterface.h"
#include "Quadrature.h"
#include "PerPairQuantity.h"
#ifdef HAS_DXA
#include "DislocationExtractor.h"
#endif
// Other Headers
#include <vector>
#include <map>
#include <set>
#include <utility>
#include <fstream>
#include <exception>
using namespace std;
static const int line_ngauss = 10;
static double line_xg[line_ngauss], line_wg[line_ngauss];
namespace ATC {
ATC_TransferPartitionOfUnity::ATC_TransferPartitionOfUnity(
string groupName,
double ** & perAtomArray,
LAMMPS_NS::Fix * thisFix,
string matParamFile)
: ATC_Transfer(groupName,perAtomArray,thisFix,matParamFile)
{
ATC::Quadrature::instance()->set_line_quadrature(line_ngauss,line_xg,line_wg);
// transform gauss points from [-1,1] to [0,1]
double lam1 = 0.0, lam2 = 1.0;
double del_lambda = 0.5*(lam2 - lam1);
double avg_lambda = 0.5*(lam2 + lam1);
for (int i = 0; i < line_ngauss; i++) {
double lambda = del_lambda*line_xg[i] +avg_lambda;
line_xg[i] = lambda;
line_wg[i] *= 0.5;
}
}
//-------------------------------------------------------------------
ATC_TransferPartitionOfUnity::~ATC_TransferPartitionOfUnity()
{
// clear out all managed memory to avoid conflicts with dependencies on class member data
interscaleManager_.clear();
}
//-------------------------------------------------------------------
void ATC_TransferPartitionOfUnity::compute_projection(
const DENS_MAT & atomData, DENS_MAT & nodeData)
{
throw ATC_Error("unimplemented function");
}
//-------------------------------------------------------------------
void ATC_TransferPartitionOfUnity::compute_bond_matrix()
{
atomicBondMatrix_ = bondMatrix_->quantity();
}
//-------------------------------------------------------------------
// kinetic energy portion of stress
/**
* @class KineticTensor
* @brief Class for computing the quantity - m v' (x) v'
*/
void ATC_TransferPartitionOfUnity::compute_kinetic_stress(
DENS_MAT& stress)
{
compute_variation_velocity();
int * type = lammpsInterface_->atom_type();
double * mass = lammpsInterface_->atom_mass();
double * rmass = lammpsInterface_->atom_rmass();
double mvv2e = lammpsInterface_->mvv2e(); // [MV^2]-->[Energy]
DENS_MAT & v = variationVelocity_;
atomicTensor_.reset(nLocal_,6);
for (int i = 0; i < nLocal_; i++) {
int atomIdx = internalToAtom_(i);
double ma = mass ? mass[type[atomIdx]]: rmass[atomIdx];
ma *= mvv2e; // convert mass to appropriate units
atomicTensor_(i,0) -= ma*v(i,0)*v(i,0);
atomicTensor_(i,1) -= ma*v(i,1)*v(i,1);
atomicTensor_(i,2) -= ma*v(i,2)*v(i,2);
atomicTensor_(i,3) -= ma*v(i,0)*v(i,1);
atomicTensor_(i,4) -= ma*v(i,0)*v(i,2);
atomicTensor_(i,5) -= ma*v(i,1)*v(i,2);
}
project_volume_normalized(atomicTensor_, stress);
}
//-------------------------------------------------------------------
// on-the-fly calculation of stress
void ATC_TransferPartitionOfUnity::compute_potential_stress(DENS_MAT& stress)
{
int nCols;
if (atomToElementMapType_ == LAGRANGIAN)
nCols = 9;
else // EULERIAN
nCols = 6;
stress.reset(nNodes_,nCols);
// neighbor lists
int *numneigh = lammpsInterface_->neighbor_list_numneigh();
int **firstneigh = lammpsInterface_->neighbor_list_firstneigh();
double ** xatom = lammpsInterface_->xatom();
Array<bool> latticePeriodicity(3);
latticePeriodicity(0) = (bool) periodicity[0];
latticePeriodicity(1) = (bool) periodicity[1];
latticePeriodicity(2) = (bool) periodicity[2];
// process differently for mesh vs translation-invariant kernels
ATC::LammpsInterface::instance()->stream_msg_once("computing potential stress: ",true,false);
int heartbeatFreq = (nLocal_ <= 10 ? 1 : (int) nLocal_ / 10);
// mesh-based kernel functions
int nodesPerElement = feEngine_->fe_mesh()->num_nodes_per_element();
Array<int> node_list(nodesPerElement);
DENS_VEC shp(nodesPerElement);
DENS_VEC xa(nsd_),xb(nsd_),xab(nsd_),xlambda(nsd_);
DENS_VEC virial(nCols);
for (int j = 0; j < nLocal_; j++) {
if (j % heartbeatFreq == 0 ) {
ATC::LammpsInterface::instance()->stream_msg_once(".",false,false);
}
// first atom location
int lammps_j = internalToAtom_(j);
xa.copy(xPointer_[lammps_j],3);
for (int k = 0; k < numneigh[lammps_j]; ++k) {
int lammps_k = firstneigh[lammps_j][k];
//if (lammps_k < lammps_j) continue; // full neighbor list
// second (neighbor) atom location
xb.copy(xPointer_[lammps_k],3);
double delx = xatom[lammps_j][0] - xatom[lammps_k][0];
double dely = xatom[lammps_j][1] - xatom[lammps_k][1];
double delz = xatom[lammps_j][2] - xatom[lammps_k][2];
double rsq = delx*delx + dely*dely + delz*delz;
double fforce = 0;
lammpsInterface_->pair_force(lammps_j,lammps_k,rsq,fforce);
fforce *= 0.5; // 1/2 sum_ab = sum_(ab)
if (atomToElementMapType_ == LAGRANGIAN) {
double delX = xref_[lammps_j][0] - xref_[lammps_k][0];
double delY = xref_[lammps_j][1] - xref_[lammps_k][1];
double delZ = xref_[lammps_j][2] - xref_[lammps_k][2];
virial[0] =-delx*fforce*delX;
virial[1] =-delx*fforce*delY;
virial[2] =-delx*fforce*delZ;
virial[3] =-dely*fforce*delX;
virial[4] =-dely*fforce*delY;
virial[5] =-dely*fforce*delZ;
virial[6] =-delz*fforce*delX;
virial[7] =-delz*fforce*delY;
virial[8] =-delz*fforce*delZ;
}
else {// EULERIAN
virial[0] =-delx*delx*fforce;
virial[1] =-dely*dely*fforce;
virial[2] =-delz*delz*fforce;
virial[3] =-delx*dely*fforce;
virial[4] =-delx*delz*fforce;
virial[5] =-dely*delz*fforce;
}
xab = xa - xb;
for (int i = 0; i < line_ngauss; i++) {
double lambda = line_xg[i];
xlambda = lambda*xab + xb;
lammpsInterface_->periodicity_correction(xlambda.ptr());
feEngine_->shape_functions(xlambda,shp,node_list);
// accumulate to nodes whose support overlaps the integration point
for (int I = 0; I < nodesPerElement; I++) {
int inode = node_list(I);
double inv_vol = (accumulantInverseVolumes_->quantity())(inode,inode);
double bond_value = inv_vol*shp(I)*line_wg[i];
for (int j = 0; j < nCols; j++)
stress(inode,j) += virial[j]*bond_value;
}
}
}
}
if (lammpsInterface_->comm_rank() == 0) {
ATC::LammpsInterface::instance()->stream_msg_once("done",false,true);
}
}
//-------------------------------------------------------------------
// compute kinetic part of heat flux
void ATC_TransferPartitionOfUnity::compute_kinetic_heatflux(
DENS_MAT& flux)
{
compute_variation_velocity();
int * type = lammpsInterface_->atom_type();
double * mass = lammpsInterface_->atom_mass();
double * rmass = lammpsInterface_->atom_rmass();
double mvv2e = lammpsInterface_->mvv2e();
double * atomPE = lammpsInterface_->compute_pe_peratom();
double atomKE, atomEnergy;
atomicVector_.reset(nLocal_,3);
for (int i = 0; i < nLocal_; i++) {
int atomIdx = internalToAtom_(i);
double ma = mass ? mass[type[atomIdx]]: rmass[atomIdx];
ma *= mvv2e; // convert mass to appropriate units
atomKE = 0.0;
for (int j = 0; j < nsd_; j++) {
atomKE += 0.5*ma*(variationVelocity_(i,j)*variationVelocity_(i,j));
}
atomEnergy = atomKE + atomPE[atomIdx];
for (int j = 0; j < nsd_; j++) {
atomicVector_(i,j) += atomEnergy*variationVelocity_(i,j);
}
}
project_volume_normalized(atomicVector_,flux);
}
//-------------------------------------------------------------------
// on-the-fly calculation of the heat flux
void ATC_TransferPartitionOfUnity::compute_potential_heatflux(DENS_MAT& flux)
{
compute_variation_velocity();
flux.zero();
// neighbor lists
int *numneigh = lammpsInterface_->neighbor_list_numneigh();
int **firstneigh = lammpsInterface_->neighbor_list_firstneigh();
double ** xatom = lammpsInterface_->xatom();
Array<bool> latticePeriodicity(3);
latticePeriodicity(0) = (bool) periodicity[0];
latticePeriodicity(1) = (bool) periodicity[1];
latticePeriodicity(2) = (bool) periodicity[2];
// process differently for mesh vs translation-invariant kernels
// mesh-based kernel functions
int nodesPerElement = feEngine_->fe_mesh()->num_nodes_per_element();
Array<int> node_list(nodesPerElement);
DENS_VEC shp(nodesPerElement);
DENS_VEC xa(nsd_),xb(nsd_),xab(nsd_),xlambda(nsd_);
for (int j = 0; j < nLocal_; j++) {
// first atom location
int lammps_j = internalToAtom_(j);
xa.copy(xPointer_[lammps_j],3);
for (int k = 0; k < numneigh[lammps_j]; ++k) {
int lammps_k = firstneigh[lammps_j][k];
// second (neighbor) atom location
xb.copy(xPointer_[lammps_k],3);
double delx = xatom[lammps_j][0] - xatom[lammps_k][0];
double dely = xatom[lammps_j][1] - xatom[lammps_k][1];
double delz = xatom[lammps_j][2] - xatom[lammps_k][2];
double rsq = delx*delx + dely*dely + delz*delz;
double fforce = 0;
lammpsInterface_->pair_force(lammps_j,lammps_k,rsq,fforce);
fforce *= 0.5; // 1/2 sum_ab = sum_(ab)
fforce *= (delx*variationVelocity_(j,0) +
dely*variationVelocity_(j,1) +
delz*variationVelocity_(j,2));
double flux_vec[3];
if (atomToElementMapType_ == LAGRANGIAN) {
double delX = xref_[lammps_j][0] - xref_[lammps_k][0];
double delY = xref_[lammps_j][1] - xref_[lammps_k][1];
double delZ = xref_[lammps_j][2] - xref_[lammps_k][2];
flux_vec[0] =fforce*delX;
flux_vec[1] =fforce*delY;
flux_vec[2] =fforce*delZ;
}
else {// EULERIAN
flux_vec[0] =fforce*delx;
flux_vec[1] =fforce*dely;
flux_vec[2] =fforce*delz;
}
xab = xa - xb;
for (int i = 0; i < line_ngauss; i++) {
double lambda = line_xg[i];
xlambda = lambda*xab + xb;
lammpsInterface_->periodicity_correction(xlambda.ptr());
feEngine_->shape_functions(xlambda,shp,node_list);
// accumulate to nodes whose support overlaps the integration point
for (int I = 0; I < nodesPerElement; I++) {
int inode = node_list(I);
double inv_vol = (accumulantInverseVolumes_->quantity())(inode,inode);
double bond_value = inv_vol*shp(I)*line_wg[i];
flux(inode,0) += flux_vec[0]*bond_value;
flux(inode,1) += flux_vec[1]*bond_value;
flux(inode,2) += flux_vec[2]*bond_value;
}
}
}
}
}
//-------------------------------------------------------------------
void ATC_TransferPartitionOfUnity::compute_variation_velocity()
{
// now compute v'_a = v_a - N_Ia v_I
variationVelocity_.reset(nLocal_,nsd_);
if (nLocal_>0) {
// interpolate nodal velocities to the atoms
vbar_.reset(nLocal_,nsd_);
double ** v = lammpsInterface_->vatom();
PerAtomQuantity<double> * vbar = interscaleManager_.per_atom_quantity(field_to_prolongation_name(VELOCITY));
if (!vbar) {
DENS_MAN * nodeVelocity = interscaleManager_.dense_matrix(field_to_string(VELOCITY));
if (this->kernel_on_the_fly()) {
vbar = new OnTheFlyShapeFunctionProlongation(this,
nodeVelocity,this->atom_coarsegraining_positions());
} else {
vbar = new FtaShapeFunctionProlongation(this,
nodeVelocity,this->interpolant());
}
interscaleManager_.add_per_atom_quantity(vbar,
field_to_prolongation_name(VELOCITY));
}
// use of prolong assumes atom system contained within mesh
vbar_ = vbar->quantity();
// compute and store variation velocities of atoms
for (int i = 0; i < nLocal_; i++) {
int atomIdx = internalToAtom_(i);
for (int j = 0; j < nsd_; j++) {
variationVelocity_(i,j) = v[atomIdx][j] - vbar_(i,j);
}
}
}
}
//-------------------------------------------------------------------
// calculation of the dislocation density tensor
void ATC_TransferPartitionOfUnity::compute_dislocation_density(DENS_MAT & A)
{
A.reset(nNodes_,9);
#ifdef HAS_DXA
double cnaCutoff = lammpsInterface_->near_neighbor_cutoff();
// Extract dislocation lines within the processor's domain.
DXADislocationExtractor extractor(lammpsInterface_->lammps_pointer(),dxaExactMode_);
extractor.extractDislocations(lammpsInterface_->neighbor_list(), cnaCutoff);
// Calculate scalar dislocation density and density tensor.
double dislocationDensity = 0.0;
double dislocationDensityTensor[9] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
const std::vector<DislocationSegment*>& segments = extractor.getSegments();
int localNumberLines = (int) segments.size();
int totalNumberLines;
lammpsInterface_->int_allsum(&localNumberLines,&totalNumberLines,1);
if (totalNumberLines == 0) {
ATC::LammpsInterface::instance()->print_msg_once("no dislocation lines found");
return;
}
// for output
int nPt = 0, nSeg = 0;
for(unsigned segmentIndex = 0; segmentIndex < segments.size(); segmentIndex++) {
DislocationSegment* segment = segments[segmentIndex];
const std::deque<Point3>& line = segment->line;
nPt += line.size();
nSeg += line.size()-1;
}
DENS_MAT segCoor(3,nPt);
Array2D<int> segConn(2,nSeg);
DENS_MAT segBurg(nPt,3);
DENS_MAT local_A(nNodes_,9);
local_A.zero();
Array<bool> latticePeriodicity(3);
latticePeriodicity(0) = (bool) periodicity[0];
latticePeriodicity(1) = (bool) periodicity[1];
latticePeriodicity(2) = (bool) periodicity[2];
// mesh-based kernel functions
int nodesPerElement = feEngine_->fe_mesh()->num_nodes_per_element();
Array<int> node_list(nodesPerElement);
DENS_VEC shp(nodesPerElement);
DENS_VEC xa(nsd_),xb(nsd_),xba(nsd_),xlambda(nsd_);
int iPt = 0, iSeg= 0;
for(unsigned segmentIndex = 0; segmentIndex < segments.size(); segmentIndex++) {
DislocationSegment* segment = segments[segmentIndex];
const std::deque<Point3>& line = segment->line;
Vector3 burgers = segment->burgersVectorWorld;
Point3 x1, x2;
for(std::deque<Point3>::const_iterator p1 = line.begin(), p2 = line.begin() + 1; p2 < line.end(); ++p1, ++p2) {
x1 = (*p1);
x2 = (*p2);
Vector3 delta = x2 - x1;
// totals
dislocationDensity += Length(delta);
for(int i = 0; i < 3; i++) {
for(int j = 0; j < 3; j++) {
dislocationDensityTensor[3*j+i] += delta[i] * burgers[j];
}
}
// nodal partition
for(int k = 0; k < 3; k++) {
xa(k) = x1[k];
xb(k) = x2[k];
xba(k) = delta[k];
}
for (int i = 0; i < line_ngauss; i++) {
double lambda = line_xg[i];
xlambda = lambda*xba + xa;
lammpsInterface_->periodicity_correction(xlambda.ptr());
feEngine_->shape_functions(xlambda,shp,node_list);
// accumulate to nodes whose support overlaps the integration point
for (int I = 0; I < nodesPerElement; I++) {
int inode = node_list(I);
double inv_vol = (accumulantInverseVolumes_->quantity())(inode,inode);
double bond_value = inv_vol*shp(I)*line_wg[i];
local_A(inode,0) += xba(0)*burgers[0]*bond_value;
local_A(inode,1) += xba(0)*burgers[1]*bond_value;
local_A(inode,2) += xba(0)*burgers[2]*bond_value;
local_A(inode,3) += xba(1)*burgers[0]*bond_value;
local_A(inode,4) += xba(1)*burgers[1]*bond_value;
local_A(inode,5) += xba(1)*burgers[2]*bond_value;
local_A(inode,6) += xba(2)*burgers[0]*bond_value;
local_A(inode,7) += xba(2)*burgers[1]*bond_value;
local_A(inode,8) += xba(2)*burgers[2]*bond_value;
}
}
segCoor(0,iPt) = x1[0];
segCoor(1,iPt) = x1[1];
segCoor(2,iPt) = x1[2];
segBurg(iPt,0) = burgers[0];
segBurg(iPt,1) = burgers[1];
segBurg(iPt,2) = burgers[2];
segConn(0,iSeg) = iPt;
segConn(1,iSeg) = iPt+1;
iPt++;
iSeg++;
}
segCoor(0,iPt) = x2[0];
segCoor(1,iPt) = x2[1];
segCoor(2,iPt) = x2[2];
segBurg(iPt,0) = burgers[0];
segBurg(iPt,1) = burgers[1];
segBurg(iPt,2) = burgers[2];
iPt++;
}
int count = nNodes_*9;
lammpsInterface_->allsum(local_A.ptr(),A.ptr(),count);
double totalDislocationDensity;
lammpsInterface_->allsum(&dislocationDensity,&totalDislocationDensity,1);
double totalDislocationDensityTensor[9];
lammpsInterface_->allsum(dislocationDensityTensor,totalDislocationDensityTensor,9);
int totalNumberSegments;
lammpsInterface_->int_allsum(&nSeg,&totalNumberSegments,1);
// output
double volume = lammpsInterface_->domain_volume();
stringstream ss;
ss << "total dislocation line length = " << totalDislocationDensity;
ss << " lines = " << totalNumberLines << " segments = " << totalNumberSegments;
ss << "\n ";
ss << "total dislocation density tensor = \n";
for(int i = 0; i < 3; i++) {
ss << " ";
for(int j = 0; j < 3; j++) {
totalDislocationDensityTensor[3*j+i] /= volume;
ss << totalDislocationDensityTensor[3*j+i] << " ";
}
ss << "\n";
}
ATC::LammpsInterface::instance()->print_msg_once(ss.str());
ss.str("");
DENS_VEC A_avg(9);
for (int i = 0; i < nNodes_; i++) {
for (int j = 0; j < 9; j++) {
A_avg(j) += A(i,j);
}
}
A_avg /= nNodes_;
ss << "average nodal dislocation density tensor = \n";
ss << A_avg(0) << " " << A_avg(1) << " " << A_avg(2) << "\n";
ss << A_avg(3) << " " << A_avg(4) << " " << A_avg(5) << "\n";
ss << A_avg(6) << " " << A_avg(7) << " " << A_avg(8) << "\n";
ATC::LammpsInterface::instance()->print_msg_once(ss.str());
if (nSeg > 0) {
set<int> otypes;
otypes.insert(VTK);
otypes.insert(FULL_GNUPLOT);
string name = "dislocation_segments_step=" ;
name += to_string(output_index());
OutputManager segOutput(name,otypes);
segOutput.write_geometry(&segCoor,&segConn);
OUTPUT_LIST segOut;
segOut["burgers_vector"] = &segBurg;
segOutput.write_data(0,&segOut);
}
#else
throw ATC_Error("TransferParititionOfUnity::compute_dislocaton_density - unimplemented function");
#endif
}
} // end namespace ATC
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