/// 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;
}
void testCannonball()
{
const double feilmargin = 0.0001;
//AcclX
assert(avvik(0.0,
acclX()) < feilmargin);
//AcclY
assert(avvik(-9.81,
acclY()) < feilmargin);
//velX
assert(avvik(50.0,
velX(50.0, 0)) < feilmargin);
assert(avvik(50.0,
velX(50.0, 2.5)) < feilmargin);
assert(avvik(50.0,
velX(50.0, 5.0)) < feilmargin);
//velY
assert(avvik(25.0,
velY(25.0, 0)) < feilmargin);
assert(avvik(0.475,
velY(25.0, 2.5)) < feilmargin);
assert(avvik(-24.05,
velY(25.0, 5.0)) < feilmargin);
//velIntY
assert(avvik(25.0,
velIntY(25.0, 0)) < feilmargin);
assert(avvik(0.475,
velIntY(25.0, 2.5)) < feilmargin);
assert(avvik(-24.05,
velIntY(25.0, 5.0)) < feilmargin);
//posX
assert(avvik(0.0,
posX(50.0, 0)) < feilmargin);
assert(avvik(125.0,
posX(50.0, 2.5)) < feilmargin);
assert(avvik(250.0,
posX(50.0, 5.0)) < feilmargin);
//posIntX
assert(avvik(0.0,
posIntX(50.0, 0)) < feilmargin);
assert(avvik(125.0,
posIntX(50.0, 2.5)) < feilmargin);
assert(avvik(250.0,
posIntX(50.0, 5.0)) < feilmargin);
//posY
assert(avvik(0.0,
posY(25.0, 0)) < feilmargin);
assert(avvik(31.84,
posY(25.0, 2.5)) < feilmargin);
assert(avvik(2.375,
posY(25.0, 5.0)) < feilmargin);
//posIntY
assert(avvik(0.0,
posIntY(25.0, 0)) < feilmargin);
assert(avvik(31.84,
posIntY(25.0, 2.5)) < feilmargin);
assert(avvik(2.375,
posIntY(25.0, 5.0)) < feilmargin);
//flightTime
assert(avvik(2.03874,
flightTime(10.0)) < feilmargin);
//getVelocityX
assert(avvik(7.071067812, getVelocityX(
asin(1) / 2, 10.0
)) < feilmargin);
//getVelocityY
assert(avvik(7.071067812, getVelocityY(
asin(1) / 2, 10.0
)) < feilmargin);
//getDistanceTraveled
assert(avvik(20.3874, getDistanceTraveled(
10.0, 10.0
)) < feilmargin);
//optimalAngleForMaxDistance
assert(avvik(0.7853981634, optimalAngleForMaxDistance(
10.0
)) < feilmargin);
//getDistanceTraveled
assert(avvik(-0.3874, targetPractice(
20.0, 10.0, 10.0
)) < feilmargin);
}
