inline double FunctionIntegral (const uint vb, MultiLevelProblem & ml_prob, double (*pt2func)(double, const std::vector<double> ) ) {
const uint mesh_vb = vb;
const uint Level = ml_prob.GetMeshTwo()._NoLevels - 1;
const uint myproc = ml_prob.GetMeshTwo()._iproc;
double time = 0.;
Mesh *mymsh = ml_prob._ml_msh->GetLevel(Level);
double integral = 0.;
//parallel sum
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 currelem(iel,myproc,Level,vb,NULL,ml_prob.GetMeshTwo(),ml_prob.GetElemType(),mymsh); //element without equation
CurrentGaussPointBase & currgp = CurrentGaussPointBase::build(currelem,ml_prob.GetQrule(currelem.GetDim()));
const uint el_ngauss = ml_prob.GetQrule(currelem.GetDim()).GetGaussPointsNumber();
//========= DOMAIN MAPPING
CurrentQuantity xyz(currgp);
xyz._dim = ml_prob.GetMeshTwo().get_dim();
xyz._FEord = MESH_MAPPING_FE;
xyz._ndof = currelem.GetElemType(xyz._FEord)->GetNDofs();
xyz.Allocate();
currelem.SetDofobjConnCoords();
currelem.ConvertElemCoordsToMappingOrd(xyz);
for (uint qp = 0; qp < el_ngauss; qp++) {
for (uint fe = 0; fe < QL; fe++) {
currgp.SetPhiElDofsFEVB_g (fe,qp);
currgp.SetDPhiDxezetaElDofsFEVB_g (fe,qp);
}
double Jac_g=0.;
if (vb==0) Jac_g = currgp.JacVectVV_g(xyz); //not xyz_refbox!
else if (vb==1) Jac_g = currgp.JacVectBB_g(xyz); //not xyz_refbox!
const double wgt_g = ml_prob.GetQrule(currelem.GetDim()).GetGaussWeight(qp);
xyz.val_g();
double myval_g = pt2func(time,xyz._val_g);
integral += wgt_g*Jac_g*myval_g;
}//gauss loop
}//element loop
std::cout << std::endl << " ^^^^^^^^^^^^^^^^^L'integrale sul processore "<< myproc << " vale: " << integral << std::endl;
// double weights_sum = 0.;
// for (uint qp = 0; qp < el_ngauss; qp++) weights_sum += ml_prob.GetQrule(currelem.GetDim()).GetGaussWeight(qp);
// std::cout << std::endl << " ^^^^^^^^^^^^^^^^^ La somma dei pesi vale: " << weights_sum << std::endl;
double J=0.;
#ifdef HAVE_MPI
// MPI_Reduce( &integral, &J, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD ); //This one gives J only to processor 0 !
MPI_Allreduce( &integral, &J, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD ); //THIS IS THE RIGHT ONE!!
#else
J = integral;
#endif
std::cout << std::endl << " ^^^^^^^^^^^^^^^^^L'integrale totale vale: " << J << std::endl;
return J;
}
void GenMatRhsNSAD(MultiLevelProblem &ml_prob) {
SystemTwo & my_system = ml_prob.get_system<SystemTwo>("Eqn_NSAD");
const unsigned Level = my_system.GetLevelToAssemble();
// ========= parameters
const double alphaVel = ml_prob.GetInputParser().get("alphaVel");
const double IRe = 1./ml_prob.GetInputParser().get("Re");
//=========== Operators
double dphijdx_g[DIMENSION];
double dphiidx_g[DIMENSION];
double curlxiXB_g3D[3];
// //======== GEOMETRICAL ELEMENT =======
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
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 currelem(iel,myproc,Level,VV,&my_system,ml_prob.GetMeshTwo(),ml_prob.GetElemType(),mymsh);
CurrentGaussPointBase & currgp = CurrentGaussPointBase::build(currelem,ml_prob.GetQrule(currelem.GetDim()));
//=========INTERNAL QUANTITIES (unknowns of the equation) ==================
CurrentQuantity VelAdjOldX(currgp);
VelAdjOldX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_VelocityAdj0");
VelAdjOldX.VectWithQtyFillBasic();
VelAdjOldX.Allocate();
CurrentQuantity VelAdjOldY(currgp);
VelAdjOldY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_VelocityAdj1");
VelAdjOldY.VectWithQtyFillBasic();
VelAdjOldY.Allocate();
CurrentQuantity VelAdjOldZ(currgp);
VelAdjOldZ._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_VelocityAdj2");
VelAdjOldZ.VectWithQtyFillBasic();
VelAdjOldZ.Allocate();
std::vector<CurrentQuantity*> VelAdjOld_vec;
VelAdjOld_vec.push_back(&VelAdjOldX);
VelAdjOld_vec.push_back(&VelAdjOldY);
VelAdjOld_vec.push_back(&VelAdjOldZ);
CurrentQuantity PressAdjOld(currgp);
PressAdjOld._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_PressureAdj");
PressAdjOld.VectWithQtyFillBasic();
PressAdjOld.Allocate();
//========= END INTERNAL QUANTITIES (unknowns of the equation) =================
//=========EXTERNAL QUANTITIES (couplings) =====
//========= DOMAIN MAPPING
CurrentQuantity xyz(currgp);
xyz._dim = space_dim;
xyz._FEord = MESH_MAPPING_FE;
xyz._ndof = currelem.GetElemType(xyz._FEord)->GetNDofs();
xyz.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);
CurrentQuantity VelDesX(currgp);
VelDesX._dim = 1;
VelDesX._FEord = VelX._FEord;
VelDesX._ndof = VelX._ndof;
VelDesX.Allocate();
CurrentQuantity VelDesY(currgp);
VelDesY._dim = 1;
VelDesY._FEord = VelX._FEord;
VelDesY._ndof = VelX._ndof;
VelDesY.Allocate();
CurrentQuantity VelDesZ(currgp);
VelDesZ._dim = 1;
VelDesZ._FEord = VelX._FEord;
VelDesZ._ndof = VelX._ndof;
VelDesZ.Allocate();
std::vector<CurrentQuantity*> VelDes_vec;
VelDes_vec.push_back(&VelDesX);
VelDes_vec.push_back(&VelDesY);
VelDes_vec.push_back(&VelDesZ);
CurrentQuantity BhomX(currgp);
BhomX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHom0");
BhomX.VectWithQtyFillBasic();
BhomX.Allocate();
CurrentQuantity BhomY(currgp);
BhomY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHom1");
BhomY.VectWithQtyFillBasic();
BhomY.Allocate();
CurrentQuantity BhomZ(currgp);
BhomZ._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHom2");
BhomZ.VectWithQtyFillBasic();
BhomZ.Allocate();
std::vector<CurrentQuantity*> Bhom_vec;
Bhom_vec.push_back(&BhomX);
Bhom_vec.push_back(&BhomY);
Bhom_vec.push_back(&BhomZ);
//Bhom only to retrieve the dofs
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);
//========= auxiliary, must be AFTER Bhom! //TODO this doesnt have any associated quantity!
CurrentQuantity Bmag(currgp); //total
Bmag._dim = Bhom_vec.size();
Bmag._FEord = BhomX._FEord;
Bmag._ndof = BhomX._ndof;
Bmag.Allocate();
//===============
CurrentQuantity BhomAdjX(currgp);
BhomAdjX._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHomAdj0");
BhomAdjX.VectWithQtyFillBasic();
BhomAdjX.Allocate();
CurrentQuantity BhomAdjY(currgp);
BhomAdjY._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHomAdj1");
BhomAdjY.VectWithQtyFillBasic();
BhomAdjY.Allocate();
CurrentQuantity BhomAdjZ(currgp);
BhomAdjZ._qtyptr = ml_prob.GetQtyMap().GetQuantity("Qty_MagnFieldHomAdj2");
BhomAdjZ.VectWithQtyFillBasic();
BhomAdjZ.Allocate();
std::vector<CurrentQuantity*> BhomAdj_vec;
BhomAdj_vec.push_back(&BhomAdjX);
BhomAdj_vec.push_back(&BhomAdjY);
BhomAdj_vec.push_back(&BhomAdjZ);
CurrentQuantity BhomAdj_vecQuant(currgp); //without quantity, nor equation
BhomAdj_vecQuant._dim = BhomAdj_vec.size();
BhomAdj_vecQuant._FEord = BhomAdj_vec[0]->_FEord;
BhomAdj_vecQuant._ndof = BhomAdj_vec[0]->_ndof;
BhomAdj_vecQuant.Allocate();
//========= END EXTERNAL QUANTITIES =================
currelem.Mat().zero();
currelem.Rhs().zero();
currelem.SetDofobjConnCoords();
currelem.ConvertElemCoordsToMappingOrd(xyz);
currelem.SetElDofsBc();
for (uint idim=0; idim < space_dim; idim++) {
VelAdjOld_vec[idim]->GetElemDofs();
Vel_vec[idim]->GetElemDofs();
BhomAdj_vec[idim]->GetElemDofs();
Bhom_vec[idim]->GetElemDofs();
Bext_vec[idim]->GetElemDofs();
VelDesired(&ml_prob,*VelDes_vec[idim],currelem,idim);
}
BhomAdj_vecQuant.GetElemDofs(BhomAdj_vec); //this must be AFTER filling the scalar components
PressAdjOld.GetElemDofs();
//======SUM Bhom and Bext //from now on, you'll only use Bmag //Bmag,Bext and Bhom must have the same orders!
Math::zeroN(&Bmag._val_dofs[0],Bmag._dim*Bmag._ndof);
for (uint ivarq=0; ivarq < Bmag._dim; ivarq++) { //ivarq is like idim
for (uint d=0; d < Bmag._ndof; d++) {
const uint indxq = d + ivarq*Bmag._ndof;
Bmag._val_dofs[indxq] = Bext_vec[ivarq]->_val_dofs[d] + Bhom_vec[ivarq]->_val_dofs[d];
}
}
//=======
///optimal control
xyz.SetElemAverage();
int el_flagdom = ElFlagControl(xyz._el_average,ml_prob._ml_msh);
const uint el_ngauss = ml_prob.GetQrule(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 the same for both QQ and LL!
const double dtxJxW_g = det*ml_prob.GetQrule(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"==================
BhomAdj_vecQuant.curl_g();
Bmag.val_g();
for (uint idim=0; idim < space_dim; idim++) {
VelAdjOld_vec[idim]->val_g();
VelDes_vec[idim]->val_g();
Vel_vec[idim]->val_g();
Vel_vec[idim]->grad_g();
}
//vector product
Math::extend(&Bmag._val_g[0],&Bmag._val_g3D[0],space_dim);
Math::cross(&BhomAdj_vecQuant._curl_g3D[0],&Bmag._val_g3D[0],curlxiXB_g3D);
//==============================================================
//========= FILLING ELEMENT MAT/RHS (i loop) ====================
//==============================================================
for (uint i = 0; i < VelAdjOldX._ndof; i++) {
const double phii_g = currgp._phi_ndsQLVB_g[VelAdjOldX._FEord][i];
for (uint idim=0; idim<space_dim; idim++) dphiidx_g[idim]= currgp._dphidxyz_ndsQLVB_g[VelAdjOldX._FEord][i+idim*VelAdjOldX._ndof];
for (uint idim=0; idim<space_dim; idim++) {
const uint irowq=i+idim*VelAdjOldX._ndof; //quadratic rows index
currelem.Rhs()(irowq) += currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
- curlxiXB_g3D[idim]*phii_g //this is due to the variation of velocity in the MAGNETIC ADVECTION, so it is due to a NONLINEAR COUPLING "u times B", "MY_STATE times OTHER_STATE"
- alphaVel*el_flagdom*(Vel_vec[idim]->_val_g[0] - VelDes_vec[idim]->_val_g[0])*phii_g //this is the dependence that counts
)
+ (1-currelem.GetBCDofFlag()[irowq])*detb*VelAdjOld_vec[idim]->_val_dofs[i]; //Dirichlet bc
}
for (uint idim=0; idim<space_dim; idim++) { // filling diagonal for Dirichlet bc
const uint irowq = i+idim*VelAdjOldX._ndof;
currelem.Mat()(irowq,irowq) += (1-currelem.GetBCDofFlag()[irowq])*detb;
}// end filling diagonal for Dirichlet bc
for (uint j=0; j<VelAdjOldX._ndof; j++) {// A element matrix
double phij_g = currgp._phi_ndsQLVB_g[VelAdjOldX._FEord][j];
for (uint idim=0; idim<space_dim; idim++) dphijdx_g[idim] = currgp._dphidxyz_ndsQLVB_g[VelAdjOldX._FEord][j+idim*VelAdjOldX._ndof];
double Lap_g = Math::dot(dphijdx_g,dphiidx_g,space_dim);
double Advphii_g = 0.;
for (uint idim=0; idim<space_dim; idim++) Advphii_g += Vel_vec[idim]->_val_g[0]*dphiidx_g[idim]; //TODO can put it outside
for (uint idim=0; idim<space_dim; idim++) { //filled in as 1-2-3 // 4-5-6 // 7-8-9
int irowq = i+idim*VelAdjOldX._ndof;
// diagonal blocks [1-5-9]
currelem.Mat()(irowq,j+idim*VelAdjOldX._ndof)
+= currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
+ IRe*(dphijdx_g[idim]*dphiidx_g[idim] + Lap_g) //Adjoint of D is D, Adjoint of Laplacian is Laplacian
+ phij_g*phii_g*/*dveldx_g*/Vel_vec[idim]->_grad_g[0][idim] //Adjoint of Advection 1 delta(u) DOT grad(u): adj of nonlinear stuff has 2 TERMS (well, not always)
+ phij_g*Advphii_g //Adjoint of Advection 2 u DOT grad (delta(u)): adj of nonlinear stuff has 2 TERMS
);
// block +1 [2-6-7]
int idimp1=(idim+1)%space_dim;
currelem.Mat()(irowq,j+idimp1*VelAdjOldX._ndof)
+= currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
+ IRe*(dphijdx_g[idim]*dphiidx_g[idimp1])
+ phij_g*phii_g*/*dveldx_g*/Vel_vec[idimp1]->_grad_g[0][idim]
);
#if (DIMENSION==3)
// block +2 [3-4-8]
int idimp2=(idim+2)%space_dim;
currelem.Mat()(irowq,j+idimp2*VelAdjOldX._ndof)
+= currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(
+ IRe*(dphijdx_g[idim]*dphiidx_g[idimp2])
+ phij_g*phii_g*/*dveldx_g*/Vel_vec[idimp2]->_grad_g[0][idim]
);
#endif
}
}
// end A element matrix
for (uint j=0; j<PressAdjOld._ndof; j++) {// B^T element matrix ( p*div(v) ) (NS eq)
const double psij_g = currgp._phi_ndsQLVB_g[PressAdjOld._FEord][j];
const int jclml= j + space_dim*VelAdjOldX._ndof;
for (uint idim=0; idim<space_dim; idim++) {
uint irowq = i+idim*VelAdjOldX._ndof;
currelem.Mat()(irowq,jclml) += currelem.GetBCDofFlag()[irowq]*dtxJxW_g*(-psij_g*dphiidx_g[idim]);
}
}
// end B^T element matrix
if (i<PressAdjOld._ndof) {// pressure equation (KOMP dp/dt=rho*div)
double psii_g = currgp._phi_ndsQLVB_g[PressAdjOld._FEord][i];
const uint irowl = i+space_dim*VelAdjOldX._ndof; //vertical offset
currelem.Rhs()(irowl)=0.; // rhs
for (uint j=0; j<VelAdjOldX._ndof; j++) { // B element matrix q*div(u)
for (uint idim=0; idim<space_dim; idim++) dphijdx_g[idim] = currgp._dphidxyz_ndsQLVB_g[VelAdjOldX._FEord][j+idim*VelAdjOldX._ndof];
for (uint idim=0; idim<space_dim; idim++) currelem.Mat()(irowl,j+idim*VelAdjOldX._ndof) += -dtxJxW_g*psii_g*dphijdx_g[idim];
}
}
// end pressure eq (cont)
}
//===================================================================
//========= 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;
}