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
// 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> ("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
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 > sysDof; // 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);
sysDof.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);
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->_elementOffset[iproc]; iel < msh->_elementOffset[iproc + 1]; iel++) {
short unsigned ielGeom = msh->GetElementType(iel);
unsigned nDofs = msh->GetElementDofNumber(iel, soluType); // number of solution element dofs
unsigned nDofs2 = msh->GetElementDofNumber(iel, xType); // number of coordinate element dofs
// resize local arrays
sysDof.resize(2 * nDofs);
solu.resize(nDofs);
solv.resize(nDofs);
for (int i = 0; i < dim; i++) {
x[i].resize(nDofs2);
}
aResu.assign(nDofs, 0.); //resize
aResv.assign(nDofs, 0.); //resize
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofs; i++) {
unsigned solDof = msh->GetSolutionDof(i, iel, 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
sysDof[i] = pdeSys->GetSystemDof(soluIndex, soluPdeIndex, i, iel); // global to global mapping between solution node and pdeSys dof
sysDof[nDofs + i] = pdeSys->GetSystemDof(solvIndex, solvPdeIndex, i, iel); // global to global mapping between solution node and pdeSys dof
}
// local storage of coordinates
for (unsigned i = 0; i < nDofs2; i++) {
unsigned xDof = msh->GetSolutionDof(i, iel, xType); // global to global mapping between coordinates node and coordinate dof
for (unsigned jdim = 0; jdim < dim; jdim++) {
x[jdim][i] = (*msh->_topology->_Sol[jdim])(xDof); // global extraction and local storage for the element coordinates
}
}
// 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[ielGeom][soluType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[ielGeom][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];
}
}
// *** phi_i loop ***
for (unsigned i = 0; i < nDofs; i++) {
adept::adouble Laplace_u = 0.;
adept::adouble Laplace_v = 0.;
for (unsigned jdim = 0; jdim < dim; jdim++) {
Laplace_u += - phi_x[i * dim + jdim] * soluGauss_x[jdim];
Laplace_v += - phi_x[i * dim + jdim] * solvGauss_x[jdim];
}
double exactSolValue = GetExactSolutionValue(xGauss);
double pi = acos(-1.);
aResv[i] += (solvGauss * phi[i] - Laplace_u) * weight;
aResu[i] += (4.*pi * pi * pi * pi * exactSolValue * phi[i] - Laplace_v) * weight;
} // end phi_i loop
} // end gauss point 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(2 * nDofs);
for (int i = 0; i < nDofs; i++) {
Res[i] = -aResu[i].value();
Res[nDofs + i] = -aResv[i].value();
}
RES->add_vector_blocked(Res, sysDof);
Jac.resize( 4 * nDofs * nDofs );
// 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], true);
KK->add_matrix_blocked(Jac, sysDof, sysDof);
s.clear_independents();
s.clear_dependents();
} //end element loop for each process
RES->close();
KK->close();
// ***************** END ASSEMBLY *******************
}
void AssemblePoisson_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> ("Poisson"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
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
unsigned solUIndex;
solUIndex = mlSol->GetIndex ("U"); // get the position of "U" in the ml_sol object = 0
unsigned solUType = mlSol->GetSolutionType (solUIndex); // get the finite element type for "T"
unsigned solUPdeIndex;
solUPdeIndex = mlPdeSys->GetSolPdeIndex ("U"); // get the position of "U" in the pdeSys object = 0
vector < adept::adouble > solU; // local solution
vector< adept::adouble > aResU; // local redidual vector
unsigned solVIndex;
solVIndex = mlSol->GetIndex ("V");
unsigned solVType = mlSol->GetSolutionType (solVIndex);
unsigned solVPdeIndex;
solVPdeIndex = mlPdeSys->GetSolPdeIndex ("V");
vector < adept::adouble > solV; // local solution
vector< adept::adouble > aResV; // local redidual vector
vector < vector < double > > crdX (dim); // local coordinates
unsigned crdXType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
solU.reserve (maxSize);
aResU.reserve (maxSize);
solV.reserve (maxSize);
aResV.reserve (maxSize);
for (unsigned k = 0; k < dim; k++) {
crdX[k].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
phi.reserve (maxSize);
phi_x.reserve (maxSize * dim);
phi_xx.reserve (maxSize * dim2);
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 weight; // gauss point weight
vector< int > sysDof; // local to global pdeSys dofs
sysDof.reserve (2 * maxSize);
vector< double > Res; // local residual vector
Res.reserve (2 * maxSize);
vector < double > Jac;
Jac.reserve (4 * maxSize * maxSize);
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->_elementOffset[iproc]; iel < msh->_elementOffset[iproc + 1]; iel++) {
short unsigned ielGeom = msh->GetElementType (iel); // element geometry type
unsigned nDofsU = msh->GetElementDofNumber (iel, solUType); // number of solution element dofs
unsigned nDofsV = msh->GetElementDofNumber (iel, solVType);
unsigned nDofsX = msh->GetElementDofNumber (iel, crdXType); // number of solution element dofs
// resize local arrays
sysDof.resize (nDofsU + nDofsV);
solU.resize (nDofsU);
solV.resize (nDofsV);
for (unsigned k = 0; k < dim; k++) {
crdX[k].resize (nDofsX);
}
aResU.assign (nDofsU, 0);
aResV.assign (nDofsV, 0);
// local storage of global mapping and solution
for (unsigned i = 0; i < nDofsU; i++) {
unsigned solUDof = msh->GetSolutionDof (i, iel, solUType); // local to global mapping of the solution U
solU[i] = (*sol->_Sol[solUIndex]) (solUDof); // value of the solution U in the dofs
sysDof[i] = pdeSys->GetSystemDof (solUIndex, solUPdeIndex, i, iel); // local to global mapping between solution U and system
}
for (unsigned i = 0; i < nDofsV; i++) {
unsigned solVDof = msh->GetSolutionDof (i, iel, solVType);
solV[i] = (*sol->_Sol[solVIndex]) (solVDof);
sysDof[i + nDofsU] = pdeSys->GetSystemDof (solVIndex, solVPdeIndex, i, iel);
}
// local storage of coordinates
for (unsigned i = 0; i < nDofsX; i++) {
unsigned coordXDof = msh->GetSolutionDof (i, iel, crdXType); // local to global mapping of the coordinate X[dim]
for (unsigned k = 0; k < dim; k++) {
crdX[k][i] = (*msh->_topology->_Sol[k]) (coordXDof); // value of the solution X[dim]
}
}
s.new_recording();
// *** Gauss point loop *** //
for (unsigned ig = 0; ig < msh->_finiteElement[ielGeom][solUType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[ielGeom][solUType]->Jacobian (crdX, ig, weight, phi, phi_x, phi_xx);
msh->_finiteElement[ielGeom][solVType]->Jacobian (crdX, ig, weight, phiV, phiV_x, phiV_xx);
adept::adouble solUig = 0; // solution U in the gauss point
vector < adept::adouble > gradSolUig (dim, 0.); // gradient of solution U in the gauss point
for (unsigned i = 0; i < nDofsU; i++) {
solUig += phi[i] * solU[i];
for (unsigned j = 0; j < dim; j++) {
gradSolUig[j] += phi_x[i * dim + j] * solU[i];
}
}
adept::adouble solVig = 0; // solution V in the gauss point
vector < adept::adouble > gradSolVig (dim, 0.); // gradient of solution U in the gauss point
for (unsigned i = 0; i < nDofsV; i++) {
solVig += phiV[i] * solV[i];
for (unsigned j = 0; j < dim; j++) {
gradSolVig[j] += phiV_x[i * dim + j] * solV[i];
}
}
double nu = 1.;
// *** phiU_i loop ***
for (unsigned i = 0; i < nDofsU; i++) {
adept::adouble LaplaceU = 0.;
for (unsigned j = 0; j < dim; j++) {
LaplaceU -= nu * phi_x[i * dim + j] * gradSolUig[j];
}
aResU[i] += (phi[i] - LaplaceU) * weight;
} // end phiU_i loop
for (unsigned i = 0; i < nDofsV; i++) {
adept::adouble LaplaceV = 0.;
for (unsigned j = 0; j < dim; j++) {
LaplaceV -= nu * phiV_x[i * dim + j] * gradSolVig[j];
}
aResV[i] += (phiV[i] * solUig - LaplaceV) * weight;
} // end phiV_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 (nDofsU + nDofsV); //resize
for (int i = 0; i < nDofsU; i++) {
Res[i] = -aResU[i].value();
}
for (int i = 0; i < nDofsV; i++) {
Res[i + nDofsU] = -aResV[i].value();
}
RES->add_vector_blocked (Res, sysDof);
//Extarct and store the Jacobian
Jac.resize ( (nDofsU + nDofsV) * (nDofsU + nDofsV));
// define the dependent variables
s.dependent (&aResU[0], nDofsU);
s.dependent (&aResV[0], nDofsV);
// define the independent variables
s.independent (&solU[0], nDofsU);
s.independent (&solV[0], nDofsV);
// get the and store jacobian matrix (row-major)
s.jacobian (&Jac[0] , true);
KK->add_matrix_blocked (Jac, sysDof, sysDof);
s.clear_independents();
s.clear_dependents();
} //end element loop for each process
RES->close();
KK->close();
// ***************** END ASSEMBLY *******************
}
void AssembleBoussinesqAppoximation(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> ("NS"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
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
bool assembleMatrix = mlPdeSys->GetAssembleMatrix();
// call the adept stack 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
unsigned solTIndex;
solTIndex = mlSol->GetIndex("T"); // get the position of "T" in the ml_sol object
unsigned solTType = mlSol->GetSolutionType(solTIndex); // get the finite element type for "T"
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"
unsigned solTPdeIndex;
solTPdeIndex = mlPdeSys->GetSolPdeIndex("T"); // get the position of "T" in the pdeSys object
// std::cout << solTIndex <<" "<<solTPdeIndex<<std::endl;
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 < double > solT; // local solution
vector < vector < double > > solV(dim); // local solution
vector < double > solP; // local solution
vector < vector < double > > coordX(dim); // local coordinates
unsigned coordXType = 2; // get the finite element type for "x", it is always 2 (LAGRANGE QUADRATIC)
solT.reserve(maxSize);
for(unsigned k = 0; k < dim; k++) {
solV[k].reserve(maxSize);
coordX[k].reserve(maxSize);
}
solP.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);
vector <double> phiT; // local test function
vector <double> phiT_x; // local test function first order partial derivatives
vector <double> phiT_xx; // local test function second order partial derivatives
phiT.reserve(maxSize);
phiT_x.reserve(maxSize * dim);
phiT_xx.reserve(maxSize * dim2);
double* phiP;
double weight; // gauss point weight
vector< int > sysDof; // local to global pdeSys dofs
sysDof.reserve((dim + 2) *maxSize);
vector< double > Res; // local redidual vector
Res.reserve((dim + 2) *maxSize);
vector < double > Jac;
Jac.reserve((dim + 2) *maxSize * (dim + 2) *maxSize);
if(assembleMatrix)
KK->zero(); // Set to zero all the entries of the Global Matrix
//BEGIN element loop
for(int iel = msh->_elementOffset[iproc]; iel < msh->_elementOffset[iproc + 1]; iel++) {
//BEGIN local dof number extraction
unsigned nDofsT = msh->GetElementDofNumber(iel, solTType); //temperature
unsigned nDofsV = msh->GetElementDofNumber(iel, solVType); //velocity
unsigned nDofsP = msh->GetElementDofNumber(iel, solPType); //pressure
unsigned nDofsX = msh->GetElementDofNumber(iel, coordXType); // coordinates
unsigned nDofsTVP = nDofsT + dim * nDofsV + nDofsP; // all solutions
//END local dof number extraction
//BEGIN memory allocation
Res.resize(nDofsTVP);
std::fill(Res.begin(), Res.end(), 0);
Jac.resize(nDofsTVP * nDofsTVP);
std::fill(Jac.begin(), Jac.end(), 0);
sysDof.resize(nDofsTVP);
solT.resize(nDofsV);
for(unsigned k = 0; k < dim; k++) {
solV[k].resize(nDofsV);
coordX[k].resize(nDofsX);
}
solP.resize(nDofsP);
//END memory allocation
//BEGIN global to local extraction
for(unsigned i = 0; i < nDofsT; i++) { //temperature
unsigned solTDof = msh->GetSolutionDof(i, iel, solTType); //local to global solution dof
solT[i] = (*sol->_Sol[solTIndex])(solTDof); //global to local solution value
sysDof[i] = pdeSys->GetSystemDof(solTIndex, solTPdeIndex, i, iel); //local to global system dof
}
for(unsigned i = 0; i < nDofsV; i++) { //velocity
unsigned solVDof = msh->GetSolutionDof(i, iel, solVType); //local to global solution dof
for(unsigned k = 0; k < dim; k++) {
solV[k][i] = (*sol->_Sol[solVIndex[k]])(solVDof); //global to local solution value
sysDof[i + nDofsT + k * nDofsV] = pdeSys->GetSystemDof(solVIndex[k], solVPdeIndex[k], i, iel); //local to global system dof
}
}
for(unsigned i = 0; i < nDofsP; i++) { //pressure
unsigned solPDof = msh->GetSolutionDof(i, iel, solPType); //local to global solution dof
solP[i] = (*sol->_Sol[solPIndex])(solPDof); //global to local solution value
sysDof[i + nDofsT + dim * nDofsV] = pdeSys->GetSystemDof(solPIndex, solPPdeIndex, i, iel); //local to global system dof
}
for(unsigned i = 0; i < nDofsX; i++) { //coordinates
unsigned coordXDof = msh->GetSolutionDof(i, iel, coordXType); //local to global coordinate dof
for(unsigned k = 0; k < dim; k++) {
coordX[k][i] = (*msh->_topology->_Sol[k])(coordXDof); //global to local coordinate value
}
}
//END global to local extraction
//BEGIN Gauss point loop
short unsigned ielGeom = msh->GetElementType(iel);
for(unsigned ig = 0; ig < msh->_finiteElement[ielGeom][solVType]->GetGaussPointNumber(); ig++) {
// *** get gauss point weight, test function and test function partial derivatives ***
msh->_finiteElement[ielGeom][solTType]->Jacobian(coordX, ig, weight, phiT, phiT_x, phiT_xx);
msh->_finiteElement[ielGeom][solVType]->Jacobian(coordX, ig, weight, phiV, phiV_x, phiV_xx);
phiP = msh->_finiteElement[ielGeom][solPType]->GetPhi(ig);
// evaluate the solution, the solution derivatives and the coordinates in the gauss point
double solT_gss = 0;
vector < double > gradSolT_gss(dim, 0.);
for(unsigned i = 0; i < nDofsT; i++) {
solT_gss += phiT[i] * solT[i];
for(unsigned j = 0; j < dim; j++) {
gradSolT_gss[j] += phiT_x[i * dim + j] * solT[i];
}
}
vector < double > solV_gss(dim, 0);
vector < vector < double > > 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];
}
}
}
double solP_gss = 0;
for(unsigned i = 0; i < nDofsP; i++) {
solP_gss += phiP[i] * solP[i];
}
double alpha = 1.;
double beta = 1.;//40000.;
double Pr = Prandtl;
double Ra = Rayleigh;
//BEGIN phiT_i loop: Energy balance
for(unsigned i = 0; i < nDofsT; i++) {
unsigned irow = i;
for(unsigned k = 0; k < dim; k++) {
Res[irow] += -alpha / sqrt(Ra * Pr) * phiT_x[i * dim + k] * gradSolT_gss[k] * weight;
Res[irow] += -phiT[i] * solV_gss[k] * gradSolT_gss[k] * weight;
if(assembleMatrix) {
unsigned irowMat = irow * nDofsTVP;
for(unsigned j = 0; j < nDofsT; j++) {
Jac[ irowMat + j ] += alpha / sqrt(Ra * Pr) * phiT_x[i * dim + k] * phiT_x[j * dim + k] * weight;
Jac[ irowMat + j ] += phiT[i] * solV_gss[k] * phiT_x[j * dim + k] * weight;
}
for(unsigned j = 0; j < nDofsV; j++) {
unsigned jcol = nDofsT + k * nDofsV + j;
Jac[ irowMat + jcol ] += phiT[i] * phiV[j] * gradSolT_gss[k] * weight;
}
}
}
}
//END phiT_i loop
//BEGIN phiV_i loop: Momentum balance
for(unsigned i = 0; i < nDofsV; i++) {
for(unsigned k = 0; k < dim; k++) {
unsigned irow = nDofsT + k * nDofsV + i;
for(unsigned l = 0; l < dim; l++) {
Res[irow] += -sqrt(Pr / Ra) * phiV_x[i * dim + l] * (gradSolV_gss[k][l] + gradSolV_gss[l][k]) * weight;
Res[irow] += -phiV[i] * solV_gss[l] * gradSolV_gss[k][l] * weight;
}
Res[irow] += solP_gss * phiV_x[i * dim + k] * weight;
if(k == 1) {
Res[irow] += beta * solT_gss * phiV[i] * weight;
}
if(assembleMatrix) {
unsigned irowMat = nDofsTVP * irow;
for(unsigned l = 0; l < dim; l++) {
for(unsigned j = 0; j < nDofsV; j++) {
unsigned jcol1 = (nDofsT + k * nDofsV + j);
unsigned jcol2 = (nDofsT + l * nDofsV + j);
Jac[ irowMat + jcol1] += sqrt(Pr / Ra) * phiV_x[i * dim + l] * phiV_x[j * dim + l] * weight;
Jac[ irowMat + jcol2] += sqrt(Pr / Ra) * phiV_x[i * dim + l] * phiV_x[j * dim + k] * weight;
Jac[ irowMat + jcol1] += phiV[i] * solV_gss[l] * phiV_x[j * dim + l] * weight;
Jac[ irowMat + jcol2] += phiV[i] * phiV[j] * gradSolV_gss[k][l] * weight;
}
}
for(unsigned j = 0; j < nDofsP; j++) {
unsigned jcol = (nDofsT + dim * nDofsV) + j;
Jac[ irowMat + jcol] += - phiV_x[i * dim + k] * phiP[j] * weight;
}
if(k == 1) {
for(unsigned j = 0; j < nDofsT; j++) {
Jac[ irowMat + j ] += -beta * phiV[i] * phiT[j] * weight;
}
}
}
}
}
//END phiV_i loop
//BEGIN phiP_i loop: mass balance
for(unsigned i = 0; i < nDofsP; i++) {
unsigned irow = nDofsT + dim * nDofsV + i;
for(int k = 0; k < dim; k++) {
Res[irow] += (gradSolV_gss[k][k]) * phiP[i] * weight;
if(assembleMatrix) {
unsigned irowMat = nDofsTVP * irow;
for(unsigned j = 0; j < nDofsV; j++) {
unsigned jcol = (nDofsT + k * nDofsV + j);
Jac[ irowMat + jcol ] += - phiP[i] * phiV_x[j * dim + k] * weight;
}
}
}
}
//END phiP_i loop
}
//END Gauss point loop
//BEGIN local to global Matrix/Vector assembly
RES->add_vector_blocked(Res, sysDof);
if(assembleMatrix) {
KK->add_matrix_blocked(Jac, sysDof, sysDof);
}
//END local to global Matrix/Vector assembly
}
//END element loop
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 *******************
}
std::pair <vector<double>, vector <double> > GetVaribleValues(MultiLevelProblem& ml_prob, const unsigned &elem, const std::vector<double>&xi) {
NonLinearImplicitSystem* mlPdeSys = &ml_prob.get_system<NonLinearImplicitSystem> ("NS"); // pointer to the linear implicit system named "Poisson"
const unsigned level = mlPdeSys->GetLevelToAssemble();
Mesh* msh = ml_prob._ml_msh->GetLevel(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
const unsigned dim = msh->GetDimension(); // get the domain dimension of the problem
//solution variable
unsigned solTIndex;
solTIndex = mlSol->GetIndex("T"); // get the position of "T" in the ml_sol object
unsigned solTType = mlSol->GetSolutionType(solTIndex); // get the finite element type for "T"
vector < double > solT; // local solution
vector <unsigned> solVIndex(dim);
solVIndex[0] = mlSol->GetIndex("U");
solVIndex[1] = mlSol->GetIndex("V");
if (dim==3) solVIndex[2] = mlSol->GetIndex("W");
unsigned solVType = mlSol->GetSolutionType(solVIndex[0]);
vector < vector <double> > solV(dim);
unsigned iproc = msh->processor_id(); // get the process_id (for parallel computation)
MyVector <double> solTXi(1, 0.);
solTXi.stack();
MyVector <double> solUXi(1, 0.);
solUXi.stack();
MyVector <double> solVXi(1, 0.);
solVXi.stack();
/*
if (dim==3) {
MyVector <double> solWXi(1, 0.);
solWXi.stack();
}
*/
//BEGIN local dof number extraction
if(elem >= msh->_elementOffset[iproc] && elem < msh->_elementOffset[iproc + 1]) {
unsigned nDofsT = msh->GetElementDofNumber(elem, solTType); //temperature
solT.reserve(nDofsT);
unsigned nDofsV = msh->GetElementDofNumber(elem, solVType); //velocity
for(unsigned k = 0; k < dim; k++) solV[k].reserve(nDofsV);
//BEGIN global to local extraction
for(unsigned i = 0; i < nDofsT; i++) { //temperature
unsigned solTDof = msh->GetSolutionDof(i, elem, solTType); //local to global solution dof
solT[i] = (*sol->_Sol[solTIndex])(solTDof); //global to local solution value
}
for(unsigned i = 0; i < nDofsV; i++){ //velocity
unsigned solVDof = msh->GetSolutionDof(i, elem, solVType);
for(unsigned k = 0; k < dim; k++) {
solV[k][i] = (*sol->_Sol[solVIndex[k]])(solVDof); // global extraction and local storage for the solution
}
}
short unsigned ielGeom = msh->GetElementType(elem);
for(unsigned i = 0; i < nDofsT; i++) {
basis *base = msh->_finiteElement[ielGeom][solTType]->GetBasis();
double phiT = base->eval_phi(base->GetIND(i), &xi[0]);
solTXi[iproc] += phiT * solT[i];
}
for(unsigned i = 0; i < nDofsV; i++) {
basis *base = msh->_finiteElement[ielGeom][solVType]->GetBasis();
double phiV = base->eval_phi(base->GetIND(i), &xi[0]);
solUXi[iproc] += phiV * solV[0][i];
solVXi[iproc] += phiV * solV[1][i];
// if(dim==3) solWXi[iproc] += phiV * solV[2][i];
}
}
std::pair <vector <double>, vector <double> > out_value;
unsigned mproc = msh->IsdomBisectionSearch(elem , 3);
solUXi.broadcast(mproc);
solVXi.broadcast(mproc);
solTXi.broadcast(mproc);
vector <double> solV_pt(dim);
solV_pt[0]= solUXi[mproc];
solV_pt[1]= solVXi[mproc];
out_value.first = solV_pt;
vector <double> solPT_pt(2);
solPT_pt[0]= 0.;
solPT_pt[1]=solTXi[mproc];
out_value.second = solPT_pt;
solUXi.clearBroadcast();
solVXi.clearBroadcast();
solTXi.clearBroadcast();
return out_value;
}
