void AssembleMatrixResNS(MultiLevelProblem &ml_prob){
//pointers
NonLinearImplicitSystem& my_nnlin_impl_sys = ml_prob.get_system<NonLinearImplicitSystem>("Navier-Stokes");
const unsigned level = my_nnlin_impl_sys.GetLevelToAssemble();
const unsigned gridn = my_nnlin_impl_sys.GetLevelMax();
bool assemble_matrix = my_nnlin_impl_sys.GetAssembleMatrix();
Solution* mysolution = ml_prob._ml_sol->GetSolutionLevel(level);
LinearEquationSolver* mylsyspde = my_nnlin_impl_sys._LinSolver[level];
const char* pdename = my_nnlin_impl_sys.name().c_str();
MultiLevelSolution* ml_sol=ml_prob._ml_sol;
Mesh* mymsh = ml_prob._ml_msh->GetLevel(level);
elem* myel = mymsh->el;
SparseMatrix* myKK = mylsyspde->_KK;
NumericVector* myRES = mylsyspde->_RES;
//data
const unsigned dim = mymsh->GetDimension();
unsigned nel= mymsh->GetNumberOfElements();
unsigned igrid= mymsh->GetLevel();
unsigned iproc = mymsh->processor_id();
double ILambda= 0;
double IRe = ml_prob.parameters.get<Fluid>("Fluid").get_IReynolds_number();
bool penalty = true; //mylsyspde->GetStabilization();
const bool symm_mat = false;//mylsyspde->GetMatrixProperties();
const bool NavierStokes = true;
unsigned nwtn_alg = 2;
bool newton = (nwtn_alg==0) ? 0:1;
// solution and coordinate variables
const char Solname[4][2] = {"U","V","W","P"};
vector < unsigned > SolPdeIndex(dim+1);
vector < unsigned > SolIndex(dim+1);
//const char coordinate_name[3][2] = {"X","Y","Z"};
//vector < unsigned > coordinate_Index(dim);
vector< vector < double> > coordinates(dim);
for(unsigned ivar=0; ivar<dim; ivar++) {
SolPdeIndex[ivar]=my_nnlin_impl_sys.GetSolPdeIndex(&Solname[ivar][0]);
SolIndex[ivar]=ml_sol->GetIndex(&Solname[ivar][0]);
//coordinate_Index[ivar]=ivar;//ml_prob.GetIndex(&coordinate_name[ivar][0]);
}
SolPdeIndex[dim]=my_nnlin_impl_sys.GetSolPdeIndex(&Solname[3][0]);
SolIndex[dim]=ml_sol->GetIndex(&Solname[3][0]);
//solution order
unsigned order_ind2 = ml_sol->GetSolutionType(SolIndex[0]);
unsigned order_ind1 = ml_sol->GetSolutionType(SolIndex[dim]);
// declare
vector < int > metis_node2;
vector < int > node1;
vector< vector< int > > KK_dof(dim+1);
vector <double> phi2;
vector <double> gradphi2;
vector <double> nablaphi2;
const double *phi1;
double Weight2;
double normal[3];
vector< vector< double > > F(dim+1);
vector< vector< vector< double > > > B(dim+1);
// reserve
const unsigned max_size = static_cast< unsigned > (ceil(pow(3,dim)));
metis_node2.reserve(max_size);
node1.reserve( static_cast< unsigned > (ceil(pow(2,dim))));
for(int i=0;i<dim;i++) {
coordinates[i].reserve(max_size);
}
phi2.reserve(max_size);
gradphi2.reserve(max_size*dim);
nablaphi2.reserve(max_size*(3*(dim-1)) );
for(int i=0;i<dim;i++) {
KK_dof[i].reserve(max_size);
}
for(int i=0;i<dim+1;i++) F[i].reserve(max_size);
if(assemble_matrix){
for(int i=0;i<dim+1;i++){
B[i].resize(dim+1);
for(int j=0;j<dim+1;j++){
B[i][j].reserve(max_size*max_size);
}
}
}
vector < double > SolVAR(dim+1);
vector < vector < double > > gradSolVAR(dim);
for(int i=0;i<dim;i++) {
gradSolVAR[i].resize(dim);
}
// Set to zeto all the entries of the matrix
if(assemble_matrix) myKK->zero();
// *** element loop ***
for (int iel=mymsh->IS_Mts2Gmt_elem_offset[iproc]; iel < mymsh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = mymsh->IS_Mts2Gmt_elem[iel];
short unsigned kelt=myel->GetElementType(kel);
unsigned nve2=myel->GetElementDofNumber(kel,order_ind2);
unsigned nve1=myel->GetElementDofNumber(kel,order_ind1);
//set to zero all the entries of the FE matrices
metis_node2.resize(nve2);
node1.resize(nve1);
phi2.resize(nve2);
gradphi2.resize(nve2*dim);
nablaphi2.resize(nve2*(3*(dim-1)) );
for(int ivar=0; ivar<dim; ivar++) {
coordinates[ivar].resize(nve2);
KK_dof[ivar].resize(nve2);
F[SolPdeIndex[ivar]].resize(nve2);
memset(&F[SolPdeIndex[ivar]][0],0,nve2*sizeof(double));
if(assemble_matrix){
B[SolPdeIndex[ivar]][SolPdeIndex[ivar]].resize(nve2*nve2);
B[SolPdeIndex[ivar]][SolPdeIndex[dim]].resize(nve2*nve1);
B[SolPdeIndex[dim]][SolPdeIndex[ivar]].resize(nve1*nve2);
memset(&B[SolPdeIndex[ivar]][SolPdeIndex[ivar]][0],0,nve2*nve2*sizeof(double));
memset(&B[SolPdeIndex[ivar]][SolPdeIndex[dim]][0],0,nve2*nve1*sizeof(double));
memset(&B[SolPdeIndex[dim]][SolPdeIndex[ivar]][0],0,nve1*nve2*sizeof(double));
}
}
KK_dof[dim].resize(nve1);
F[SolPdeIndex[dim]].resize(nve1);
memset(&F[SolPdeIndex[dim]][0],0,nve1*sizeof(double));
if(assemble_matrix*nwtn_alg==2){
for(int ivar=0; ivar<dim; ivar++) {
for(int ivar2=1; ivar2<dim; ivar2++) {
B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]].resize(nve2*nve2);
memset(&B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]][0],0,nve2*nve2*sizeof(double));
}
}
}
if(assemble_matrix*penalty){
B[SolPdeIndex[dim]][SolPdeIndex[dim]].resize(nve1*nve1,0.);
memset(&B[SolPdeIndex[dim]][SolPdeIndex[dim]][0],0,nve1*nve1*sizeof(double));
}
for( unsigned i=0;i<nve2;i++){
unsigned inode=myel->GetElementVertexIndex(kel,i)-1u;
unsigned inode_metis=mymsh->GetMetisDof(inode,2);
metis_node2[i]=inode_metis;
for(unsigned ivar=0; ivar<dim; ivar++) {
coordinates[ivar][i]=(*mymsh->_coordinate->_Sol[ivar])(inode_metis);
KK_dof[ivar][i]=mylsyspde->GetKKDof(SolIndex[ivar],SolPdeIndex[ivar],inode);
}
}
for(unsigned i=0;i<nve1;i++) {
unsigned inode=(order_ind1<3)?(myel->GetElementVertexIndex(kel,i)-1u):(kel+i*nel);
node1[i]=inode;
KK_dof[dim][i]=mylsyspde->GetKKDof(SolIndex[dim],SolPdeIndex[dim],inode);
}
if(igrid==gridn || !myel->GetRefinedElementIndex(kel)) {
// *** Gauss poit loop ***
for(unsigned ig=0;ig < ml_prob._ml_msh->_finiteElement[kelt][order_ind2]->GetGaussPointNumber(); ig++) {
// *** get Jacobian and test function and test function derivatives ***
ml_prob._ml_msh->_finiteElement[kelt][order_ind2]->Jacobian(coordinates,ig,Weight2,phi2,gradphi2,nablaphi2);
phi1=ml_prob._ml_msh->_finiteElement[kelt][order_ind1]->GetPhi(ig);
//velocity variable
for(unsigned ivar=0; ivar<dim; ivar++) {
SolVAR[ivar]=0;
for(unsigned ivar2=0; ivar2<dim; ivar2++){
gradSolVAR[ivar][ivar2]=0;
}
unsigned SolIndex=ml_sol->GetIndex(&Solname[ivar][0]);
unsigned SolType=ml_sol->GetSolutionType(&Solname[ivar][0]);
for(unsigned i=0; i<nve2; i++) {
double soli = (*mysolution->_Sol[SolIndex])(metis_node2[i]);
SolVAR[ivar]+=phi2[i]*soli;
for(unsigned ivar2=0; ivar2<dim; ivar2++){
gradSolVAR[ivar][ivar2] += gradphi2[i*dim+ivar2]*soli;
}
}
}
//pressure variable
SolVAR[dim]=0;
unsigned SolIndex=ml_sol->GetIndex(&Solname[3][0]);
unsigned SolType=ml_sol->GetSolutionType(&Solname[3][0]);
for(unsigned i=0; i<nve1; i++){
unsigned sol_dof = mymsh->GetMetisDof(node1[i],SolType);
double soli = (*mysolution->_Sol[SolIndex])(sol_dof);
SolVAR[dim]+=phi1[i]*soli;
}
// *** phi_i loop ***
for(unsigned i=0; i<nve2; i++){
//BEGIN RESIDUALS A block ===========================
for(unsigned ivar=0; ivar<dim; ivar++) {
double Adv_rhs=0;
double Lap_rhs=0;
for(unsigned ivar2=0; ivar2<dim; ivar2++) {
Lap_rhs += gradphi2[i*dim+ivar2]*gradSolVAR[ivar][ivar2];
Adv_rhs += SolVAR[ivar2]*gradSolVAR[ivar][ivar2];
}
F[SolPdeIndex[ivar]][i]+= (-IRe*Lap_rhs-NavierStokes*Adv_rhs*phi2[i]+SolVAR[dim]*gradphi2[i*dim+ivar])*Weight2;
}
//END RESIDUALS A block ===========================
if(assemble_matrix){
// *** phi_j loop ***
for(unsigned j=0; j<nve2; j++) {
double Lap=0;
double Adv1=0;
double Adv2 = phi2[i]*phi2[j]*Weight2;
for(unsigned ivar=0; ivar<dim; ivar++) {
// Laplacian
Lap += gradphi2[i*dim+ivar]*gradphi2[j*dim+ivar]*Weight2;
// advection term I
Adv1 += SolVAR[ivar]*gradphi2[j*dim+ivar]*phi2[i]*Weight2;
}
for(unsigned ivar=0; ivar<dim; ivar++) {
B[SolPdeIndex[ivar]][SolPdeIndex[ivar]][i*nve2+j] += IRe*Lap+ NavierStokes*newton*Adv1;
if(nwtn_alg==2){
// Advection term II
B[SolPdeIndex[ivar]][SolPdeIndex[ivar]][i*nve2+j] += Adv2*gradSolVAR[ivar][ivar];
for(unsigned ivar2=1; ivar2<dim; ivar2++) {
B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]][i*nve2+j] += Adv2*gradSolVAR[ivar][(ivar+ivar2)%dim];
}
}
}
} //end phij loop
// *** phi1_j loop ***
for(unsigned j=0; j<nve1; j++){
for(unsigned ivar=0; ivar<dim; ivar++) {
B[SolPdeIndex[ivar]][SolPdeIndex[dim]][i*nve1+j] -= gradphi2[i*dim+ivar]*phi1[j]*Weight2;
}
} //end phi1_j loop
} // endif assemble_matrix
} //end phii loop
// *** phi1_i loop ***
for(unsigned i=0; i<nve1; i++){
//BEGIN RESIDUALS B block ===========================
double div = 0;
for(unsigned ivar=0; ivar<dim; ivar++) {
div += gradSolVAR[ivar][ivar];
}
F[SolPdeIndex[dim]][i]+= (phi1[i]*div +penalty*ILambda*phi1[i]*SolVAR[dim])*Weight2;
//END RESIDUALS B block ===========================
if(assemble_matrix){
// *** phi_j loop ***
for(unsigned j=0; j<nve2; j++) {
for(unsigned ivar=0; ivar<dim; ivar++) {
B[SolPdeIndex[dim]][SolPdeIndex[ivar]][i*nve2+j]-= phi1[i]*gradphi2[j*dim+ivar]*Weight2;
}
} //end phij loop
} // endif assemble_matrix
} //end phi1_i loop
if(assemble_matrix * penalty){ //block nve1 nve1
// *** phi_i loop ***
for(unsigned i=0; i<nve1; i++){
// *** phi_j loop ***
for(unsigned j=0; j<nve1; j++){
B[SolPdeIndex[dim]][SolPdeIndex[dim]][i*nve1+j]-= ILambda*phi1[i]*phi1[j]*Weight2;
}
}
} //end if penalty
} // end gauss point loop
//--------------------------------------------------------------------------------------------------------
// Boundary Integral --> to be addded
//number of faces for each type of element
// if (igrid==gridn || !myel->GetRefinedElementIndex(kel) ) {
//
// unsigned nfaces = myel->GetElementFaceNumber(kel);
//
// // loop on faces
// for(unsigned jface=0;jface<nfaces;jface++){
//
// // look for boundary faces
// if(myel->GetFaceElementIndex(kel,jface)<0){
// for(unsigned ivar=0; ivar<dim; ivar++) {
// ml_prob.ComputeBdIntegral(pdename, &Solname[ivar][0], kel, jface, level, ivar);
// }
// }
// }
// }
//--------------------------------------------------------------------------------------------------------
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
//Sum the local matrices/vectors into the Global Matrix/Vector
for(unsigned ivar=0; ivar<dim; ivar++) {
myRES->add_vector_blocked(F[SolPdeIndex[ivar]],KK_dof[ivar]);
if(assemble_matrix){
myKK->add_matrix_blocked(B[SolPdeIndex[ivar]][SolPdeIndex[ivar]],KK_dof[ivar],KK_dof[ivar]);
myKK->add_matrix_blocked(B[SolPdeIndex[ivar]][SolPdeIndex[dim]],KK_dof[ivar],KK_dof[dim]);
myKK->add_matrix_blocked(B[SolPdeIndex[dim]][SolPdeIndex[ivar]],KK_dof[dim],KK_dof[ivar]);
if(nwtn_alg==2){
for(unsigned ivar2=1; ivar2<dim; ivar2++) {
myKK->add_matrix_blocked(B[SolPdeIndex[ivar]][SolPdeIndex[(ivar+ivar2)%dim]],KK_dof[ivar],KK_dof[(ivar+ivar2)%dim]);
}
}
}
}
//Penalty
if(assemble_matrix*penalty) myKK->add_matrix_blocked(B[SolPdeIndex[dim]][SolPdeIndex[dim]],KK_dof[dim],KK_dof[dim]);
myRES->add_vector_blocked(F[SolPdeIndex[dim]],KK_dof[dim]);
//--------------------------------------------------------------------------------------------------------
} //end list of elements loop for each subdomain
if(assemble_matrix) myKK->close();
myRES->close();
// ***************** END ASSEMBLY *******************
}
//------------------------------------------------------------------------------------------------------------
void AssembleMatrixResT(MultiLevelProblem &ml_prob){
//pointers and references
LinearImplicitSystem& mylin_impl_sys = ml_prob.get_system<LinearImplicitSystem>("Temperature");
const unsigned level = mylin_impl_sys.GetLevelToAssemble();
const unsigned gridn = mylin_impl_sys.GetLevelMax();
bool assemble_matrix = mylin_impl_sys.GetAssembleMatrix();
Solution* mysolution = ml_prob._ml_sol->GetSolutionLevel(level);
LinearEquationSolver* mylsyspde = mylin_impl_sys._LinSolver[level];
Mesh* mymsh = ml_prob._ml_msh->GetLevel(level);
elem* myel = mymsh->el;
SparseMatrix* myKK = mylsyspde->_KK;
NumericVector* myRES = mylsyspde->_RES;
MultiLevelSolution* ml_sol = ml_prob._ml_sol;
//data
const unsigned dim = mymsh->GetDimension();
unsigned nel = mymsh->GetNumberOfElements();
unsigned igrid = mymsh->GetLevel();
unsigned iproc = mymsh->processor_id();
double IPe = 1./(ml_prob.parameters.get<Fluid>("Fluid").get_Peclet_number());
//solution variable
unsigned SolIndex;
unsigned SolPdeIndex;
SolIndex=ml_sol->GetIndex("T");
SolPdeIndex=mylin_impl_sys.GetSolPdeIndex("T");
//solution order
unsigned order_ind = ml_sol->GetSolutionType(SolIndex);
//coordinates
vector< vector < double> > coordinates(dim);
//const char coordinate_name[3][2] = {"X","Y","Z"};
//vector < unsigned > coordinate_Index(dim);
// for(unsigned ivar=0; ivar<dim; ivar++) {
// coordinate_Index[ivar]=ivar;//ml_prob.GetIndex(coordinate_name[ivar]);
// }
// declare
vector< int > metis_node;
vector< int > KK_dof;
vector <double> phi;
vector <double> gradphi;
vector <double> nablaphi;
double weight;
vector< double > F;
vector< double > B;
// reserve
const unsigned max_size = static_cast< unsigned > (ceil(pow(3,dim)));
metis_node.reserve(max_size);
KK_dof.reserve(max_size);
for(int i=0;i<dim;i++)
coordinates[i].reserve(max_size);
phi.reserve(max_size);
gradphi.reserve(max_size*dim);
nablaphi.reserve(max_size*(3*(dim-1)) );
F.reserve(max_size);
B.reserve(max_size*max_size);
// Set to zeto all the entries of the Global Matrix
if(assemble_matrix) myKK->zero();
// *** element loop ***
for (int iel=mymsh->IS_Mts2Gmt_elem_offset[iproc]; iel < mymsh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = mymsh->IS_Mts2Gmt_elem[iel];
short unsigned kelt=myel->GetElementType(kel);
unsigned nve=myel->GetElementDofNumber(kel,order_ind);
// resize
metis_node.resize(nve);
KK_dof.resize(nve);
phi.resize(nve);
gradphi.resize(nve*dim);
nablaphi.resize( nve*(3*(dim-1)) );
for(int i=0;i<dim;i++){
coordinates[i].resize(nve);
}
// set to zero all the entries of the FE matrices
F.resize(nve);
memset(&F[0],0,nve*sizeof(double));
if(assemble_matrix){
B.resize(nve*nve);
memset(&B[0],0,nve*nve*sizeof(double));
}
// get local to global mappings
for( unsigned i=0;i<nve;i++){
unsigned inode=myel->GetElementVertexIndex(kel,i)-1u;
unsigned inode_metis=mymsh->GetMetisDof(inode,2);
metis_node[i]=inode_metis;
for(unsigned ivar=0; ivar<dim; ivar++) {
coordinates[ivar][i]=(*mymsh->_coordinate->_Sol[ivar])(inode_metis);
}
KK_dof[i]=mylsyspde->GetKKDof(SolIndex,SolPdeIndex,inode);
}
if(igrid==gridn || !myel->GetRefinedElementIndex(kel)) {
// *** Gauss poit loop ***
for(unsigned ig=0;ig < ml_prob._ml_msh->_finiteElement[kelt][order_ind]->GetGaussPointNumber(); ig++) {
// *** get Jacobian and test function and test function derivatives ***
ml_prob._ml_msh->_finiteElement[kelt][order_ind]->Jacobian(coordinates,ig,weight,phi,gradphi,nablaphi);
//Temperature and velocity current solution
double SolT=0;
vector < double > gradSolT(dim,0.);
for(unsigned ivar=0; ivar<dim; ivar++){
gradSolT[ivar]=0;
}
vector < double > SolU(dim,0.);
vector < unsigned > SolIndexU(dim);
SolIndexU[0]=ml_sol->GetIndex("U");
SolIndexU[1]=ml_sol->GetIndex("V");
if(dim==3) SolIndexU[2]=ml_sol->GetIndex("W");
unsigned SolType=ml_sol->GetSolutionType("T");
for(unsigned i=0; i<nve; i++) {
double soli = (*mysolution->_Sol[SolIndex])(metis_node[i]);
SolT+=phi[i]*soli;
for(unsigned ivar2=0; ivar2<dim; ivar2++) gradSolT[ivar2] += gradphi[i*dim+ivar2]*soli;
for(int j=0;j<dim;j++) {
SolU[j]+=phi[i]*(*mysolution->_Sol[SolIndexU[j]])(metis_node[i]);
}
}
// *** phi_i loop ***
for(unsigned i=0; i<nve; i++){
//BEGIN RESIDUALS A block ===========================
double Adv_rhs=0;
double Lap_rhs=0;
for(unsigned ivar=0; ivar<dim; ivar++) {
Lap_rhs += gradphi[i*dim+ivar]*gradSolT[ivar];
Adv_rhs += SolU[ivar]*gradSolT[ivar];
}
F[i]+= (-IPe*Lap_rhs-Adv_rhs*phi[i])*weight;
//END RESIDUALS A block ===========================
if(assemble_matrix){
// *** phi_j loop ***
for(unsigned j=0; j<nve; j++) {
double Lap=0;
double Adv1=0;
for(unsigned ivar=0; ivar<dim; ivar++) {
// Laplacian
Lap += gradphi[i*dim+ivar]*gradphi[j*dim+ivar]*weight;
// advection term I
Adv1 += SolU[ivar]*gradphi[j*dim+ivar]*phi[i]*weight;
}
B[i*nve+j] += IPe*Lap + Adv1;
} // end phij loop
} // end phii loop
} // endif assemble_matrix
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
//Sum the local matrices/vectors into the global Matrix/vector
myRES->add_vector_blocked(F,KK_dof);
if(assemble_matrix) myKK->add_matrix_blocked(B,KK_dof,KK_dof);
} //end list of elements loop for each subdomain
myRES->close();
if(assemble_matrix) myKK->close();
// ***************** END ASSEMBLY *******************
}
void AssembleMatrixResNS(MultiLevelProblem &ml_prob){
adept::Stack & adeptStack = FemusInit::_adeptStack;
clock_t AssemblyTime=0;
clock_t start_time, end_time;
//pointers and references
NonLinearImplicitSystem& my_nnlin_impl_sys = ml_prob.get_system<NonLinearImplicitSystem>("Navier-Stokes");
const unsigned level = my_nnlin_impl_sys.GetLevelToAssemble();
const unsigned gridn = my_nnlin_impl_sys.GetLevelMax();
bool assemble_matrix = my_nnlin_impl_sys.GetAssembleMatrix();
MultiLevelSolution* ml_sol = ml_prob._ml_sol;
Solution* mysolution = ml_sol->GetSolutionLevel(level);
LinearEquationSolver* myLinEqSolver = my_nnlin_impl_sys._LinSolver[level];
Mesh *mymsh = ml_prob._ml_msh->GetLevel(level);
elem *myel = mymsh->el;
SparseMatrix *myKK = myLinEqSolver->_KK;
NumericVector *myRES = myLinEqSolver->_RES;
const unsigned dim = mymsh->GetDimension();
const unsigned nabla_dim = 3*(dim-1);
const unsigned max_size = static_cast< unsigned > (ceil(pow(3,dim)));
// local objects
vector<adept::adouble> SolVAR(dim+1);
vector<vector<adept::adouble> > GradSolVAR(dim+1);
vector<vector<adept::adouble> > NablaSolVAR(dim+1);
for(int i=0;i<dim+1;i++){
GradSolVAR[i].resize(dim);
NablaSolVAR[i].resize(nabla_dim);
}
vector <double > phi;
vector <adept::adouble> gradphi;
vector <adept::adouble> nablaphi;
adept::adouble Weight;
phi.reserve(max_size);
gradphi.reserve(max_size*dim);
nablaphi.reserve(max_size*nabla_dim);
vector <double > phi1;
vector <adept::adouble> gradphi1;
vector <adept::adouble> nablaphi1;
adept::adouble Weight1;
phi1.reserve(max_size);
gradphi1.reserve(max_size*dim);
nablaphi1.reserve(max_size*nabla_dim);
vector <vector < adept::adouble> > vx(dim);
vector <vector < adept::adouble> > vx_face(dim);
for(int i=0;i<dim;i++){
vx[i].reserve(max_size);
vx_face[i].resize(9);
}
vector< vector< adept::adouble > > Soli(dim+1);
vector< vector< int > > dofsVAR(dim+1);
for(int i=0;i<dim+1;i++){
Soli[i].reserve(max_size);
dofsVAR[i].reserve(max_size);
}
vector< vector< double > > Rhs(dim+1);
vector< vector< adept::adouble > > aRhs(dim+1);
for(int i=0;i<dim+1;i++){
aRhs[i].reserve(max_size);
Rhs[i].reserve(max_size);
}
vector < int > dofsAll;
dofsAll.reserve(max_size*(dim+1));
vector < double > KKloc;
KKloc.reserve(dim*max_size*(dim+1)*dim*max_size*(dim+1));
vector < double > Jac;
Jac.reserve(dim*max_size*(dim+1)*dim*max_size*(dim+1));
// ------------------------------------------------------------------------
// Physical parameters
double rhof = ml_prob.parameters.get<Fluid>("Fluid").get_density();
double IRe = ml_prob.parameters.get<Fluid>("Fluid").get_IReynolds_number();
double betans = 1.;
// gravity
double _gravity[3]={0.,0.,0.};
double DRe = 1+(counter*counter)*5;
//double DRe=150;
IRe =( DRe*(counter+1) < 10000 )? 1./(DRe*(counter+1)):1./10000.;
cout<<"iteration="<<counter<<" Reynolds Number = "<<1./IRe<<endl;
counter++;
// -----------------------------------------------------------------
// space discretization parameters
unsigned SolType2 = ml_sol->GetSolutionType(ml_sol->GetIndex("U"));
unsigned SolType1 = ml_sol->GetSolutionType(ml_sol->GetIndex("P"));
unsigned SolTypeVx = 2;
// mesh and procs
unsigned nel = mymsh->GetNumberOfElements();
unsigned igrid = mymsh->GetLevel();
unsigned iproc = mymsh->processor_id();
//----------------------------------------------------------------------------------
//variable-name handling
const char varname[4][3] = {"U","V","W","P"};
vector <unsigned> indexVAR(dim+1);
vector <unsigned> indVAR(dim+1);
vector <unsigned> SolType(dim+1);
for(unsigned ivar=0; ivar<dim; ivar++) {
indVAR[ivar]=ml_sol->GetIndex(&varname[ivar][0]);
SolType[ivar]=ml_sol->GetSolutionType(&varname[ivar][0]);
indexVAR[ivar]=my_nnlin_impl_sys.GetSolPdeIndex(&varname[ivar][0]);
}
indVAR[dim]=ml_sol->GetIndex(&varname[3][0]);
SolType[dim]=ml_sol->GetSolutionType(&varname[3][0]);
indexVAR[dim]=my_nnlin_impl_sys.GetSolPdeIndex(&varname[3][0]);
unsigned indLmbd=ml_sol->GetIndex("lmbd");
//----------------------------------------------------------------------------------
start_time=clock();
myKK->zero();
// *** element loop ***
for(int iel=mymsh->IS_Mts2Gmt_elem_offset[iproc]; iel < mymsh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = mymsh->IS_Mts2Gmt_elem[iel];
short unsigned kelt = myel->GetElementType(kel);
unsigned nve2 = myel->GetElementDofNumber(kel,SolType2);
unsigned nve1 = myel->GetElementDofNumber(kel,SolType1);
unsigned nveVx = myel->GetElementDofNumber(kel,SolTypeVx);
// *******************************************************************************************************
//cout<<SolType1<<" "<<SolType2<<" "<<SolTypeVx<<" "<<nve1<<" "<<nve2<<" "<<nveVx<<endl;
//Rhs
for(int i=0; i<dim; i++) {
dofsVAR[i].resize(nve2);
Soli[indexVAR[i]].resize(nve2);
aRhs[indexVAR[i]].resize(nve2);
Rhs[indexVAR[i]].resize(nve2);
}
dofsVAR[dim].resize(nve1);
Soli[indexVAR[dim]].resize(nve1);
aRhs[indexVAR[dim]].resize(nve1);
Rhs[indexVAR[dim]].resize(nve1);
dofsAll.resize(0);
KKloc.resize((dim*nve2+nve1)*(dim*nve2+nve1));
Jac.resize((dim*nve2+nve1)*(dim*nve2+nve1));
// ----------------------------------------------------------------------------------------
// coordinates
for(int i=0;i<dim;i++){
vx[i].resize(nveVx);
}
for (unsigned i=0;i<nveVx;i++) {
unsigned inode=myel->GetMeshDof(kel,i,SolTypeVx);
unsigned inode_Metis=mymsh->GetMetisDof(inode,SolTypeVx);
for(int j=0; j<dim; j++) {
//coordinates
vx[j][i]= (*mymsh->_coordinate->_Sol[j])(inode_Metis);
}
}
// Velocity
for (unsigned i=0;i<nve2;i++) {
unsigned inode=myel->GetMeshDof(kel,i,SolType2);
unsigned inode_Metis=mymsh->GetMetisDof(inode,SolType2);
for(int j=0; j<dim; j++) {
// velocity dofs
Soli[indexVAR[j]][i] = (*mysolution->_Sol[indVAR[j]])(inode_Metis);
dofsVAR[j][i] = myLinEqSolver->GetKKDof(indVAR[j],indexVAR[j],inode);
aRhs[indexVAR[j]][i] = 0.;
}
}
// Pressure dofs
for (unsigned i=0;i<nve1;i++) {
unsigned inode=myel->GetMeshDof(kel,i,SolType1);
unsigned inode_Metis =mymsh->GetMetisDof(inode,SolType1);
Soli[indexVAR[dim]][i] = (*mysolution->_Sol[indVAR[dim]])(inode_Metis);
dofsVAR[dim][i]=myLinEqSolver->GetKKDof(indVAR[dim],indexVAR[dim],inode);
aRhs[indexVAR[dim]][i] = 0.;
}
// build dof composition
for(int idim=0;idim<dim;idim++){
dofsAll.insert( dofsAll.end(), dofsVAR[idim].begin(), dofsVAR[idim].end() );
}
dofsAll.insert( dofsAll.end(), dofsVAR[dim].begin(), dofsVAR[dim].end() );
if (igrid==gridn || !myel->GetRefinedElementIndex(kel) ) {
adeptStack.new_recording();
// *** Gauss point loop ***
adept::adouble hk;
for (unsigned ig=0;ig < mymsh->_finiteElement[kelt][SolType2]->GetGaussPointNumber(); ig++) {
// *** get Jacobian and test function and test function derivatives in the moving frame***
mymsh->_finiteElement[kelt][SolType2]->Jacobian(vx,ig,Weight,phi,gradphi,nablaphi);
mymsh->_finiteElement[kelt][SolType1]->Jacobian(vx,ig,Weight1,phi1,gradphi1,nablaphi1);
for(int i=0;i<nve1;i++){
for(int j=0;j<nabla_dim;j++){
//cout<<nablaphi[i*nabla_dim+j]<<" ";
}
//cout<<endl;
}
//cout<<endl;
if(ig==0){
double referenceElementArea[6]={8, 1./6., 1., 4., 1., 2.};
double GaussWeight = mymsh->_finiteElement[kelt][SolType2]->GetGaussWeight(ig);
double area=referenceElementArea[kelt]*Weight.value()/GaussWeight;
hk = pow(area,1./dim);
//cout<<hk<<" ";
}
// velocity: solution, gradient and laplace
for(int i=0; i<dim; i++){
SolVAR[i]=0.;
for(int j=0; j<dim; j++) {
GradSolVAR[i][j]=0.;
}
for(int j=0; j<nabla_dim; j++) {
NablaSolVAR[i][j]=0.;
}
for (unsigned inode=0; inode<nve2; inode++) {
adept::adouble soli = Soli[indexVAR[i]][inode];
SolVAR[i]+=phi[inode]*soli;
for(int j=0; j<dim; j++) {
GradSolVAR[i][j]+=gradphi[inode*dim+j]*soli;
}
for(int j=0; j<nabla_dim; j++) {
NablaSolVAR[i][j]+=nablaphi[inode*nabla_dim+j]*soli;
}
}
}
// pressure, solution and gradient
SolVAR[dim]=0.;
for(int j=0; j<dim; j++) {
GradSolVAR[dim][j]=0.;
}
for (unsigned inode=0; inode<nve1; inode++) {
adept::adouble soli = Soli[indexVAR[dim]][inode];
SolVAR[dim]+=phi1[inode]*soli;
for(int j=0; j<dim; j++) {
GradSolVAR[dim][j]+=gradphi1[inode*dim+j]*soli;
}
}
bool Tezduyare=0;
bool FrancaAndFrey=!Tezduyare;
if( Tezduyare ){
//BEGIN TAU_SUPG, TAU_PSPG EVALUATION
// ******** T.E. Tezduyar, S. Mittal, S.E. Ray and R. Shih *****************************
// Computer Methods in Applied Mechanics and Engineering 95 (1992) 221-242 North-Holland
// *************************************************************************************
// velocity
vector < adept::adouble > u(dim);
for(int ivar=0; ivar<dim; ivar++){
u[ivar]=SolVAR[ivar];
}
// speed
adept::adouble uL2Norm=0.;
for(int ivar=0;ivar<dim;ivar++){
uL2Norm += u[ivar]*u[ivar];
}
uL2Norm=sqrt(uL2Norm);
adept::adouble tauSupg=0.;
adept::adouble tauPspg=0.;
if( uL2Norm/(2.*IRe) > 1.0e-10){
// velocity direction s = u/|u|
vector < adept::adouble > s(dim);
for(int ivar=0;ivar<dim;ivar++)
s[ivar]=u[ivar]/uL2Norm;
// element lenght h(s) = 2. ( \sum_i |s . gradphi_i | )^(-1)
adept::adouble h=0.;
for (unsigned i=0; i<nve2; i++) {
adept::adouble sDotGradphi=0.;
for(int ivar=0; ivar<dim; ivar++)
sDotGradphi += s[ivar]*gradphi[i*dim+ivar];
//Start WARNING!!! do not change the following if into h += fabs(sDotGradphi).
//Adept does not like it, and convergence is bad
if( sDotGradphi.value() < 0.)
h -= sDotGradphi;
else
h += sDotGradphi;
//End WARNING
}
h = 2./h;
//tauSupg
adept::adouble Reu = 1./3.*(uL2Norm*h)/(2.*IRe);
adept::adouble zReu = (Reu.value() < 1.)? Reu : 1.;
tauSupg = h / (2.*uL2Norm)*zReu;
uL2Norm=0.01;
h = 2.*hk/sqrt(acos(-1.));
Reu = 1./3.*(uL2Norm*h)/(2.*IRe);
zReu = (Reu.value() < 1.)? Reu : 1.;
tauPspg = h / (2.*uL2Norm)*zReu;
}
//END TAU_SUPG, TAU_PSPG EVALUATION
//BEGIN FLUID ASSEMBLY
{
vector < adept::adouble > Res(dim,0.);
for(unsigned ivar=0; ivar<dim; ivar++) {
Res[ivar] += 0. - GradSolVAR[dim][ivar];
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Res[ivar] += - SolVAR[jvar]*GradSolVAR[ivar][jvar]
+ IRe * ( NablaSolVAR[ivar][jvar] + NablaSolVAR[jvar][kvar] );
}
}
adept::adouble div_vel=0.;
for(int ivar=0; ivar<dim; ivar++) {
div_vel +=GradSolVAR[ivar][ivar];
}
//BEGIN redidual momentum block
for (unsigned i=0; i<nve2; i++){
for(unsigned ivar=0; ivar<dim; ivar++) {
adept::adouble Advection = 0.;
adept::adouble Laplacian = 0.;
adept::adouble phiSupg=0.;
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Advection += SolVAR[jvar]*GradSolVAR[ivar][jvar]*phi[i];
Laplacian += IRe*gradphi[i*dim+jvar]*(GradSolVAR[ivar][jvar]+GradSolVAR[jvar][ivar]);
phiSupg += ( SolVAR[jvar]*gradphi[i*dim+jvar] ) * tauSupg;
}
aRhs[indexVAR[ivar]][i]+= ( - Advection - Laplacian
+ SolVAR[dim] * gradphi[i*dim+ivar]
+ Res[ivar] * phiSupg ) * Weight;
}
}
//END redidual momentum block
//BEGIN continuity block
for (unsigned i=0; i<nve1; i++) {
adept::adouble MinusGradPhi1DotRes = 0.;
for(int ivar=0;ivar<dim;ivar++){
MinusGradPhi1DotRes += -gradphi1[i*dim+ivar] * Res[ivar] * tauPspg;
}
aRhs[indexVAR[dim]][i] += ( - (-div_vel) * phi1[i] + MinusGradPhi1DotRes ) * Weight;
}
//END continuity block
}
//END FLUID ASSEMBLY
}
else if(FrancaAndFrey){
//BEGIN TAU_SUPG EVALUATION
// ********************************* Tau_Supg FRANCA and FREY **************************
// Computer Methods in Applied Mechanics and Engineering 99 (1992) 209-233 North-Holland
// *************************************************************************************
// velocity
// double Ck[6][3]={{1.,1.,1.},{1.,1.,1.},{1.,1.,1.},{0.5, 11./270., 11./270.},{0.,1./42.,1./42.},{1.,1.,1.}};
vector < adept::adouble > a(dim);
for(int ivar=0; ivar<dim; ivar++){
a[ivar]=SolVAR[ivar];
}
// speed
adept::adouble aL2Norm=0.;
for(int ivar=0;ivar<dim;ivar++){
aL2Norm += a[ivar]*a[ivar];
}
aL2Norm=sqrt(aL2Norm);
adept::adouble deltaSupg=0.;
double sqrtlambdak = (*mysolution->_Sol[indLmbd])(iel);
adept::adouble tauSupg=1. / ( sqrtlambdak*sqrtlambdak *4.*IRe);
adept::adouble Rek = aL2Norm / ( 4.*sqrtlambdak*IRe);
/*adept::adouble mk=std::min(1./3., 2.*Ck[kelt][SolType2]);
adept::adouble Rek = mk * aL2Norm * hk / ( 4.*IRe);
adept::adouble tauSupg = (mk*hk*hk/2.) / ( 4.*IRe);
*/
if( Rek > 1.0e-15){
adept::adouble xiRek = ( Rek >= 1. ) ? 1.:Rek;
tauSupg = xiRek/(aL2Norm*sqrtlambdak);
deltaSupg = (xiRek*aL2Norm)/sqrtlambdak;
// tauSupg = hk / (2.*aL2Norm)*xiRek;
// double lambda=1.;
// deltaSupg = lambda*aL2Norm*hk*xiRek;
}
//END TAU_SUPG EVALUATION ============
//BEGIN FLUID ASSEMBLY ============
{
vector < adept::adouble > Res(dim,0.);
for(unsigned ivar=0; ivar<dim; ivar++) {
Res[ivar] += 0. - GradSolVAR[dim][ivar];
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Res[ivar] += - SolVAR[jvar]*GradSolVAR[ivar][jvar]
+ IRe * ( NablaSolVAR[ivar][jvar] + NablaSolVAR[jvar][kvar] );
}
}
adept::adouble div_vel=0.;
for(int ivar=0; ivar<dim; ivar++) {
div_vel +=GradSolVAR[ivar][ivar];
}
//BEGIN redidual momentum block
for (unsigned i=0; i<nve2; i++){
for(unsigned ivar=0; ivar<dim; ivar++) {
adept::adouble Advection = 0.;
adept::adouble Laplacian = 0.;
adept::adouble phiSupg=0.;
for(unsigned jvar=0; jvar<dim; jvar++) {
unsigned kvar;
if(ivar == jvar) kvar = jvar;
else if (1 == ivar + jvar ) kvar = dim; // xy
else if (2 == ivar + jvar ) kvar = dim+2; // xz
else if (3 == ivar + jvar ) kvar = dim+1; // yz
Advection += SolVAR[jvar]*GradSolVAR[ivar][jvar]*phi[i];
Laplacian += IRe*gradphi[i*dim+jvar]*(GradSolVAR[ivar][jvar]+GradSolVAR[jvar][ivar]);
phiSupg += ( SolVAR[jvar]*gradphi[i*dim+jvar] ) * tauSupg;
aRhs[indexVAR[ivar]][i] += Res[ivar] * (-IRe * nablaphi[i*nabla_dim+jvar])* tauSupg * Weight;
aRhs[indexVAR[jvar]][i] += Res[ivar] * (-IRe * nablaphi[i*nabla_dim+kvar])* tauSupg * Weight;
}
aRhs[indexVAR[ivar]][i]+= ( - Advection - Laplacian
+ ( SolVAR[dim] - deltaSupg * div_vel) * gradphi[i*dim+ivar]
+ Res[ivar] * phiSupg ) * Weight;
}
}
//END redidual momentum block
//BEGIN continuity block
for (unsigned i=0; i<nve1; i++) {
adept::adouble MinusGradPhi1DotRes = 0.;
for(int ivar=0;ivar<dim;ivar++){
MinusGradPhi1DotRes += -gradphi1[i*dim+ivar] * Res[ivar] * tauSupg;
}
aRhs[indexVAR[dim]][i] += ( - (-div_vel) * phi1[i] + MinusGradPhi1DotRes ) * Weight;
}
//END continuity block ===========================
}
//END FLUID ASSEMBLY ============
}
}
}
//BEGIN local to global assembly
//copy adouble aRhs into double Rhs
for (unsigned i=0;i<dim;i++) {
for(int j=0; j<nve2; j++) {
Rhs[indexVAR[i]][j] = aRhs[indexVAR[i]][j].value();
}
}
for (unsigned j=0;j<nve1;j++) {
Rhs[indexVAR[dim]][j] = aRhs[indexVAR[dim]][j].value();
}
for(int i=0; i<dim+1; i++) {
myRES->add_vector_blocked(Rhs[indexVAR[i]],dofsVAR[i]);
}
//Store equations
for(int i=0; i<dim; i++) {
adeptStack.dependent(&aRhs[indexVAR[i]][0], nve2);
adeptStack.independent(&Soli[indexVAR[i]][0], nve2);
}
adeptStack.dependent(&aRhs[indexVAR[dim]][0], nve1);
adeptStack.independent(&Soli[indexVAR[dim]][0], nve1);
adeptStack.jacobian(&Jac[0]);
unsigned nveAll=(dim*nve2+nve1);
for (int inode=0;inode<nveAll;inode++){
for (int jnode=0;jnode<nveAll;jnode++){
KKloc[inode*nveAll+jnode]=-Jac[jnode*nveAll+inode];
}
}
myKK->add_matrix_blocked(KKloc,dofsAll,dofsAll);
adeptStack.clear_independents();
adeptStack.clear_dependents();
//END local to global assembly
} //end list of elements loop
myKK->close();
myRES->close();
// *************************************
end_time=clock();
AssemblyTime+=(end_time-start_time);
// ***************** END ASSEMBLY RESIDUAL + MATRIX *******************
}
void AssembleBoussinesqAppoximation_AD(MultiLevelProblem& ml_prob) {
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// levelMax is the Maximum level of the MultiLevelProblem
// assembleMatrix is a flag that tells if only the residual or also the matrix should be assembled
// call the adept stack object
adept::Stack& s = FemusInit::_adeptStack;
// extract pointers to the several objects that we are going to use
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system<NonLinearImplicitSystem> ("NS"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
const unsigned levelMax = mlPdeSys->GetLevelMax();
const bool assembleMatrix = mlPdeSys->GetAssembleMatrix();
Mesh* msh = ml_prob._ml_msh->GetLevel(level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel(level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned dim2 = (3 * (dim - 1) + !(dim - 1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
// reserve memory for the local standar vectors
const unsigned maxSize = static_cast< unsigned >(ceil(pow(3, dim))); // conservative: based on line3, quad9, hex27
//solution variable
vector < unsigned > solVIndex(dim);
solVIndex[0] = mlSol->GetIndex("U"); // get the position of "U" in the ml_sol object
solVIndex[1] = mlSol->GetIndex("V"); // get the position of "V" in the ml_sol object
if (dim == 3) solVIndex[2] = mlSol->GetIndex("W"); // get the position of "V" in the ml_sol object
unsigned solVType = mlSol->GetSolutionType(solVIndex[0]); // get the finite element type for "u"
unsigned solPIndex;
solPIndex = mlSol->GetIndex("P"); // get the position of "P" in the ml_sol object
unsigned solPType = mlSol->GetSolutionType(solPIndex); // get the finite element type for "u"
vector < unsigned > solVPdeIndex(dim);
solVPdeIndex[0] = mlPdeSys->GetSolPdeIndex("U"); // get the position of "U" in the pdeSys object
solVPdeIndex[1] = mlPdeSys->GetSolPdeIndex("V"); // get the position of "V" in the pdeSys object
if (dim == 3) solVPdeIndex[2] = mlPdeSys->GetSolPdeIndex("W");
unsigned solPPdeIndex;
solPPdeIndex = mlPdeSys->GetSolPdeIndex("P"); // get the position of "P" in the pdeSys object
vector < vector < adept::adouble > > solV(dim); // local solution
vector < adept::adouble > solP; // local solution
vector< vector < adept::adouble > > aResV(dim); // local redidual vector
vector< adept::adouble > aResP; // local redidual vector
vector < vector < double > > coordX(dim); // local coordinates
unsigned coordXType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
for (unsigned k = 0; k < dim; k++) {
solV[k].reserve(maxSize);
aResV[k].reserve(maxSize);
coordX[k].reserve(maxSize);
}
solP.reserve(maxSize);
aResP.reserve(maxSize);
vector <double> phiV; // local test function
vector <double> phiV_x; // local test function first order partial derivatives
vector <double> phiV_xx; // local test function second order partial derivatives
phiV.reserve(maxSize);
phiV_x.reserve(maxSize * dim);
phiV_xx.reserve(maxSize * dim2);
double* phiP;
double weight; // gauss point weight
vector< int > KKDof; // local to global pdeSys dofs
KKDof.reserve((dim + 1) *maxSize);
vector< double > Res; // local redidual vector
Res.reserve((dim + 1) *maxSize);
vector < double > Jac;
Jac.reserve((dim + 1) *maxSize * (dim + 1) *maxSize);
if (assembleMatrix)
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel = msh->IS_Mts2Gmt_elem_offset[iproc]; iel < msh->IS_Mts2Gmt_elem_offset[iproc + 1]; iel++) {
unsigned kel = msh->IS_Mts2Gmt_elem[iel]; // mapping between paralell dof and mesh dof
short unsigned kelGeom = el->GetElementType(kel); // element geometry type
unsigned nDofsV = el->GetElementDofNumber(kel, solVType); // number of solution element dofs
unsigned nDofsP = el->GetElementDofNumber(kel, solPType); // number of solution element dofs
unsigned nDofsX = el->GetElementDofNumber(kel, coordXType); // number of coordinate element dofs
unsigned nDofsVP = dim * nDofsV + nDofsP;
// resize local arrays
KKDof.resize(nDofsVP);
for (unsigned k = 0; k < dim; k++) {
solV[k].resize(nDofsV);
coordX[k].resize(nDofsX);
}
solP.resize(nDofsP);
for (unsigned k = 0; k < dim; k++) {
aResV[k].resize(nDofsV); //resize
std::fill(aResV[k].begin(), aResV[k].end(), 0); //set aRes to zero
}
aResP.resize(nDofsP); //resize
std::fill(aResP.begin(), aResP.end(), 0); //set aRes to zero
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofsV; i++) {
unsigned iNode = el->GetMeshDof(kel, i, solVType); // local to global solution node
unsigned solVDof = msh->GetMetisDof(iNode, solVType); // global to global mapping between solution node and solution dof
for (unsigned k = 0; k < dim; k++) {
solV[k][i] = (*sol->_Sol[solVIndex[k]])(solVDof); // global extraction and local storage for the solution
KKDof[i + k * nDofsV] = pdeSys->GetKKDof(solVIndex[k], solVPdeIndex[k], iNode); // global to global mapping between solution node and pdeSys dof
}
}
for (unsigned i = 0; i < nDofsP; i++) {
unsigned iNode = el->GetMeshDof(kel, i, solPType); // local to global solution node
unsigned solPDof = msh->GetMetisDof(iNode, solPType); // global to global mapping between solution node and solution dof
solP[i] = (*sol->_Sol[solPIndex])(solPDof); // global extraction and local storage for the solution
KKDof[i + dim * nDofsV] = pdeSys->GetKKDof(solPIndex, solPPdeIndex, iNode); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for (unsigned i = 0; i < nDofsX; i++) {
unsigned iNode = el->GetMeshDof(kel, i, coordXType); // local to global coordinates node
unsigned coordXDof = msh->GetMetisDof(iNode, coordXType); // global to global mapping between coordinates node and coordinate dof
for (unsigned k = 0; k < dim; k++) {
coordX[k][i] = (*msh->_coordinate->_Sol[k])(coordXDof); // global extraction and local storage for the element coordinates
}
}
if (level == levelMax || !el->GetRefinedElementIndex(kel)) { // do not care about this if now (it is used for the AMR)
// start a new recording of all the operations involving adept::adouble variables
s.new_recording();
// *** Gauss point loop ***
for (unsigned ig = 0; ig < msh->_finiteElement[kelGeom][solVType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[kelGeom][solVType]->Jacobian(coordX, ig, weight, phiV, phiV_x, phiV_xx);
phiP = msh->_finiteElement[kelGeom][solPType]->GetPhi(ig);
vector < adept::adouble > solV_gss(dim, 0);
vector < vector < adept::adouble > > gradSolV_gss(dim);
for (unsigned k = 0; k < dim; k++) {
gradSolV_gss[k].resize(dim);
std::fill(gradSolV_gss[k].begin(), gradSolV_gss[k].end(), 0);
}
for (unsigned i = 0; i < nDofsV; i++) {
for (unsigned k = 0; k < dim; k++) {
solV_gss[k] += phiV[i] * solV[k][i];
}
for (unsigned j = 0; j < dim; j++) {
for (unsigned k = 0; k < dim; k++) {
gradSolV_gss[k][j] += phiV_x[i * dim + j] * solV[k][i];
}
}
}
adept::adouble solP_gss = 0;
for (unsigned i = 0; i < nDofsP; i++) {
solP_gss += phiP[i] * solP[i];
}
double nu = 1.;
// *** phiV_i loop ***
for (unsigned i = 0; i < nDofsV; i++) {
vector < adept::adouble > NSV(dim, 0.);
for (unsigned j = 0; j < dim; j++) {
for (unsigned k = 0; k < dim; k++) {
NSV[k] += nu * phiV_x[i * dim + j] * (gradSolV_gss[k][j] + gradSolV_gss[j][k]);
NSV[k] += phiV[i] * (solV_gss[j] * gradSolV_gss[k][j]);
}
}
for (unsigned k = 0; k < dim; k++) {
NSV[k] += -solP_gss * phiV_x[i * dim + k];
}
for (unsigned k = 0; k < dim; k++) {
aResV[k][i] += - NSV[k] * weight;
}
} // end phiV_i loop
// *** phiP_i loop ***
for (unsigned i = 0; i < nDofsP; i++) {
for (int k = 0; k < dim; k++) {
aResP[i] += - (gradSolV_gss[k][k]) * phiP[i] * weight;
}
} // end phiP_i loop
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
// Add the local Matrix/Vector into the global Matrix/Vector
//copy the value of the adept::adoube aRes in double Res and store them in RES
Res.resize(nDofsVP); //resize
for (int i = 0; i < nDofsV; i++) {
for (unsigned k = 0; k < dim; k++) {
Res[ i + k * nDofsV ] = -aResV[k][i].value();
}
}
for (int i = 0; i < nDofsP; i++) {
Res[ i + dim * nDofsV ] = -aResP[i].value();
}
RES->add_vector_blocked(Res, KKDof);
//Extarct and store the Jacobian
if (assembleMatrix) {
Jac.resize(nDofsVP * nDofsVP);
// define the dependent variables
for (unsigned k = 0; k < dim; k++) {
s.dependent(&aResV[k][0], nDofsV);
}
s.dependent(&aResP[0], nDofsP);
// define the independent variables
for (unsigned k = 0; k < dim; k++) {
s.independent(&solV[k][0], nDofsV);
}
s.independent(&solP[0], nDofsP);
// get the and store jacobian matrix (row-major)
s.jacobian(&Jac[0] , true);
KK->add_matrix_blocked(Jac, KKDof, KKDof);
s.clear_independents();
s.clear_dependents();
}
} //end element loop for each process
RES->close();
if (assembleMatrix) KK->close();
// ***************** END ASSEMBLY *******************
}
void AssembleBilaplaceProblem_AD(MultiLevelProblem &ml_prob){
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// levelMax is the Maximum level of the MultiLevelProblem
// assembleMatrix is a flag that tells if only the residual or also the matrix should be assembled
// call the adept stack object
adept::Stack & s = FemusInit::_adeptStack;
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system<NonLinearImplicitSystem>("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
const unsigned levelMax = mlPdeSys->GetLevelMax();
const bool assembleMatrix = mlPdeSys->GetAssembleMatrix();
// extract pointers to the several objects that we are going to use
Mesh* msh = ml_prob._ml_msh->GetLevel(level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel(level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
//solution variable
unsigned soluIndex;
soluIndex = mlSol->GetIndex("u"); // get the position of "u" in the ml_sol object
unsigned soluType = mlSol->GetSolutionType(soluIndex); // get the finite element type for "u"
unsigned soluPdeIndex;
soluPdeIndex = mlPdeSys->GetSolPdeIndex("u"); // get the position of "u" in the pdeSys object
vector < adept::adouble > solu; // local solution
unsigned solvIndex;
solvIndex = mlSol->GetIndex("v"); // get the position of "v" in the ml_sol object
unsigned solvType = mlSol->GetSolutionType(solvIndex); // get the finite element type for "v"
unsigned solvPdeIndex;
solvPdeIndex = mlPdeSys->GetSolPdeIndex("v"); // get the position of "v" in the pdeSys object
vector < adept::adouble > solv; // local solution
vector < vector < double > > x(dim); // local coordinates
unsigned xType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
vector< int > KKDof; // local to global pdeSys dofs
vector <double> phi; // local test function
vector <double> phi_x; // local test function first order partial derivatives
vector <double> phi_xx; // local test function second order partial derivatives
double weight; // gauss point weight
vector< double > Res; // local redidual vector
vector< adept::adouble > aResu; // local redidual vector
vector< adept::adouble > aResv; // local redidual vector
// reserve memory for the local standar vectors
const unsigned maxSize = static_cast< unsigned > (ceil(pow(3,dim))); // conservative: based on line3, quad9, hex27
solu.reserve(maxSize);
solv.reserve(maxSize);
for(unsigned i = 0; i < dim; i++)
x[i].reserve(maxSize);
KKDof.reserve(2*maxSize);
phi.reserve(maxSize);
phi_x.reserve(maxSize*dim);
unsigned dim2=(3*(dim-1)+!(dim-1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
phi_xx.reserve(maxSize*dim2);
Res.reserve(2*maxSize);
aResu.reserve(maxSize);
aResv.reserve(maxSize);
vector < double > Jac; // local Jacobian matrix (ordered by column, adept)
Jac.reserve(4*maxSize*maxSize);
vector< double > Jact; // local Jacobian matrix (ordered by raw, PETSC)
Jact.reserve(4*maxSize*maxSize);
if( assembleMatrix )
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel=msh->IS_Mts2Gmt_elem_offset[iproc]; iel < msh->IS_Mts2Gmt_elem_offset[iproc+1]; iel++) {
unsigned kel = msh->IS_Mts2Gmt_elem[iel]; // mapping between paralell dof and mesh dof
short unsigned kelGeom = el->GetElementType( kel ); // element geometry type
unsigned nDofs = el->GetElementDofNumber( kel, soluType); // number of solution element dofs
unsigned nDofs2 = el->GetElementDofNumber( kel, xType); // number of coordinate element dofs
// resize local arrays
KKDof.resize(2*nDofs);
solu.resize(nDofs);
solv.resize(nDofs);
for(int i=0; i<dim; i++) {
x[i].resize(nDofs2);
}
Res.resize(2*nDofs); //resize
aResu.resize(nDofs); //resize
aResv.resize(nDofs); //resize
std::fill(aResu.begin(), aResu.end(), 0); //set aRes to zero
std::fill(aResv.begin(), aResv.end(), 0); //set aRes to zero
if(assembleMatrix) { //resize
Jact.resize(4*nDofs*nDofs);
Jac.resize(4*nDofs*nDofs);
}
// local storage of global mapping and solution
for( unsigned i=0; i<nDofs; i++) {
unsigned iNode = el->GetMeshDof(kel, i, soluType); // local to global solution node
unsigned solDof = msh->GetMetisDof(iNode, soluType); // global to global mapping between solution node and solution dof
solu[i] = (*sol->_Sol[soluIndex])(solDof); // global extraction and local storage for the solution
solv[i] = (*sol->_Sol[solvIndex])(solDof); // global extraction and local storage for the solution
KKDof[i] = pdeSys->GetKKDof(soluIndex, soluPdeIndex, iNode); // global to global mapping between solution node and pdeSys dof
KKDof[nDofs+i] = pdeSys->GetKKDof(solvIndex, solvPdeIndex, iNode); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for( unsigned i=0; i<nDofs2; i++) {
unsigned iNode = el->GetMeshDof(kel, i, xType); // local to global coordinates node
unsigned xDof = msh->GetMetisDof(iNode, xType); // global to global mapping between coordinates node and coordinate dof
for(unsigned jdim=0; jdim<dim; jdim++) {
x[jdim][i] = (*msh->_coordinate->_Sol[jdim])(xDof); // global extraction and local storage for the element coordinates
}
}
if( level == levelMax || !el->GetRefinedElementIndex(kel)) { // do not care about this if now (it is used for the AMR)
// start a new recording of all the operations involving adept::adouble variables
s.new_recording();
// *** Gauss point loop ***
for(unsigned ig=0; ig < msh->_finiteElement[kelGeom][soluType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[kelGeom][soluType]->Jacobian(x,ig,weight,phi,phi_x,phi_xx);
// evaluate the solution, the solution derivatives and the coordinates in the gauss point
adept::adouble soluGauss = 0;
vector < adept::adouble > soluGauss_x(dim,0.);
adept::adouble solvGauss = 0;
vector < adept::adouble > solvGauss_x(dim,0.);
vector < double > xGauss(dim,0.);
for(unsigned i=0; i<nDofs; i++) {
soluGauss+=phi[i]*solu[i];
solvGauss+=phi[i]*solv[i];
for(unsigned jdim=0; jdim<dim; jdim++) {
soluGauss_x[jdim] += phi_x[i*dim+jdim]*solu[i];
solvGauss_x[jdim] += phi_x[i*dim+jdim]*solv[i];
xGauss[jdim] += x[jdim][i]*phi[i];
}
}
double c=.1;
double Id[2][2]={{1.,0.},{0.,1.}};
adept::adouble A2 = 1.;
vector < vector < adept::adouble> > B(dim);
for(unsigned jdim=0; jdim<dim; jdim++){
B[jdim].resize(dim);
A2 += soluGauss_x[jdim]*soluGauss_x[jdim];
}
adept::adouble A = sqrt(A2);
for(unsigned jdim=0; jdim<dim; jdim++){
for(unsigned kdim=0; kdim<dim; kdim++){
B[jdim][kdim]= Id[jdim][kdim] - (soluGauss_x[jdim] * soluGauss_x[kdim]) / A2;
}
}
// *** phi_i loop ***
for(unsigned i=0; i<nDofs; i++) {
adept::adouble nonLinearLaplaceU = 0.;
adept::adouble nonLinearLaplaceV = 0.;
for(unsigned jdim=0; jdim<dim; jdim++) {
nonLinearLaplaceU += - 1. / A * soluGauss_x[jdim] * phi_x[i*dim+jdim];
nonLinearLaplaceV += 1. / A * ( - ( B[jdim][0] * solvGauss_x[0] + B[jdim][1] * solvGauss_x[1] ) * phi_x[i*dim+jdim]
+ ( solvGauss*solvGauss/A2 + c ) * soluGauss_x[jdim] * phi_x[i*dim+jdim] );
}
aResu[i]+= ( 2.*solvGauss/A * phi[i] - nonLinearLaplaceU ) * weight;
aResv[i]+= nonLinearLaplaceV * weight;
} // end phi_i loop
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
// Add the local Matrix/Vector into the global Matrix/Vector
//copy the value of the adept::adoube aRes in double Res and store
for(int i=0; i<nDofs; i++) {
Res[i] = aResu[i].value();
Res[nDofs+i] = aResv[i].value();
}
RES->add_vector_blocked(Res,KKDof);
if(assembleMatrix) {
// define the dependent variables
s.dependent(&aResu[0], nDofs);
s.dependent(&aResv[0], nDofs);
// define the independent variables
s.independent(&solu[0], nDofs);
s.independent(&solv[0], nDofs);
// get the jacobian matrix (ordered by column)
s.jacobian(&Jac[0]);
// get the jacobian matrix (ordered by raw, i.e. Jact=Jac^t)
for (int inode=0;inode<2*nDofs;inode++){
for (int jnode=0;jnode<2*nDofs;jnode++){
Jact[inode*2*nDofs+jnode]=-Jac[jnode*2*nDofs+inode];
}
}
//store Jact in the global matrix KK
KK->add_matrix_blocked(Jact,KKDof,KKDof);
s.clear_independents();
s.clear_dependents();
}
} //end element loop for each process
RES->close();
if( assembleMatrix ) KK->close();
// ***************** END ASSEMBLY *******************
}
void AssembleNonlinearProblem(MultiLevelProblem& ml_prob) {
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// levelMax is the Maximum level of the MultiLevelProblem
// assembleMatrix is a flag that tells if only the residual or also the matrix should be assembled
// extract pointers to the several objects that we are going to use
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system< NonLinearImplicitSystem > ("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
const unsigned levelMax = mlPdeSys->GetLevelMax();
bool assembleMatrix = mlPdeSys->GetAssembleMatrix();
Mesh* msh = ml_prob._ml_msh->GetLevel(level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel(level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
//solution variable
unsigned soluIndex;
soluIndex = mlSol->GetIndex("u"); // get the position of "u" in the ml_sol object
unsigned soluType = mlSol->GetSolutionType(soluIndex); // get the finite element type for "u"
unsigned soluPdeIndex;
soluPdeIndex = mlPdeSys->GetSolPdeIndex("u"); // get the position of "u" in the pdeSys object
vector < double > solu; // local solution
vector < vector < double > > x(dim); // local coordinates
unsigned xType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
vector< int > KKDof; // local to global pdeSys dofs
vector <double> phi; // local test function
vector <double> phi_x; // local test function first order partial derivatives
vector <double> phi_xx; // local test function second order partial derivatives
double weight; // gauss point weight
vector< double > Res; // local redidual vector
vector< double > J; // local Jacobian matrix
// reserve memory for the local standar vectors
const unsigned maxSize = static_cast< unsigned >(ceil(pow(3, dim))); // conservative: based on line3, quad9, hex27
solu.reserve(maxSize);
for (unsigned i = 0; i < dim; i++)
x[i].reserve(maxSize);
KKDof.reserve(maxSize);
phi.reserve(maxSize);
phi_x.reserve(maxSize * dim);
unsigned dim2 = (3 * (dim - 1) + !(dim - 1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
phi_xx.reserve(maxSize * dim2);
Res.reserve(maxSize);
J.reserve(maxSize * maxSize);
if (assembleMatrix)
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel = msh->IS_Mts2Gmt_elem_offset[iproc]; iel < msh->IS_Mts2Gmt_elem_offset[iproc + 1]; iel++) {
unsigned kel = msh->IS_Mts2Gmt_elem[iel]; // mapping between paralell dof and mesh dof
short unsigned kelGeom = el->GetElementType(kel); // element geometry type
unsigned nDofs = el->GetElementDofNumber(kel, soluType); // number of solution element dofs
unsigned nDofs2 = el->GetElementDofNumber(kel, xType); // number of coordinate element dofs
// resize local arrays
KKDof.resize(nDofs);
solu.resize(nDofs);
for (int i = 0; i < dim; i++) {
x[i].resize(nDofs2);
}
Res.resize(nDofs); //resize
std::fill(Res.begin(), Res.end(), 0); //set Res to zero
if (assembleMatrix) {
J.resize(nDofs * nDofs); //resize
std::fill(J.begin(), J.end(), 0); //set K to zero
}
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofs; i++) {
unsigned iNode = el->GetMeshDof(kel, i, soluType); // local to global solution node
unsigned solDof = msh->GetMetisDof(iNode, soluType); // global to global mapping between solution node and solution dof
solu[i] = (*sol->_Sol[soluIndex])(solDof); // global extraction and local storage for the solution
KKDof[i] = pdeSys->GetKKDof(soluIndex, soluPdeIndex, iNode); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for (unsigned i = 0; i < nDofs2; i++) {
unsigned iNode = el->GetMeshDof(kel, i, xType); // local to global coordinates node
unsigned xDof = msh->GetMetisDof(iNode, xType); // global to global mapping between coordinates node and coordinate dof
for (unsigned jdim = 0; jdim < dim; jdim++) {
x[jdim][i] = (*msh->_coordinate->_Sol[jdim])(xDof); // global extraction and local storage for the element coordinates
}
}
if (level == levelMax || !el->GetRefinedElementIndex(kel)) { // do not care about this if now (it is used for the AMR)
// *** Gauss point loop ***
for (unsigned ig = 0; ig < msh->_finiteElement[kelGeom][soluType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[kelGeom][soluType]->Jacobian(x, ig, weight, phi, phi_x, phi_xx);
// evaluate the solution, the solution derivatives and the coordinates in the gauss point
double soluGauss = 0;
vector < double > soluGauss_x(dim, 0.);
vector < double > xGauss(dim, 0.);
for (unsigned i = 0; i < nDofs; i++) {
soluGauss += phi[i] * solu[i];
for (unsigned jdim = 0; jdim < dim; jdim++) {
soluGauss_x[jdim] += phi_x[i * dim + jdim] * solu[i];
xGauss[jdim] += x[jdim][i] * phi[i];
}
}
// *** phi_i loop ***
for (unsigned i = 0; i < nDofs; i++) {
double nonLinearTerm = 0.;
double mLaplace = 0.;
for (unsigned jdim = 0; jdim < dim; jdim++) {
mLaplace += phi_x[i * dim + jdim] * soluGauss_x[jdim];
nonLinearTerm += soluGauss * soluGauss_x[jdim] * phi[i];
}
double exactSolValue = GetExactSolutionValue(xGauss);
vector < double > exactSolGrad(dim);
GetExactSolutionGradient(xGauss , exactSolGrad);
double exactSolLaplace = GetExactSolutionLaplace(xGauss);
double f = (- exactSolLaplace + exactSolValue * (exactSolGrad[0] + exactSolGrad[1])) * phi[i] ;
Res[i] += (f - (mLaplace + nonLinearTerm)) * weight;
if (assembleMatrix) {
// *** phi_j loop ***
for (unsigned j = 0; j < nDofs; j++) {
mLaplace = 0.;
nonLinearTerm = 0.;
for (unsigned kdim = 0; kdim < dim; kdim++) {
mLaplace += (phi_x[i * dim + kdim] * phi_x[j * dim + kdim]);
nonLinearTerm += phi[i] * (phi[j] * soluGauss_x[kdim] + soluGauss * phi_x[j * dim + kdim]);
}
J[i * nDofs + j] += (mLaplace + nonLinearTerm) * weight;
} // end phi_j loop
} // endif assemble_matrix
} // end phi_i loop
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
// Add the local Matrix/Vector into the global Matrix/Vector
RES->add_vector_blocked(Res, KKDof);
if (assembleMatrix) KK->add_matrix_blocked(J, KKDof, KKDof);
} //end element loop for each process
RES->close();
if (assembleMatrix) KK->close();
// ***************** END ASSEMBLY *******************
}
/**
* This function assemble the stiffnes matrix KK and the residual vector Res
* Using automatic differentiation for Newton iterative scheme
* J(u0) w = - F(u0) ,
* with u = u0 + w
* - F = f(x) - J u = Res
* J = \grad_u F
*
* thus
* J w = f(x) - J u0
**/
void AssemblePoissonProblem_AD(MultiLevelProblem& ml_prob) {
// ml_prob is the global object from/to where get/set all the data
// level is the level of the PDE system to be assembled
// levelMax is the Maximum level of the MultiLevelProblem
// assembleMatrix is a flag that tells if only the residual or also the matrix should be assembled
// call the adept stack object
adept::Stack& s = FemusInit::_adeptStack;
// extract pointers to the several objects that we are going to use
LinearImplicitSystem* mlPdeSys = &ml_prob.get_system<LinearImplicitSystem> ("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
const unsigned levelMax = mlPdeSys->GetLevelMax();
const bool assembleMatrix = mlPdeSys->GetAssembleMatrix();
Mesh* msh = ml_prob._ml_msh->GetLevel(level); // pointer to the mesh (level) object
elem* el = msh->el; // pointer to the elem object in msh (level)
MultiLevelSolution* mlSol = ml_prob._ml_sol; // pointer to the multilevel solution object
Solution* sol = ml_prob._ml_sol->GetSolutionLevel(level); // pointer to the solution (level) object
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level]; // pointer to the equation (level) object
SparseMatrix* KK = pdeSys->_KK; // pointer to the global stifness matrix object in pdeSys (level)
NumericVector* RES = pdeSys->_RES; // pointer to the global residual vector object in pdeSys (level)
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
unsigned dim2 = (3 * (dim - 1) + !(dim - 1)); // dim2 is the number of second order partial derivatives (1,3,6 depending on the dimension)
const unsigned maxSize = static_cast< unsigned >(ceil(pow(3, dim))); // conservative: based on line3, quad9, hex27
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
//solution variable
unsigned soluIndex;
soluIndex = mlSol->GetIndex("u"); // get the position of "u" in the ml_sol object
unsigned soluType = mlSol->GetSolutionType(soluIndex); // get the finite element type for "u"
unsigned soluPdeIndex;
soluPdeIndex = mlPdeSys->GetSolPdeIndex("u"); // get the position of "u" in the pdeSys object
vector < adept::adouble > solu; // local solution
solu.reserve(maxSize);
vector < vector < double > > x(dim); // local coordinates
unsigned xType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
for (unsigned i = 0; i < dim; i++) {
x[i].reserve(maxSize);
}
vector <double> phi; // local test function
vector <double> phi_x; // local test function first order partial derivatives
vector <double> phi_xx; // local test function second order partial derivatives
double weight; // gauss point weight
phi.reserve(maxSize);
phi_x.reserve(maxSize * dim);
phi_xx.reserve(maxSize * dim2);
vector< adept::adouble > aRes; // local redidual vector
aRes.reserve(maxSize);
vector< int > l2GMap; // local to global mapping
l2GMap.reserve(maxSize);
vector< double > Res; // local redidual vector
Res.reserve(maxSize);
vector < double > Jac;
Jac.reserve(maxSize * maxSize);
if (assembleMatrix)
KK->zero(); // Set to zero all the entries of the Global Matrix
// element loop: each process loops only on the elements that owns
for (int iel = msh->IS_Mts2Gmt_elem_offset[iproc]; iel < msh->IS_Mts2Gmt_elem_offset[iproc + 1]; iel++) {
unsigned kel = msh->IS_Mts2Gmt_elem[iel]; // mapping between paralell dof and mesh dof
short unsigned kelGeom = el->GetElementType(kel); // element geometry type
unsigned nDofu = el->GetElementDofNumber(kel, soluType); // number of solution element dofs
unsigned nDofx = el->GetElementDofNumber(kel, xType); // number of coordinate element dofs
// resize local arrays
l2GMap.resize(nDofu);
solu.resize(nDofu);
for (int i = 0; i < dim; i++) {
x[i].resize(nDofx);
}
aRes.resize(nDofu); //resize
std::fill(aRes.begin(), aRes.end(), 0); //set aRes to zero
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofu; i++) {
unsigned iNode = el->GetMeshDof(kel, i, soluType); // local to global solution node
unsigned solDof = msh->GetMetisDof(iNode, soluType); // global to global mapping between solution node and solution dof
solu[i] = (*sol->_Sol[soluIndex])(solDof); // global extraction and local storage for the solution
l2GMap[i] = pdeSys->GetKKDof(soluIndex, soluPdeIndex, iNode); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for (unsigned i = 0; i < nDofx; i++) {
unsigned iNode = el->GetMeshDof(kel, i, xType); // local to global coordinates node
unsigned xDof = msh->GetMetisDof(iNode, xType); // global to global mapping between coordinates node and coordinate dof
for (unsigned jdim = 0; jdim < dim; jdim++) {
x[jdim][i] = (*msh->_coordinate->_Sol[jdim])(xDof); // global extraction and local storage for the element coordinates
}
}
if (level == levelMax || !el->GetRefinedElementIndex(kel)) { // do not care about this if now (it is used for the AMR)
// start a new recording of all the operations involving adept::adouble variables
s.new_recording();
// *** Gauss point loop ***
for (unsigned ig = 0; ig < msh->_finiteElement[kelGeom][soluType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[kelGeom][soluType]->Jacobian(x, ig, weight, phi, phi_x, phi_xx);
// evaluate the solution, the solution derivatives and the coordinates in the gauss point
adept::adouble solu_gss = 0;
vector < adept::adouble > gradSolu_gss(dim, 0.);
vector < double > x_gss(dim, 0.);
for (unsigned i = 0; i < nDofu; i++) {
solu_gss += phi[i] * solu[i];
for (unsigned jdim = 0; jdim < dim; jdim++) {
gradSolu_gss[jdim] += phi_x[i * dim + jdim] * solu[i];
x_gss[jdim] += x[jdim][i] * phi[i];
}
}
// *** phi_i loop ***
for (unsigned i = 0; i < nDofu; i++) {
adept::adouble laplace = 0.;
for (unsigned jdim = 0; jdim < dim; jdim++) {
laplace += phi_x[i * dim + jdim] * gradSolu_gss[jdim];
}
double srcTerm = - GetExactSolutionLaplace(x_gss);
aRes[i] += (srcTerm * phi[i] - laplace) * weight;
} // end phi_i loop
} // end gauss point loop
} // endif single element not refined or fine grid loop
//--------------------------------------------------------------------------------------------------------
// Add the local Matrix/Vector into the global Matrix/Vector
//copy the value of the adept::adoube aRes in double Res and store
Res.resize(nDofu); //resize
for (int i = 0; i < nDofu; i++) {
Res[i] = - aRes[i].value();
}
RES->add_vector_blocked(Res, l2GMap);
if (assembleMatrix) {
// define the dependent variables
s.dependent(&aRes[0], nDofu);
// define the independent variables
s.independent(&solu[0], nDofu);
// get the jacobian matrix (ordered by row major )
Jac.resize(nDofu * nDofu); //resize
s.jacobian(&Jac[0], true);
//store K in the global matrix KK
KK->add_matrix_blocked(Jac, l2GMap, l2GMap);
s.clear_independents();
s.clear_dependents();
}
} //end element loop for each process
RES->close();
if (assembleMatrix) KK->close();
// ***************** END ASSEMBLY *******************
}