bool
MAST::HeatConductionElementBase::internal_residual (bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac) {
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const unsigned int
n_phi = _fe->n_shape_functions(),
dim = _elem.dim();
RealMatrixX
material_mat = RealMatrixX::Zero(dim, dim),
dmaterial_mat = RealMatrixX::Zero(dim, dim), // for calculation of Jac when k is temp. dep.
mat_n2n2 = RealMatrixX::Zero(n_phi, n_phi);
RealVectorX
vec1 = RealVectorX::Zero(1),
vec2_n2 = RealVectorX::Zero(n_phi),
flux = RealVectorX::Zero(dim);
std::auto_ptr<MAST::FieldFunction<RealMatrixX> > conductance =
_property.thermal_conductance_matrix(*this);
libMesh::Point p;
std::vector<MAST::FEMOperatorMatrix> dBmat(dim);
MAST::FEMOperatorMatrix Bmat; // for calculation of Jac when k is temp. dep.
for (unsigned int qp=0; qp<JxW.size(); qp++) {
// initialize the Bmat operator for this term
_initialize_mass_fem_operator(qp, Bmat);
Bmat.right_multiply(vec1, _sol);
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->set_element_quadrature_point_solution(vec1);
_local_elem->global_coordinates_location(xyz[qp], p);
(*conductance)(p, _time, material_mat);
_initialize_flux_fem_operator(qp, dBmat);
// calculate the flux for each dimension and add its weighted
// component to the residual
flux.setZero();
for (unsigned int j=0; j<dim; j++) {
dBmat[j].right_multiply(vec1, _sol); // dT_dxj
for (unsigned int i=0; i<dim; i++)
flux(i) += vec1(0) * material_mat(i,j); // q_i = k_ij dT_dxj
}
// now add to the residual vector
for (unsigned int i=0; i<dim; i++) {
vec1(0) = flux(i);
dBmat[i].vector_mult_transpose(vec2_n2, vec1);
f += JxW[qp] * vec2_n2;
}
if (request_jacobian) {
// Jacobian contribution from int_omega dB_dxi^T k_ij dB_dxj
for (unsigned int i=0; i<dim; i++)
for (unsigned int j=0; j<dim; j++) {
dBmat[i].right_multiply_transpose(mat_n2n2, dBmat[j]);
jac += JxW[qp] * material_mat(i,j) * mat_n2n2;
}
// Jacobian contribution from int_omega dB_dxi dT_dxj dk_ij/dT B
if (_active_sol_function) {
// get derivative of the conductance matrix wrt temperature
conductance->derivative(MAST::PARTIAL_DERIVATIVE,
*_active_sol_function,
p,
_time, dmaterial_mat);
for (unsigned int j=0; j<dim; j++) {
dBmat[j].right_multiply(vec1, _sol); // dT_dxj
for (unsigned int i=0; i<dim; i++)
if (dmaterial_mat(i,j) != 0.) { // no need to process for zero terms
// dB_dxi^T B
dBmat[i].right_multiply_transpose(mat_n2n2, Bmat);
// dB_dxi^T (dT_dxj dk_ij/dT) B
jac += JxW[qp] * vec1(0) * dmaterial_mat(i,j) * mat_n2n2;
}
}
}
}
}
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->clear_element_quadrature_point_solution();
return request_jacobian;
}
bool
MAST::HeatConductionElementBase::velocity_residual (bool request_jacobian,
RealVectorX& f,
RealMatrixX& jac_xdot,
RealMatrixX& jac) {
MAST::FEMOperatorMatrix Bmat;
const std::vector<Real>& JxW = _fe->get_JxW();
const std::vector<libMesh::Point>& xyz = _fe->get_xyz();
const unsigned int
n_phi = _fe->n_shape_functions(),
dim = _elem.dim();
RealMatrixX
material_mat = RealMatrixX::Zero(dim, dim),
mat_n2n2 = RealMatrixX::Zero(n_phi, n_phi);
RealVectorX
vec1 = RealVectorX::Zero(1),
vec2_n2 = RealVectorX::Zero(n_phi);
std::auto_ptr<MAST::FieldFunction<RealMatrixX> > capacitance =
_property.thermal_capacitance_matrix(*this);
libMesh::Point p;
for (unsigned int qp=0; qp<JxW.size(); qp++) {
_initialize_mass_fem_operator(qp, Bmat);
Bmat.right_multiply(vec1, _sol); // B * T
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->set_element_quadrature_point_solution(vec1);
_local_elem->global_coordinates_location(xyz[qp], p);
(*capacitance)(p, _time, material_mat);
Bmat.right_multiply(vec1, _vel); // B * T_dot
Bmat.vector_mult_transpose(vec2_n2, vec1); // B^T * B * T_dot
f += JxW[qp] * material_mat(0,0) * vec2_n2; // (rho*cp)*JxW B^T B T_dot
if (request_jacobian) {
Bmat.right_multiply_transpose(mat_n2n2, Bmat); // B^T B
jac_xdot += JxW[qp] * material_mat(0,0) * mat_n2n2; // B^T B * JxW (rho*cp)
// Jacobian contribution from int_omega B T d(rho*cp)/dT B
if (_active_sol_function) {
// get derivative of the conductance matrix wrt temperature
capacitance->derivative(MAST::PARTIAL_DERIVATIVE,
*_active_sol_function,
p,
_time, material_mat);
if (material_mat(0,0) != 0.) { // no need to process for zero terms
// B^T (T d(rho cp)/dT) B
jac += JxW[qp] * vec1(0) * material_mat(0,0) * mat_n2n2;
}
}
}
}
if (_active_sol_function)
dynamic_cast<MAST::MeshFieldFunction<RealVectorX>*>
(_active_sol_function)->clear_element_quadrature_point_solution();
return request_jacobian;
}
