void GenMatRhsMHD(MultiLevelProblem &ml_prob) {
SystemTwo & my_system = ml_prob.get_system<SystemTwo>("Eqn_MHD");
const unsigned Level = my_system.GetLevelToAssemble();
//========= reference values =========
const double IRem = 1./ml_prob.GetInputParser().get("Rem");
//============================
//======== GEOMETRICAL ELEMENT =======
const uint space_dim = ml_prob._ml_msh->GetDimension();
//==== Operators @ gauss ========
std::vector<double> Vel_vec_val_g(space_dim);
std::vector<double> Vel_vec_val_g3D(3);
std::vector<double> Bext_vec_val_g(space_dim);
std::vector<double> Bext_vec_val_g3D(3);
double vXBe_g3D[3];
double vXBeXdphii_g3D[3];
double curlBeXdphii_g3D[3];
double LapBe_g[DIMENSION];
//============================
my_system._LinSolver[Level]->_KK->zero();
my_system._LinSolver[Level]->_RESC->zero();
// ==========================================
Mesh *mymsh = ml_prob._ml_msh->GetLevel(Level);
elem *myel = mymsh->el;
const unsigned myproc = mymsh->processor_id();
// ==========================================
// ==========================================
{//BEGIN VOLUME
const uint mesh_vb = VV;
const uint nel_e = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level+1];
const uint nel_b = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level];
for (uint iel=0; iel < (nel_e - nel_b); iel++) {
CurrentElem<double> currelem(iel,myproc,Level,VV,&my_system,ml_prob.GetMeshTwo(),ml_prob.GetElemType(),mymsh);
CurrentGaussPointBase & currgp = CurrentGaussPointBase::build(currelem,ml_prob.GetQuadratureRule(currelem.GetDim()));
//=========INTERNAL QUANTITIES (unknowns of the equation) ==================
CurrentQuantity BhomOldX(currgp);
BhomOldX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHom0");
BhomOldX.VectWithQtyFillBasic();
BhomOldX.Allocate();
CurrentQuantity BhomOldY(currgp);
BhomOldY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHom1");
BhomOldY.VectWithQtyFillBasic();
BhomOldY.Allocate();
CurrentQuantity BhomOldZ(currgp);
BhomOldZ._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHom2");
BhomOldZ.VectWithQtyFillBasic();
BhomOldZ.Allocate();
std::vector<CurrentQuantity*> BhomOld_vec;
BhomOld_vec.push_back(&BhomOldX);
BhomOld_vec.push_back(&BhomOldY);
BhomOld_vec.push_back(&BhomOldZ);
CurrentQuantity LagMultOld(currgp);
LagMultOld._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHomLagMult");
LagMultOld.VectWithQtyFillBasic();
LagMultOld.Allocate();
//========= END INTERNAL QUANTITIES (unknowns of the equation) =================
//========= tEST AND SHAPE FOR QTYZERO AND QTYONE =================
//QTYZERO SHAPE: shape of the first Unknown
CurrentQuantity Phij(currgp); //TODO this is another Vect that doesnt have an associated quantity still
Phij._dim = 1; //scalar!
Phij._FEord = BhomOldX._FEord;
Phij._ndof = currelem.GetElemType(Phij._FEord)->GetNDofs();
Phij.Allocate();
//QTYZERO tEST: test of the first Unknown
CurrentQuantity Phii(currgp);
Phii._dim = 1;
Phii._FEord = BhomOldX._FEord;
Phii._ndof = currelem.GetElemType(Phii._FEord)->GetNDofs();
Phii.Allocate();
//QTYONE SHAPE: Shape of the second Unknown
CurrentQuantity Psij(currgp);
Psij._dim = 1;
Psij._FEord = LagMultOld._FEord;
Psij._ndof = currelem.GetElemType(Psij._FEord)->GetNDofs();
Psij.Allocate();
//QTYONE tEST: test of the second Unknown
CurrentQuantity Psii(currgp);
Psii._dim = 1;
Psii._FEord = LagMultOld._FEord;
Psii._ndof = currelem.GetElemType(Psii._FEord)->GetNDofs();
Psii.Allocate();
//========= END tEST AND SHAPE FOR QTYZERO AND QTYONE =================
//=========EXTERNAL QUANTITIES (couplings) =====
//========= //DOMAIN MAPPING
CurrentQuantity xyz(currgp);
xyz._dim = DIMENSION;
xyz._FEord = MESH_MAPPING_FE;
xyz._ndof = currelem.GetElemType(xyz._FEord)->GetNDofs();
xyz.Allocate();
CurrentQuantity BextX(currgp);
BextX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldExt0");
BextX.VectWithQtyFillBasic();
BextX.Allocate();
CurrentQuantity BextY(currgp);
BextY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldExt1");
BextY.VectWithQtyFillBasic();
BextY.Allocate();
CurrentQuantity BextZ(currgp);
BextZ._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldExt2");
BextZ.VectWithQtyFillBasic();
BextZ.Allocate();
std::vector<CurrentQuantity*> Bext_vec;
Bext_vec.push_back(&BextX);
Bext_vec.push_back(&BextY);
Bext_vec.push_back(&BextZ);
CurrentQuantity Bext_vecQuant(currgp); //without quantity, nor equation
Bext_vecQuant._dim = Bext_vec.size();
Bext_vecQuant._FEord = Bext_vec[0]->_FEord;
Bext_vecQuant._ndof = Bext_vec[0]->_ndof;
Bext_vecQuant.Allocate();
CurrentQuantity VelX(currgp);
VelX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity0");
VelX.VectWithQtyFillBasic();
VelX.Allocate();
CurrentQuantity VelY(currgp);
VelY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity1");
VelY.VectWithQtyFillBasic();
VelY.Allocate();
CurrentQuantity VelZ(currgp);
VelZ._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity2");
VelZ.VectWithQtyFillBasic();
VelZ.Allocate();
std::vector<CurrentQuantity*> Vel_vec;
Vel_vec.push_back(&VelX);
Vel_vec.push_back(&VelY);
Vel_vec.push_back(&VelZ);
//=========END EXTERNAL QUANTITIES (couplings) =====
//======================
//======================
currelem.Mat().zero();
currelem.Rhs().zero();
currelem.SetDofobjConnCoords();
currelem.SetElDofsBc();
currelem.ConvertElemCoordsToMappingOrd(xyz);
for (uint idim=0; idim < space_dim; idim++) {
BhomOld_vec[idim]->GetElemDofs();
Vel_vec[idim]->GetElemDofs();
Bext_vec[idim]->GetElemDofs();
}
Bext_vecQuant.GetElemDofs(Bext_vec);
const uint el_ngauss = ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussPointsNumber();
for (uint qp = 0; qp < el_ngauss; qp++) {
//======= here starts the "COMMON SHAPE PART"==================
for (uint fe = 0; fe < QL; fe++) {
currgp.SetPhiElDofsFEVB_g (fe,qp);
currgp.SetDPhiDxezetaElDofsFEVB_g (fe,qp);
}
const double det = currgp.JacVectVV_g(xyz); //InvJac: is unique!
const double dtxJxW_g = det*ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussWeight(qp);
const double detb = det/el_ngauss;
for (uint fe = 0; fe < QL; fe++) {
currgp.SetDPhiDxyzElDofsFEVB_g (fe,qp);
currgp.ExtendDphiDxyzElDofsFEVB_g (fe);
}
//======= end of the "COMMON SHAPE PART"==================
for (uint idim=0; idim < space_dim; idim++) {
BhomOld_vec[idim]->val_g();
Vel_vec[idim]->val_g(); //---- for Advection MAT & RHS
Vel_vec_val_g[idim] = Vel_vec[idim]->_val_g[0];
Bext_vec[idim]->val_g(); //----- for Advection RHS
Bext_vec_val_g[idim] = Bext_vec[idim]->_val_g[0];
Bext_vec[idim]->grad_g(); //----- for Laplacian RHS
}
Bext_vecQuant.curl_g(); //----- for Curl Curl RHS //THE EXTENSION of the DOFS to 3D is done INSIDE!!
Math::extend(&Vel_vec_val_g[0],&Vel_vec_val_g3D[0],space_dim); //----- for Advection RHS
Math::extend(&Bext_vec_val_g[0],&Bext_vec_val_g3D[0],space_dim); //----- for Advection RHS
Math::cross(&Vel_vec_val_g3D[0],&Bext_vec_val_g3D[0],vXBe_g3D); //----- for Advection RHS
//================================
//========= FILLING ELEMENT MAT/RHS
//=================================
for (uint i=0; i < BhomOldX._ndof; i++) {
//============ preparation for (i) (Phii) ============
Phii._val_g[0] = currgp._phi_ndsQLVB_g[Phii._FEord][i]; /*const double phii_g*/
for (uint idim=0; idim<space_dim; idim++)
Phii._grad_g[0][idim] = currgp._dphidxyz_ndsQLVB_g[Phii._FEord][i+idim*Phii._ndof]; /*dphiidx_g*/
//=== from this point on, the dependency on /*(i)*/, the ROW INDEX, of the quantities is given by Phii
//=== /*(i)*/ is ONLY used for the POSITIONS, later
//--------- LAPLACIAN: Operator, RHS: grad Be . grad phi ---------------------
for (uint idim=0; idim<space_dim/*Bext._dim*/; idim++) LapBe_g[idim]=0.;
for (uint idim=0; idim<space_dim/*Bext._dim*/; idim++) {
for (uint jdim=0; jdim<space_dim; jdim++) {
LapBe_g[idim] += Bext_vec[idim]->_grad_g[0][jdim]*Phii._grad_g[0][jdim];
}
}
Math::extend(&Phii._grad_g[0][0],&Phii._grad_g3D[0][0],space_dim);
//--------- CURL CURL: Operator, RHS: curl Be . curl phi -------------------
Math::cross(&Bext_vecQuant._curl_g3D[0],&Phii._grad_g3D[0][0],curlBeXdphii_g3D);
//--------- ADVECTION: Operator, RHS: v x Be . curl phi -------------------
Math::cross( vXBe_g3D,&Phii._grad_g3D[0][0], vXBeXdphii_g3D); // _utils.cross(vXBe_g3D,dphiidx_g3D,vXBeXdphii_g3D);
//============end preparation for (i) ============
for (uint idim=0; idim<space_dim/*bhomOld._dim*/; idim++) {
const uint irowq = i + idim*BhomOldX._ndof;
currelem.Rhs()(irowq) += currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
- LAP_MHD*IRem*LapBe_g[idim]
- (1-LAP_MHD)*IRem*curlBeXdphii_g3D[idim] //phii of bhomOld /*CurlCurl(RHS,vb,Phij,Phii,idim,idimp1);*/
+ ADV_MHD* vXBeXdphii_g3D[idim] //phii of bhomOld
)
+ (1-currelem.GetBCDofFlag()[irowq])*detb*BhomOld_vec[idim]->_val_dofs[i]; //Dirichlet bc
}
for (uint idim=0; idim<space_dim/*bhomOld._dim*/; idim++) { // filling diagonal block for Dirichlet bc
const uint irowq = i + idim*BhomOldX._ndof;
currelem.Mat()(irowq,irowq) += (1-currelem.GetBCDofFlag()[irowq])*detb;
}
// end filling diagonal for Dirichlet bc
for (uint j=0; j<BhomOldX._ndof; j++) { // A element matrix
//============ preparation for (j) (Phij) ============
Phij._val_g[0] = currgp._phi_ndsQLVB_g[Phij._FEord][j];
for (uint idim=0; idim<space_dim; idim++)
Phij._grad_g[0][idim] = currgp._dphidxyz_ndsQLVB_g[Phij._FEord][j+idim*Phij._ndof]; //real shape /*dphijdx_g[idim]*/
//=== from this point on, the dependency on /*(j)*/, the COLUMN INDEX, of the quantities is given by Phij
//=== /*(j)*/ is ONLY used for the POSITIONS, later
//--------- LAPLACIAN: Operator, MAT: grad b . grad phi ---------------------
double Lap_g = Math::dot(&Phij._grad_g[0][0],&Phii._grad_g[0][0],space_dim); /*(i,j)*/ //part independent of idim
//--------- ADVECTION: Operator, MAT: v x b . curl phi -------------------
double Advphii_g = Math::dot( &Vel_vec_val_g[0],&Phii._grad_g[0][0],space_dim); /*(i)*/ //part independent of idim //TODO what about putting it OUTSIDE?
for (uint idim=0; idim<space_dim/*bhomOld._dim*/; idim++) { //filled in as 1-2-3 // 5-6-4 // 9-7-8
int irowq=i+idim*BhomOldX._ndof; //idim gives the row index //test of bhomOld
// diagonal blocks [1-5-9] idim = row index = column index //shape of bhomOld
currelem.Mat()(irowq,j+idim*BhomOldX._ndof)
+= currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
+ LAP_MHD*IRem*(Lap_g)
+ (1-LAP_MHD)*IRem*( Lap_g - Phij._grad_g[0][idim]*Phii._grad_g[0][idim] )
- ADV_MHD * Phij._val_g[0]* (Advphii_g - Vel_vec[idim]->_val_g[0] *Phii._grad_g[0][idim] ) //TODO Phij here does not depend on idim, but it depends on j
);
// block +1 [2-6-7]
int idimp1=(idim+1)%space_dim;
//idim: component of the SHAPE
//idimp1: component of the tEST
currelem.Mat()(irowq,j+idimp1*BhomOldX._ndof)
+= currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
+ (1-LAP_MHD)*IRem*( - Phij._grad_g[0][idim]*Phii._grad_g[0][idimp1] ) /*(i,j)*/ /*CurlCurl(MAT,vb,Phij,Phii,idim,idimp1);*/
- ADV_MHD * Phij._val_g[0]* ( - Vel_vec[idim]->_val_g[0] * Phii._grad_g[0][idimp1] ) /*(i,j)*/ /*AdvCurl(MAT,Vel,Phij,Phii,idim,idimp1)*/
);
#if (DIMENSION==3)
// block +2 [3-4-8]
int idimp2=(idim+2)%space_dim;//idimp2 column index
currelem.Mat()(irowq,j+idimp2*BhomOldX._ndof)
+= currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
+ (1-LAP_MHD)*IRem*( - Phij._grad_g[0][idim]*Phii._grad_g[0][idimp2] ) /*(i,j)*/
- ADV_MHD * Phij._val_g[0]* ( - Vel_vec[idim]->_val_g[0] *Phii._grad_g[0][idimp2] ) /*(i,j)*/
);
#endif
}
}
// end A element matrix
for (uint j = 0; j < LagMultOld._ndof; j++) {// B^T element matrix ( p*div(v) )
Psij._val_g[0] = currgp._phi_ndsQLVB_g[Psij._FEord][j]; /*const double psij_g */
const int jclml= j+/*bhomOld._dim*/space_dim*BhomOldX._ndof;
for (uint idim=0; idim<space_dim; idim++) { //bhomOld._dim==spacedimension
uint irowq=i+idim*BhomOldX._ndof;
currelem.Mat()(irowq,jclml) += currelem.GetBCDofFlag()[irowq]*dtxJxW_g*( - Psij._val_g[0]*Phii._grad_g[0][idim] ); /*(i,j)*/ /*PDiv(MAT,Psij,Phii,idim)*/
}
}
// end B^T element matrix
//============ begin linear rows
if (i < LagMultOld._ndof) {
Psii._val_g[0] = currgp._phi_ndsQLVB_g[Psii._FEord][i]; /*double psii_g*/
const uint irowl=i+space_dim*BhomOldX._ndof;
currelem.Rhs()(irowl)=0.;
for (uint j=0; j<BhomOldX._ndof; j++) { // B element matrix q*div(u)
for (uint idim=0; idim<space_dim; idim++) Phij._grad_g[0][idim] = currgp._dphidxyz_ndsQLVB_g[Phij._FEord][j+idim*Phij._ndof];
for (uint idim=0; idim<space_dim; idim++) currelem.Mat()(irowl,j+idim*BhomOldX._ndof) += - dtxJxW_g*Psii._val_g[0]*Phij._grad_g[0][idim]; /*(i,j)*/ /*PDiv(MAT,Psii,Phij,idim)*/
}
}
//============ end linear rows
}
//end filling element mat/rhs (i loop)
}
// end element gaussian integration loop
/// Add element matrix and rhs to the global ones.
my_system._LinSolver[Level]->_KK->add_matrix(currelem.Mat(),currelem.GetDofIndices());
my_system._LinSolver[Level]->_RESC->add_vector(currelem.Rhs(),currelem.GetDofIndices());
}
// end of element loop
}//END VOLUME
my_system._LinSolver[Level]->_KK->close();
my_system._LinSolver[Level]->_RESC->close();
#ifdef DEFAULT_PRINT_INFO
std::cout << " GenMatRhs " << my_system.name() << ": assembled Level " << Level
<< " with " << my_system._LinSolver[Level]->_KK->m() << " dofs " << std::endl;
#endif
return;
}
void GenMatRhsT(MultiLevelProblem &ml_prob) {
SystemTwo & my_system = ml_prob.get_system<SystemTwo>("Eqn_T");
const unsigned Level = my_system.GetLevelToAssemble();
const double time = 0.;
//======== ELEMENT MAPPING =======
const uint space_dim = ml_prob._ml_msh->GetDimension();
my_system._LinSolver[Level]->_KK->zero();
my_system._LinSolver[Level]->_RESC->zero();
// ==========================================
Mesh *mymsh = ml_prob._ml_msh->GetLevel(Level);
elem *myel = mymsh->el;
const unsigned myproc = mymsh->processor_id();
// ==========================================
// ==========================================
{//BEGIN VOLUME
//==== AUXILIARY ==============
double* dphijdx_g = new double[space_dim];
double* dphiidx_g = new double[space_dim];
const uint mesh_vb = VV;
const uint nel_e = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level+1];
const uint nel_b = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level];
for (uint iel=0; iel < (nel_e - nel_b); iel++) {
CurrentElem<double> currelem(iel,myproc,Level,VV,&my_system,ml_prob.GetMeshTwo(),ml_prob.GetElemType(),mymsh);
CurrentGaussPointBase & currgp = CurrentGaussPointBase::build(currelem,ml_prob.GetQuadratureRule(currelem.GetDim()));
//=========INTERNAL QUANTITIES (unknowns of the equation) =========
CurrentQuantity Tempold(currgp);
Tempold._qtyptr = my_system.GetUnknownQuantitiesVector()[0];
Tempold.VectWithQtyFillBasic();
Tempold.Allocate();
//=========EXTERNAL QUANTITIES (couplings) =====
//========= //DOMAIN MAPPING
CurrentQuantity xyz(currgp); //no quantity
xyz._dim = space_dim;
xyz._FEord = MESH_MAPPING_FE;
xyz._ndof = currelem.GetElemType(xyz._FEord)->GetNDofs();
xyz.Allocate();
currelem.Mat().zero();
currelem.Rhs().zero();
currelem.SetDofobjConnCoords();
currelem.SetElDofsBc();
currelem.ConvertElemCoordsToMappingOrd(xyz);
Tempold.GetElemDofs();
//====================
const uint el_ngauss = ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussPointsNumber();
for (uint qp=0; qp< el_ngauss; qp++) {
//======= "COMMON SHAPE PART"==================
for (uint fe = 0; fe < QL; fe++) {
currgp.SetPhiElDofsFEVB_g (fe,qp);
currgp.SetDPhiDxezetaElDofsFEVB_g (fe,qp);
}
const double det = currgp.JacVectVV_g(xyz);
const double dtxJxW_g = det*ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussWeight(qp);
const double detb = det/el_ngauss;
for (uint fe = 0; fe < QL; fe++) {
currgp.SetDPhiDxyzElDofsFEVB_g (fe,qp);
currgp.ExtendDphiDxyzElDofsFEVB_g(fe);
}
//======= end of the "COMMON SHAPE PART"==================
Tempold.val_g();
for (uint i=0; i < Tempold._ndof/*the maximum number is for biquadratic*/; i++) {
const double phii_g = currgp._phi_ndsQLVB_g[Tempold._FEord][i];
for (uint idim = 0; idim < space_dim; idim++) dphiidx_g[idim] = currgp._dphidxyz_ndsQLVB_g[Tempold._FEord][i+idim*Tempold._ndof];
//=========== FIRST ROW ===============
currelem.Rhs()(i) +=
currelem.GetBCDofFlag()[i]*dtxJxW_g*(
7.*phii_g
)
+ (1-currelem.GetBCDofFlag()[i])*detb*(Tempold._val_dofs[i]);
currelem.Mat()(i,i) += (1-currelem.GetBCDofFlag()[i])*detb;
// Matrix Assemblying ---------------------------
for (uint j=0; j<Tempold._ndof; j++) {
double phij_g = currgp._phi_ndsQLVB_g[Tempold._FEord][j];
for (uint idim = 0; idim < space_dim; idim++) {
dphijdx_g [idim] = currgp._dphidxyz_ndsQLVB_g[Tempold._FEord][j+idim*Tempold._ndof];
}
double Lap_g = Math::dot(dphijdx_g,dphiidx_g,space_dim);
int ip1 = i + Tempold._ndof;
int jp1 = j + Tempold._ndof;
//============ FIRST ROW state delta T ===============
//======= DIAGONAL =============================
currelem.Mat()(i,j) +=
currelem.GetBCDofFlag()[i]*dtxJxW_g*(
Lap_g
);
} //end j (col)
} //end i (row)
} // end of the quadrature point qp-loop
currelem.Mat().print_scientific(std::cout);
my_system._LinSolver[Level]->_KK->add_matrix(currelem.Mat(),currelem.GetDofIndices());
my_system._LinSolver[Level]->_RESC->add_vector(currelem.Rhs(),currelem.GetDofIndices());
} // end of element loop
// *****************************************************************
delete [] dphijdx_g;
delete [] dphiidx_g;
}//END VOLUME
my_system._LinSolver[Level]->_KK->close();
my_system._LinSolver[Level]->_RESC->close();
#ifdef DEFAULT_PRINT_INFO
std::cout << " Matrix and RHS assembled for equation " << my_system.name()
<< " Level "<< Level << " dofs " << my_system._LinSolver[Level]->_KK->n() << std::endl;
#endif
return;
}
//------------------------------------------------------------------------------------------------------------
void AssembleMatrixRes_VC(MultiLevelProblem &ml_prob) {
TransientNonlinearImplicitSystem* mlPdeSys = & ml_prob.get_system<TransientNonlinearImplicitSystem>("Timedep");
const unsigned level = mlPdeSys->GetLevelToAssemble();
MultiLevelSolution *ml_sol = ml_prob._ml_sol;
Solution* sol = ml_sol->GetSolutionLevel(level);
LinearEquationSolver* pdeSys = mlPdeSys->_LinSolver[level];
const char* pdename = mlPdeSys->name().c_str();
Mesh* msh = ml_prob._ml_msh->GetLevel(level);
elem* myel = msh->el;
SparseMatrix* JAC = pdeSys->_KK;
NumericVector* RES = pdeSys->_RES;
// data
const unsigned dim = msh->GetDimension();
const unsigned max_size = static_cast< unsigned >(ceil(pow(3, dim))); // conservative: based on line3, quad9, hex27
unsigned nel = msh->GetNumberOfElements();
unsigned igrid = msh->GetLevel();
unsigned iproc = msh->processor_id();
// time dep data
double dt = mlPdeSys->GetIntervalTime();
// double theta = 0.5;
//************** geometry (at dofs and quadrature points) *************************************
vector < vector < double > > coords_at_dofs(dim);
unsigned coords_fe_type = BIQUADR_FE; // get the finite element type for "x", it is always 2 (LAGRANGE BIQUADRATIC)
for (unsigned i = 0; i < coords_at_dofs.size(); i++) coords_at_dofs[i].reserve(max_size);
vector < double > coord_at_qp(dim);
//************* shape functions (at dofs and quadrature points) **************************************
const int solType_max = BIQUADR_FE; //biquadratic
double weight_qp; // gauss point weight
vector < vector < double > > phi_fe_qp(NFE_FAMS);
vector < vector < double > > phi_x_fe_qp(NFE_FAMS);
vector < vector < double > > phi_xx_fe_qp(NFE_FAMS);
for(int fe=0; fe < NFE_FAMS; fe++) {
phi_fe_qp[fe].reserve(max_size);
phi_x_fe_qp[fe].reserve(max_size*dim);
phi_xx_fe_qp[fe].reserve(max_size*(3*(dim-1)));
}
//***************************************************
//********* WHOLE SET OF VARIABLES ******************
//***************************************************
const unsigned int n_unknowns = mlPdeSys->GetSolPdeIndex().size();
vector < std::string > Solname(n_unknowns); Solname[0] = "u";
vector < unsigned > SolPdeIndex(n_unknowns);
vector < unsigned > SolIndex(n_unknowns);
vector < unsigned int > SolFEType(n_unknowns); //FEtype of each MultilevelSolution
vector < unsigned int > Sol_n_el_dofs(n_unknowns); //number of element dofs
std::fill(Sol_n_el_dofs.begin(), Sol_n_el_dofs.end(), 0);
for(unsigned ivar=0; ivar < n_unknowns; ivar++) {
SolPdeIndex[ivar] = mlPdeSys->GetSolPdeIndex( Solname[ivar].c_str() );
SolIndex[ivar] = ml_sol->GetIndex ( Solname[ivar].c_str() );
SolFEType[ivar] = ml_sol->GetSolutionType ( SolIndex[ivar]);
}
//------------ quantities (at quadrature points) ---------------------
vector<double> sol_qp(n_unknowns);
vector<double> sol_old_qp(n_unknowns);
vector< vector<double> > sol_grad_qp(n_unknowns);
vector< vector<double> > sol_old_grad_qp(n_unknowns);
std::fill(sol_qp.begin(), sol_qp.end(), 0.);
std::fill(sol_old_qp.begin(), sol_old_qp.end(), 0.);
for (unsigned k = 0; k < n_unknowns; k++) {
sol_grad_qp[k].resize(dim);
std::fill(sol_grad_qp[k].begin(), sol_grad_qp[k].end(), 0.);
sol_old_grad_qp[k].resize(dim);
std::fill(sol_old_grad_qp[k].begin(), sol_old_grad_qp[k].end(), 0.);
}
//----------- quantities (at dof objects) ------------------------------
vector < vector < double > > sol_eldofs(n_unknowns);
vector < vector < double > > sol_old_eldofs(n_unknowns);
for(int k=0; k<n_unknowns; k++) { sol_eldofs[k].reserve(max_size);
sol_old_eldofs[k].reserve(max_size);
}
//******** linear system *******************************************
vector < vector < int > > L2G_dofmap(n_unknowns); for(int i = 0; i < n_unknowns; i++) { L2G_dofmap[i].reserve(max_size); }
vector< int > L2G_dofmap_AllVars; L2G_dofmap_AllVars.reserve( n_unknowns*max_size );
vector< vector< double > > Res_el(n_unknowns);
vector< vector< vector< double > > > Jac_el(n_unknowns);
for(int i = 0; i < n_unknowns; i++) Res_el[i].reserve(max_size);
for(int i = 0; i < n_unknowns; i++) {
Jac_el[i].resize(n_unknowns);
for(int j = 0; j < n_unknowns; j++) {
Jac_el[i][j].reserve(max_size*max_size);
}
}
// Set to zero all the entries of the matrix
RES->zero();
JAC->zero();
const double deltat_term = 1.;
const double lapl_term = 1.;
const double delta_g_term = 1.;
// *** element loop ***
for (int iel = msh->_elementOffset[iproc]; iel < msh->_elementOffset[iproc+1]; iel++) {
short unsigned ielGeom = msh->GetElementType(iel); // element geometry type
//******************** GEOMETRY *********************
unsigned nDofx = msh->GetElementDofNumber(iel, coords_fe_type); // number of coordinate element dofs
for (int i = 0; i < dim; i++) coords_at_dofs[i].resize(nDofx);
// local storage of coordinates
for (unsigned i = 0; i < nDofx; i++) {
unsigned xDof = msh->GetSolutionDof(i, iel, coords_fe_type); // global to global mapping between coordinates node and coordinate dof
for (unsigned jdim = 0; jdim < dim; jdim++) {
coords_at_dofs[jdim][i] = (*msh->_topology->_Sol[jdim])(xDof); // global extraction and local storage for the element coordinates
}
}
//***************************************************
//all vars###################################################################
for (unsigned k = 0; k < n_unknowns; k++) {
unsigned ndofs_unk = msh->GetElementDofNumber(iel, SolFEType[k]);
Sol_n_el_dofs[k] = ndofs_unk;
sol_eldofs[k].resize(ndofs_unk);
sol_old_eldofs[k].resize(ndofs_unk);
L2G_dofmap[k].resize(ndofs_unk);
for (unsigned i = 0; i < ndofs_unk; i++) {
unsigned solDof = msh->GetSolutionDof(i, iel, SolFEType[k]); // global to global mapping between solution node and solution dof
// via local to global solution node
sol_eldofs[k][i] = (*sol->_Sol[SolIndex[k]])(solDof); // global extraction and local storage for the solution
sol_old_eldofs[k][i] = (*sol->_SolOld[SolIndex[k]])(solDof); // This is OLD in TIME, not in nonlinear loop
L2G_dofmap[k][i] = pdeSys->GetSystemDof(SolIndex[k], SolPdeIndex[k], i, iel); // global to global mapping between solution node and pdeSys dof
}
}
unsigned nDof_AllVars = 0;
for (unsigned k = 0; k < n_unknowns; k++) { nDof_AllVars += Sol_n_el_dofs[k]; }
// TODO COMPUTE MAXIMUM maximum number of element dofs for one scalar variable
int nDof_max = 0;
for (unsigned k = 0; k < n_unknowns; k++) {
if(Sol_n_el_dofs[k] > nDof_max) nDof_max = Sol_n_el_dofs[k];
}
for(int k = 0; k < n_unknowns; k++) {
L2G_dofmap[k].resize(Sol_n_el_dofs[k]);
Res_el[SolPdeIndex[k]].resize(Sol_n_el_dofs[k]);
memset(& Res_el[SolPdeIndex[k]][0], 0., Sol_n_el_dofs[k] * sizeof(double) );
Jac_el[SolPdeIndex[k]][SolPdeIndex[k]].resize(Sol_n_el_dofs[k] * Sol_n_el_dofs[k]);
memset(& Jac_el[SolPdeIndex[k]][SolPdeIndex[k]][0], 0., Sol_n_el_dofs[k] * Sol_n_el_dofs[k] * sizeof(double));
}
//all vars###################################################################
// *** quadrature loop ***
for(unsigned ig = 0; ig < ml_prob.GetQuadratureRule(ielGeom).GetGaussPointsNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
for(int fe=0; fe < NFE_FAMS; fe++) {
msh->_finiteElement[ielGeom][fe]->Jacobian(coords_at_dofs,ig,weight_qp,phi_fe_qp[fe],phi_x_fe_qp[fe],phi_xx_fe_qp[fe]);
}
//HAVE TO RECALL IT TO HAVE BIQUADRATIC JACOBIAN
msh->_finiteElement[ielGeom][coords_fe_type]->Jacobian(coords_at_dofs,ig,weight_qp,phi_fe_qp[coords_fe_type],phi_x_fe_qp[coords_fe_type],phi_xx_fe_qp[coords_fe_type]);
//========= fill gauss value quantities ==================
std::fill(sol_qp.begin(), sol_qp.end(), 0.);
std::fill(sol_old_qp.begin(), sol_old_qp.end(), 0.);
for (unsigned k = 0; k < n_unknowns; k++) { std::fill(sol_grad_qp[k].begin(), sol_grad_qp[k].end(), 0.);
std::fill(sol_old_grad_qp[k].begin(), sol_old_grad_qp[k].end(), 0.);
}
for (unsigned k = 0; k < n_unknowns; k++) {
for (unsigned i = 0; i < Sol_n_el_dofs[k]; i++) {
sol_qp[k] += sol_eldofs[k][i] * phi_fe_qp[SolFEType[k]][i];
sol_old_qp[k] += sol_old_eldofs[k][i] * phi_fe_qp[SolFEType[k]][i];
for (unsigned d = 0; d < dim; d++) { sol_grad_qp[k][d] += sol_eldofs[k][i] * phi_x_fe_qp[SolFEType[k]][i * dim + d];
sol_old_grad_qp[k][d] += sol_old_eldofs[k][i] * phi_x_fe_qp[SolFEType[k]][i * dim + d];
}
}
}
//========= fill gauss value quantities ==================
// *** phi_i loop ***
for(unsigned i = 0; i < nDof_max; i++) {
//BEGIN RESIDUALS A block ===========================
double Lap_rhs_i = 0.;
double Lap_old_rhs_i = 0.;
for(unsigned d = 0; d < dim; d++) {
Lap_rhs_i += phi_x_fe_qp[SolFEType[0]][i * dim + d] * sol_grad_qp[0][d];
Lap_old_rhs_i += phi_x_fe_qp[SolFEType[0]][i * dim + d] * sol_old_grad_qp[0][d];
}
Res_el[SolPdeIndex[0]][i] += - weight_qp * (
delta_g_term * Singularity::function(sol_qp[0]) * Singularity::g_vc(sol_qp[0]) * phi_fe_qp[ SolFEType[0] ][i]
- delta_g_term * Singularity::function(sol_qp[0]) * Singularity::g_vc(sol_old_qp[0]) * phi_fe_qp[ SolFEType[0] ][i]
+ deltat_term * Singularity::function(sol_qp[0]) * dt * phi_fe_qp[ SolFEType[0] ][i]
+ lapl_term * dt * Lap_rhs_i
);
//END RESIDUALS A block ===========================
// *** phi_j loop ***
for(unsigned j = 0; j<nDof_max; j++) {
double Lap_mat_i_j = 0.;
for(unsigned d = 0; d < dim; d++) Lap_mat_i_j += phi_x_fe_qp[SolFEType[0]][i * dim + d] *
phi_x_fe_qp[SolFEType[0]][j * dim + d];
Jac_el[SolPdeIndex[0]][SolPdeIndex[0]][i * Sol_n_el_dofs[0] + j] += weight_qp * (
+ delta_g_term * phi_fe_qp[ SolFEType[0] ][i] * Singularity::derivative( phi_fe_qp[ SolFEType[0] ][j] ) * phi_fe_qp[ SolFEType[0] ][j] * Singularity::g_vc( phi_fe_qp[ SolFEType[0] ][j] )
+ delta_g_term * phi_fe_qp[ SolFEType[0] ][i] * Singularity::function ( phi_fe_qp[ SolFEType[0] ][j] ) * Singularity::g_vc_derivative( phi_fe_qp[ SolFEType[0] ][j] ) * phi_fe_qp[ SolFEType[0] ][j]
- delta_g_term * phi_fe_qp[ SolFEType[0] ][i] * Singularity::derivative( phi_fe_qp[ SolFEType[0] ][j] ) * phi_fe_qp[ SolFEType[0] ][j] * Singularity::g_vc( sol_old_qp[0] )
+ deltat_term * phi_fe_qp[ SolFEType[0] ][i] * Singularity::derivative( phi_fe_qp[ SolFEType[0] ][j] ) * phi_fe_qp[ SolFEType[0] ][j] * dt
+ lapl_term * dt * Lap_mat_i_j
);
} //end phij loop
} //end phii loop
} // end gauss point loop
//--------------------------------------------------------------------------------------------------------
//Sum the local matrices/vectors into the Global Matrix/Vector
for(unsigned ivar=0; ivar < n_unknowns; ivar++) {
RES->add_vector_blocked(Res_el[SolPdeIndex[ivar]],L2G_dofmap[ivar]);
JAC->add_matrix_blocked(Jac_el[SolPdeIndex[ivar]][SolPdeIndex[ivar]],L2G_dofmap[ivar],L2G_dofmap[ivar]);
}
//--------------------------------------------------------------------------------------------------------
} //end list of elements loop for each subdomain
JAC->close();
RES->close();
// ***************** END ASSEMBLY *******************
}
/// This function assembles the matrix and the rhs:
void GenMatRhsT(MultiLevelProblem &ml_prob){
//if we are just a function not inside a class, we have to retrieve ourselves...
SystemTwo & my_system = ml_prob.get_system<SystemTwo>("Eqn_T");
const unsigned Level = my_system.GetLevelToAssemble();
// ==========================================
Mesh *mymsh = ml_prob._ml_msh->GetLevel(Level);
elem *myel = mymsh->el;
const unsigned myproc = mymsh->processor_id();
//======== ELEMENT MAPPING =======
const uint space_dim = ml_prob._ml_msh->GetDimension();
//====== reference values ========================
const double IRe = 1./ml_prob.GetInputParser().get("Re");
const double IPr = 1./ml_prob.GetInputParser().get("Pr");
const double alphaT = ml_prob.GetInputParser().get("alphaT");
const double alphaL2 = ml_prob.GetInputParser().get("alphaL2");
const double alphaH1 = ml_prob.GetInputParser().get("alphaH1");
//==== AUXILIARY ==============
std::vector<double> dphijdx_g(space_dim);
std::vector<double> dphiidx_g(space_dim);
my_system._LinSolver[Level]->_KK->zero();
my_system._LinSolver[Level]->_RESC->zero();
// ==========================================
// ==========================================
{//BEGIN VOLUME
const uint mesh_vb = VV;
const uint nel_b = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level];
const uint nel_e = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level+1];
// const uint nel_beg = mymsh->_elementOffset[myproc];
// const uint nel_end = mymsh->_elementOffset[myproc+1];
for (uint iel = 0; iel < (nel_e - nel_b); iel++) {
// for (uint iel_two = nel_beg; iel_two < nel_end; iel_two++) {
CurrentElem<double> currelem(iel,myproc,Level,VV,&my_system,ml_prob.GetMeshTwo(),ml_prob.GetElemType(),mymsh);
CurrentGaussPointBase & currgp = CurrentGaussPointBase::build(currelem,ml_prob.GetQuadratureRule(currelem.GetDim()));
//=========INTERNAL QUANTITIES (unknowns of the equation) =========
CurrentQuantity Tempold(currgp);
Tempold._SolName = "Qty_Temperature";
Tempold._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Temperature");
Tempold.VectWithQtyFillBasic();
Tempold.Allocate();
//====================================
CurrentQuantity Tlift(currgp);
Tlift._SolName = "Qty_TempLift";
Tlift._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_TempLift");
Tlift.VectWithQtyFillBasic();
Tlift.Allocate();
//=====================================
CurrentQuantity TAdj(currgp);
TAdj._SolName = "Qty_TempAdj";
TAdj._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_TempAdj");
TAdj.VectWithQtyFillBasic();
TAdj.Allocate();
//=========EXTERNAL QUANTITIES (couplings) =====
//========= //DOMAIN MAPPING
CurrentQuantity xyz(currgp); //no quantity
xyz._dim = space_dim;
xyz._FEord = MESH_MAPPING_FE;
xyz._ndof = currelem.GetElemType(xyz._FEord)->GetNDofs();
xyz.Allocate();
//==================
CurrentQuantity velX(currgp);
velX._SolName = "Qty_Velocity0";
velX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity0");
velX.VectWithQtyFillBasic();
velX.Allocate();
//==================
CurrentQuantity velY(currgp);
velY._SolName = "Qty_Velocity1";
velY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity1");
velY.VectWithQtyFillBasic();
velY.Allocate();
//===============Tdes=====================
CurrentQuantity Tdes(currgp);
Tdes._SolName = "Qty_TempDes";
Tdes._dim = Tempold._dim;
Tdes._FEord = Tempold._FEord;
Tdes._ndof = Tempold._ndof;
Tdes.Allocate();
// ==========================================
// ==========================================
currelem.Mat().zero();
currelem.Rhs().zero();
currelem.SetDofobjConnCoords();
currelem.SetElDofsBc();
Tempold.GetElemDofs();
Tlift.GetElemDofs();
TAdj.GetElemDofs();
velX.GetElemDofs();
velY.GetElemDofs();
TempDesired(Tdes,currelem);
currelem.ConvertElemCoordsToMappingOrd(xyz);
xyz.SetElemAverage();
int domain_flag = ElFlagControl(xyz._el_average,ml_prob._ml_msh);
//====================
const uint el_ngauss = ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussPointsNumber();
for (uint qp=0; qp< el_ngauss; qp++) {
//======= "COMMON SHAPE PART"==================
for (uint fe = 0; fe < QL; fe++) {
currgp.SetPhiElDofsFEVB_g (fe,qp);
currgp.SetDPhiDxezetaElDofsFEVB_g (fe,qp);
}
const double det = currgp.JacVectVV_g(xyz);
const double dtxJxW_g = det*ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussWeight(qp);
const double detb = det/el_ngauss;
for (uint fe = 0; fe < QL; fe++) {
currgp.SetDPhiDxyzElDofsFEVB_g (fe,qp);
currgp.ExtendDphiDxyzElDofsFEVB_g(fe);
}
//======= end of the "COMMON SHAPE PART"==================
Tempold.val_g();
Tlift.val_g();
TAdj.val_g();
velX.val_g();
velY.val_g();
Tdes.val_g();
for (uint i=0; i < Tempold._ndof; i++) {
const double phii_g = currgp._phi_ndsQLVB_g[Tempold._FEord][i];
for (uint idim = 0; idim < space_dim; idim++) dphiidx_g[idim] = currgp._dphidxyz_ndsQLVB_g[Tempold._FEord][i+idim*Tempold._ndof];
//=========== FIRST ROW ===============
currelem.Rhs()(i) +=
currelem.GetBCDofFlag()[i]*dtxJxW_g*( 0. )
+ (1-currelem.GetBCDofFlag()[i])*detb*(Tempold._val_dofs[i]);
currelem.Mat()(i,i) += (1-currelem.GetBCDofFlag()[i])*detb;
//========= SECOND ROW (CONTROL) =====================
int ip1 = i + /* 1* */Tempold._ndof; //suppose that T' T_0 T_adj have the same order
currelem.Rhs()(ip1) +=
currelem.GetBCDofFlag()[ip1]*dtxJxW_g*(
+ alphaT*domain_flag*(Tdes._val_g[0])*phii_g // T_d delta T_0
)
+ (1-currelem.GetBCDofFlag()[ip1])*detb*(Tlift._val_dofs[i]);
currelem.Mat()(ip1,ip1) += (1-currelem.GetBCDofFlag()[ip1])*detb;
//======= THIRD ROW (ADJOINT) ===================================
int ip2 = i + 2 * Tempold._ndof; //suppose that T' T_0 T_adj have the same order
currelem.Rhs()(ip2) +=
currelem.GetBCDofFlag()[ip2]*dtxJxW_g*(
+ alphaT*domain_flag*(Tdes._val_g[0])*phii_g // T_d delta T'
)
+ (1-currelem.GetBCDofFlag()[ip2])*detb*(Tempold._val_dofs[i]);
currelem.Mat()(ip2,ip2) += (1-currelem.GetBCDofFlag()[ip2])*detb;
// Matrix Assemblying ---------------------------
for (uint j=0; j<Tempold._ndof; j++) {
double phij_g = currgp._phi_ndsQLVB_g[Tempold._FEord][j];
for (uint idim = 0; idim < space_dim; idim++) dphijdx_g[idim] = currgp._dphidxyz_ndsQLVB_g[Tempold._FEord][j+idim*Tempold._ndof];
double Lap_g = Math::dot(&dphijdx_g[0],&dphiidx_g[0],space_dim);
double Advection = velX._val_g[0]*dphijdx_g[0] + velY._val_g[0]*dphijdx_g[1]; //Math::dot(&vel._val_g[0],&dphijdx_g[0],space_dim);
int ip1 = i + Tempold._ndof;
int jp1 = j + Tempold._ndof;
int ip2 = i + 2*Tempold._ndof;
int jp2 = j + 2*Tempold._ndof;
// T T_0 T_adj
// T X X O
// T_0
// T_adj
//============ FIRST ROW state delta T ===============
//======= DIAGONAL =============================
currelem.Mat()(i,j) +=
currelem.GetBCDofFlag()[i]*dtxJxW_g*(
+ Advection*phii_g
+ IRe*IPr*Lap_g
);
//===============================
//same operators for T and T_0
currelem.Mat()(i,jp1) +=
currelem.GetBCDofFlag()[i]*dtxJxW_g*(
+ Advection*phii_g
+ IRe*IPr*Lap_g
);
//====================================
currelem.Mat()(i,jp2) +=
currelem.GetBCDofFlag()[i]*dtxJxW_g*(
0.
);
//============= SECOND ROW (LIFTING) delta T_0 =============
//===== DIAGONAL ===========================
currelem.Mat()(ip1,jp1) +=
currelem.GetBCDofFlag()[ip1]*
dtxJxW_g*(
+ alphaL2*phij_g*phii_g //L_2 control norm
+ alphaH1*Lap_g //H_1 control norm
+ alphaT*domain_flag*(phij_g)*phii_g //T_0 delta T_0 //ADDED///////////////
);
//====================================
currelem.Mat()(ip1,j) +=
currelem.GetBCDofFlag()[ip1]*
dtxJxW_g*(
+ alphaT*domain_flag*(phij_g)*phii_g //T' delta T_0 //ADDED///////////////
);
//====================================
currelem.Mat()(ip1,jp2) +=
currelem.GetBCDofFlag()[ip1]*
dtxJxW_g*(
-Advection*phii_g
+ IRe*IPr*Lap_g
);
//============= THIRD ROW (ADJOINT) =============
//======= DIAGONAL ==================
currelem.Mat()(ip2,jp2) +=
currelem.GetBCDofFlag()[ip2]*
dtxJxW_g*(
- Advection*phii_g //minus sign
+ IRe*IPr*Lap_g
);
//====================================
currelem.Mat()(ip2,j) +=
currelem.GetBCDofFlag()[ip2]*
dtxJxW_g*(
+ alphaT*domain_flag*(phij_g)*phii_g //T' delta T'
);
//====================================
currelem.Mat()(ip2,jp1) +=
currelem.GetBCDofFlag()[ip2]*
dtxJxW_g*(
+ alphaT*domain_flag*(phij_g)*phii_g //T_0 delta T' ///ADDED///////
);
} //end j (col)
} //end i (row)
} // end of the quadrature point qp-loop
my_system._LinSolver[Level]->_KK->add_matrix(currelem.Mat(),currelem.GetDofIndices());
my_system._LinSolver[Level]->_RESC->add_vector(currelem.Rhs(),currelem.GetDofIndices());
} // end of element loop
// *****************************************************************
}//END VOLUME
my_system._LinSolver[Level]->_KK->close();
my_system._LinSolver[Level]->_RESC->close();
#ifdef DEFAULT_PRINT_INFO
std::cout << " Matrix and RHS assembled for equation " << my_system.name()
<< " Level "<< Level << " dofs " << my_system._LinSolver[Level]->_KK->n() << std::endl;
#endif
return;
}
//===================================================
/// This function assembles the matrix and the rhs:
void GenMatRhsNS(MultiLevelProblem &ml_prob) {
SystemTwo & my_system = ml_prob.get_system<SystemTwo>("Eqn_NS");
const unsigned Level = my_system.GetLevelToAssemble();
const uint _AdvPic_fl = 1;
const uint _AdvNew_fl = 0;
const uint _Stab_fl = 0;
const double _Komp_fac = 0.;
//========== GEOMETRIC ELEMENT ========
const uint space_dim = ml_prob._ml_msh->GetDimension();
//====== reference values ========================
//====== related to Quantities on which Operators act, and to the choice of the "LEADING" EQUATION Operator
const double IRe = 1./ml_prob.GetInputParser().get("Re");
const double IFr = 1./ml_prob.GetInputParser().get("Fr");
//================================================
//================================================
//=======Operators @ gauss =======================
std::vector<double> dphijdx_g(space_dim); // ShapeDer(): used for Laplacian,Divergence, ..., associated to an Unknown Quantity
std::vector<double> dphiidx_g(space_dim); // Test(): used for Laplacian,Advection,Divergence... associated to an Unknown Quantity
std::vector<double> AdvRhs_g(space_dim); //Operator: Adv(u,u,phi)
//================================================
my_system._LinSolver[Level]->_KK->zero();
my_system._LinSolver[Level]->_RESC->zero();
// ==========================================
Mesh *mymsh = ml_prob._ml_msh->GetLevel(Level);
elem *myel = mymsh->el;
const unsigned myproc = mymsh->processor_id();
// ==========================================
// ==========================================
{//BEGIN VOLUME
//========================
//========================
const uint mesh_vb = VV;
const uint nel_e = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level+1];
const uint nel_b = ml_prob.GetMeshTwo()._off_el[mesh_vb][ml_prob.GetMeshTwo()._NoLevels*myproc+Level];
for (int iel=0; iel < (nel_e - nel_b); iel++) {
CurrentElem<double> currelem(iel,myproc,Level,VV,&my_system,ml_prob.GetMeshTwo(),ml_prob.GetElemType(),mymsh);
CurrentGaussPointBase & currgp = CurrentGaussPointBase::build(currelem,ml_prob.GetQuadratureRule(currelem.GetDim()));
//=========INTERNAL QUANTITIES (unknowns of the equation) ==================
CurrentQuantity VelOldX(currgp);
VelOldX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity0");
VelOldX._SolName = "Qty_Velocity0";
VelOldX.VectWithQtyFillBasic();
VelOldX.Allocate();
CurrentQuantity VelOldY(currgp);
VelOldY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Velocity1");
VelOldY._SolName = "Qty_Velocity1";
VelOldY.VectWithQtyFillBasic();
VelOldY.Allocate();
std::vector<CurrentQuantity*> VelOld_vec;
VelOld_vec.push_back(&VelOldX);
VelOld_vec.push_back(&VelOldY);
const uint qtyzero_ord = VelOldX._FEord;
const uint qtyzero_ndof = VelOldX._ndof; //same as Y
//=========
CurrentQuantity pressOld(currgp);
pressOld._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_Pressure");
pressOld._SolName = "Qty_Pressure";
pressOld.VectWithQtyFillBasic();
pressOld.Allocate();
const uint qtyone_ord = pressOld._FEord;
const uint qtyone_ndof = pressOld._ndof;
//order
const uint qtyZeroToOne_DofOffset = VelOldX._ndof + VelOldY._ndof;//VelOld._ndof*VelOld._dim;
//========= END INTERNAL QUANTITIES (unknowns of the equation) =================
//=========EXTERNAL QUANTITIES (couplings) =====
//========= //DOMAIN MAPPING
CurrentQuantity xyz(currgp); //domain
xyz._dim = space_dim;
xyz._FEord = MESH_MAPPING_FE;
xyz._ndof = currelem.GetElemType(xyz._FEord)->GetNDofs();
xyz.Allocate();
//other Physical constant Quantities
//=======gravity==================================
CurrentQuantity gravity(currgp);
gravity._dim = space_dim;
// gravity.Allocate(); CANNOT DO THIS NOW BECAUSE NOT ALL THE DATA FOR THE ALLOCATION ARE FILLED
gravity._val_g.resize(gravity._dim);
gravity._val_g[0] = ml_prob.GetInputParser().get("dirgx");
gravity._val_g[1] = ml_prob.GetInputParser().get("dirgy");
if ( space_dim == 3 ) gravity._val_g[2] = ml_prob.GetInputParser().get("dirgz");
//========================
//========================
currelem.Mat().zero();
currelem.Rhs().zero();
currelem.SetDofobjConnCoords();
currelem.SetElDofsBc();
currelem.ConvertElemCoordsToMappingOrd(xyz);
//=======RETRIEVE the DOFS of the UNKNOWN QUANTITIES,i.e. MY EQUATION
VelOldX.GetElemDofs();
VelOldY.GetElemDofs();
pressOld.GetElemDofs();
const uint el_ngauss = ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussPointsNumber();
for (uint qp = 0; qp < el_ngauss; qp++) {
//=======here starts the "COMMON SHAPE PART"==================
// the call of these things should be related to the Operator
//also, the choice of the QuadratureRule should be dependent of the Involved Operators
//and the FE orders on which these Operators act
//these phi and dphi are used for the different stages:
//BEFORE i: by the interpolation functions
//INSIDE i: for the tEST functions and derivatives
//INSIDE j: for the SHAPE functions and derivatives
//again, it should be the Operator to decide what functions to be called,
//for what FE ORDER and what DERIVATIVE ORDER
//if we decide that the PREPARATION of the tEST and SHAPE
//of a certain Unknown are COMMON TO ALL,
//Then we must only concentrate on preparing the OTHER involved quantities in that Operator
for (uint fe = 0; fe < QL; fe++) {
currgp.SetPhiElDofsFEVB_g (fe,qp);
currgp.SetDPhiDxezetaElDofsFEVB_g (fe,qp);
}
const double det = currgp.JacVectVV_g(xyz);
const double dtxJxW_g = det*ml_prob.GetQuadratureRule(currelem.GetDim()).GetGaussWeight(qp);
const double detb = det/el_ngauss;
for (uint fe = 0; fe < QL; fe++) {
currgp.SetDPhiDxyzElDofsFEVB_g (fe,qp);
currgp.ExtendDphiDxyzElDofsFEVB_g(fe);
}
//=======end of the "COMMON SHAPE PART"==================
//now we want to fill the element matrix and rhs with ONLY values AT GAUSS POINTS
//we can divide the values at Gauss points into three parts:
//1-constant values
//2-values which depend on (i)
//3-values which depend on (i,j)
//1- can be used for filling both Ke and Fe
//2- can be used to fill Fe and also Ke
//3- can be used only for filling Ke
//Here, before entering the (i,j) loop, you compute quantities that DO NOT depend on (i,j),
//therefore the ELEMENT SUM, GAUSS SUM And tEST/SHAPE sums have ALL been performed
//but, these quantities depend on idim and jdim, because they are involved in multiplications with tEST and SHAPE functions
//Internal Quantities
VelOldX.val_g();
VelOldX.grad_g();
VelOldY.val_g();
VelOldY.grad_g();
//Advection all VelOld
for (uint idim=0; idim<space_dim; idim++) { AdvRhs_g[idim]=0.;}
for (uint idim=0; idim<space_dim; idim++) {
for (uint b=0; b<space_dim; b++) {
AdvRhs_g[idim] += VelOld_vec[b]->_val_g[0]*VelOld_vec[idim]->_grad_g[0][b];
}
} // grad is [ivar][idim], i.e. [u v w][x y z]
//Divergence VelOld
double Div_g=0.;
for (uint idim=0; idim<space_dim; idim++) Div_g += VelOld_vec[idim]->_grad_g[0][idim];
//==============================================================
//========= FILLING ELEMENT MAT/RHS (i loop) ====================
//==============================================================
// TODO according to the order we should switch DIM loop and DOF loop
for (uint i=0; i<qtyzero_ndof; i++) {
//======="COMMON tEST PART for QTYZERO": func and derivative, of the QTYZERO FE ORD ==========
const double phii_g = currgp._phi_ndsQLVB_g[qtyzero_ord][i];
for (uint idim=0; idim<space_dim; idim++) dphiidx_g[idim] = currgp._dphidxyz_ndsQLVB_g[qtyzero_ord][i+idim*qtyzero_ndof];
//======= END "COMMON tEST PART for QTYZERO" ==========
for (uint idim=0; idim<space_dim; idim++) {
const uint irowq=i+idim*qtyzero_ndof; // (i): dof of the tEST function
//(idim): component of the tEST function
currelem.Rhs()(irowq) +=
currelem.GetBCDofFlag()[irowq]*
dtxJxW_g*( + _AdvNew_fl* AdvRhs_g[idim]*phii_g // NONLIN
+ IFr*gravity._val_g[idim]*phii_g // gravity
)
+ (1-currelem.GetBCDofFlag()[irowq])*detb*VelOld_vec[idim]->_val_dofs[i] //Dirichlet bc
;
}
// end filling element rhs u
for (uint idim=0; idim<space_dim; idim++) { // filling diagonal for Dirichlet bc
const uint irowq = i+idim*qtyzero_ndof;
currelem.Mat()(irowq,irowq) += (1-currelem.GetBCDofFlag()[irowq])*detb;
}
// end filling diagonal for Dirichlet bc
//============ QTYZERO x QTYZERO dofs matrix (A matrix) ============
for (uint j=0; j< qtyzero_ndof; j++) {
//======="COMMON SHAPE PART for QTYZERO": func and derivative, of the QTYZERO FE ORD ==========
// (j): dof of the SHAPE function
double phij_g = currgp._phi_ndsQLVB_g[qtyzero_ord][j];
for (uint idim=0; idim<space_dim; idim++) dphijdx_g[idim] = currgp._dphidxyz_ndsQLVB_g[qtyzero_ord][j+idim*qtyzero_ndof];
//======= END "COMMON SHAPE PART for QTYZERO" ==========
double Lap_g = Math::dot(&dphijdx_g[0],&dphiidx_g[0],space_dim);
double Adv_g=0.;
for (uint idim=0; idim<space_dim; idim++) Adv_g += VelOld_vec[idim]->_val_g[0] * dphijdx_g[idim]; // =Math::dot(&VelOld._val_g[0],dphijdx_g,space_dim);
for (uint idim=0; idim<space_dim; idim++) { //filled in as 1-2-3 // 4-5-6 // 7-8-9
int irowq = i+idim*qtyzero_ndof; //(i) is still the dof of the tEST functions
//(idim): component of the tEST functions
currelem.Mat()(irowq,j+idim*qtyzero_ndof) // diagonal blocks [1-5-9] [idim(rows),idim(columns)] //(idim): component of the SHAPE functions
+=
currelem.GetBCDofFlag()[irowq]*
dtxJxW_g*(
+ _AdvPic_fl* Adv_g*phii_g //TODO NONLIN
+ _AdvNew_fl*phij_g*VelOld_vec[idim]->_grad_g[0][idim]*phii_g //TODO NONLIN
+ _AdvPic_fl*_Stab_fl* 0.5*Div_g*phij_g*phii_g //TODO NONLIN
+ IRe*( dphijdx_g[idim]*dphiidx_g[idim] + Lap_g)
);
int idimp1=(idim+1)%space_dim; // block +1 [2-6-7] [idim(rows),idim+1(columns)] //(idimp1): component of the SHAPE functions
currelem.Mat()(irowq,j+idimp1*qtyzero_ndof)
+=
currelem.GetBCDofFlag()[irowq]*
dtxJxW_g*(
_AdvNew_fl*phij_g*VelOld_vec[idim]->_grad_g[0][idimp1]*phii_g //TODO NONLIN
+ IRe*( dphijdx_g[idim]*dphiidx_g[idimp1])
);
}
}
//============ END QTYZERO x QTYZERO dofs matrix (A matrix) ============
//============ QTYZERO x QTYONE dofs matrix (B^T matrix) // ( p*div(v) ) (NS eq) ============
for (uint j=0; j<qtyone_ndof; j++) {
//======="COMMON SHAPE PART for QTYONE" ==================
const double psij_g = currgp._phi_ndsQLVB_g[qtyone_ord][j];
//======="COMMON SHAPE PART for QTYONE" - END ============
const int jclml = j + qtyZeroToOne_DofOffset;
for (uint idim=0; idim<space_dim; idim++) {
uint irowq = i+idim*qtyzero_ndof;
currelem.Mat()(irowq,jclml) +=
currelem.GetBCDofFlag()[irowq]*
dtxJxW_g*(-psij_g*dphiidx_g[idim]); /** (-1.)*/
}
}
//============ END QTYZERO x QTYONE dofs matrix (B^T matrix) ============
if (i < qtyone_ndof) {
//======="COMMON tEST PART for QTYONE" ============
double psii_g = currgp._phi_ndsQLVB_g[qtyone_ord][i];
//======= "COMMON tEST PART for QTYONE" - END ============
const uint irowl = i + qtyZeroToOne_DofOffset;
currelem.Rhs()(irowl)=0.; // rhs
// Mat()(irowl,j+space_dim*qtyzero_ndof) += (1./dt)*dtxJxW_g*(psii_g*psij_g)*_Komp_fac/dt; //no bc here (KOMP dp/dt=rho*div)
for (uint j=0; j<qtyzero_ndof; j++) { // B element matrix q*div(u)
//======="COMMON SHAPE PART for QTYZERO" ==================
for (uint idim=0; idim<space_dim; idim++) dphijdx_g[idim] = currgp._dphidxyz_ndsQLVB_g[qtyzero_ord][j+idim*qtyzero_ndof];
//======="COMMON SHAPE PART for QTYZERO" - END ============
for (uint idim=0; idim<space_dim; idim++) currelem.Mat()(irowl,j+idim*qtyzero_ndof) += -/*(1./dt)**/dtxJxW_g*psii_g*dphijdx_g[idim];
}
}
// end pressure eq (cont)
}
//===================================================================
//========= END FILLING ELEMENT MAT/RHS (i loop) =====================
//===================================================================
}
//==============================================================
//================== END GAUSS LOOP (qp loop) ======================
//==============================================================
/// Add element matrix and rhs to the global ones.
my_system._LinSolver[Level]->_KK->add_matrix(currelem.Mat(),currelem.GetDofIndices());
my_system._LinSolver[Level]->_RESC->add_vector(currelem.Rhs(),currelem.GetDofIndices());
}
// end of element loop
}//END VOLUME
my_system._LinSolver[Level]->_KK->close();
my_system._LinSolver[Level]->_RESC->close();
#ifdef DEFAULT_PRINT_INFO
std::cout << " GenMatRhs " << my_system.name() << ": assembled Level " << Level
<< " with " << my_system._LinSolver[Level]->_KK->m() << " dofs" << std::endl;
#endif
return;
}