bool L2System::element_time_derivative (bool request_jacobian,
DiffContext & context)
{
FEMContext & c = cast_ref<FEMContext &>(context);
// First we get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration
const std::vector<Real> & JxW = c.get_element_fe(0)->get_JxW();
const std::vector<std::vector<Real>> & phi = c.get_element_fe(0)->get_phi();
const std::vector<Point> & xyz = c.get_element_fe(0)->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = c.n_dof_indices(0);
// The subvectors and submatrices we need to fill:
DenseSubMatrix<Number> & K = c.get_elem_jacobian(0, 0);
DenseSubVector<Number> & F = c.get_elem_residual(0);
unsigned int n_qpoints = c.get_element_qrule().n_points();
libmesh_assert (input_contexts.find(&c) != input_contexts.end());
FEMContext & input_c = *input_contexts[&c];
input_c.pre_fe_reinit(*input_system, &c.get_elem());
input_c.elem_fe_reinit();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
Number u = c.interior_value(0, qp);
Number ufunc = (*goal_func)(input_c, xyz[qp]);
for (unsigned int i=0; i != n_u_dofs; i++)
F(i) += JxW[qp] * ((u - ufunc) * phi[i][qp]);
if (request_jacobian)
{
const Number JxWxD = JxW[qp] *
context.get_elem_solution_derivative();
for (unsigned int i=0; i != n_u_dofs; i++)
for (unsigned int j=0; j != n_u_dofs; ++j)
K(i,j) += JxWxD * (phi[i][qp] * phi[j][qp]);
}
} // end of the quadrature point qp-loop
return request_jacobian;
}
//for non-Dirichlet boundary conditions and the bit from diffusion term
bool ConvDiff_AuxSadjSys::side_time_derivative(bool request_jacobian, DiffContext & context)
{
const unsigned int dim = this->get_mesh().mesh_dimension();
FEMContext &ctxt = cast_ref<FEMContext&>(context);
// First we get some references to cell-specific data that
// will be used to assemble the linear system.
FEBase* side_fe = NULL;
ctxt.get_side_fe(aux_c_var, side_fe );
// Element Jacobian * quadrature weights for interior integration
const std::vector<Real> &JxW = side_fe->get_JxW();
// Side basis functions
const std::vector<std::vector<Real> > &phi = side_fe->get_phi();
// Side Quadrature points
const std::vector<Point > &qside_point = side_fe->get_xyz();
//normal vector
const std::vector<Point> &face_normals = side_fe->get_normals();
// The number of local degrees of freedom in each variable
const unsigned int n_c_dofs = ctxt.get_dof_indices(aux_c_var).size();
// The subvectors and submatrices we need to fill:
DenseSubMatrix<Number> &J_c_auxz = ctxt.get_elem_jacobian(aux_c_var, aux_zc_var);
DenseSubVector<Number> &Rc = ctxt.get_elem_residual( aux_c_var );
//Rf gets no contribution from sides
unsigned int n_qpoints = ctxt.get_side_qrule().n_points();
bool isEast = false;
if (dim == 3) {
isEast = ctxt.has_side_boundary_id(2);
}
else if (dim == 2) {
isEast = ctxt.has_side_boundary_id(1);
}
//set (in)flux boundary condition on west side
//homogeneous neumann (Danckwerts) outflow boundary condition on east side
//no-flux (equivalently, homoegenous neumann) boundary conditions on north, south, top, bottom sides
//"strong" enforcement of boundary conditions
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
Number aux_z = ctxt.side_value(aux_zc_var, qp);
//velocity vector
NumberVectorValue U(porosity*vx, 0., 0.);
for (unsigned int i=0; i != n_c_dofs; i++)
{
if(isEast)
Rc(i) += JxW[qp]*(-U*face_normals[qp]*aux_z)*phi[i][qp];
if(request_jacobian && context.get_elem_solution_derivative())
{
for (unsigned int j=0; j != n_c_dofs; j++)
{
if(isEast)
J_c_auxz(i,j) += JxW[qp]*(-U*face_normals[qp]*phi[j][qp])*phi[i][qp];
}
} // end - if (request_jacobian && context.get_elem_solution_derivative())
} //end of outer dof (i) loop
}
return request_jacobian;
}
bool HeatSystem::element_time_derivative (bool request_jacobian,
DiffContext & context)
{
FEMContext & c = libmesh_cast_ref<FEMContext &>(context);
const unsigned int mesh_dim =
c.get_system().get_mesh().mesh_dimension();
// First we get some references to cell-specific data that
// will be used to assemble the linear system.
const unsigned int dim = c.get_elem().dim();
FEBase * fe = libmesh_nullptr;
c.get_element_fe(T_var, fe, dim);
// Element Jacobian * quadrature weights for interior integration
const std::vector<Real> & JxW = fe->get_JxW();
const std::vector<Point> & xyz = fe->get_xyz();
const std::vector<std::vector<Real> > & phi = fe->get_phi();
const std::vector<std::vector<RealGradient> > & dphi = fe->get_dphi();
// The number of local degrees of freedom in each variable
const unsigned int n_T_dofs = c.get_dof_indices(T_var).size();
// The subvectors and submatrices we need to fill:
DenseSubMatrix<Number> & K = c.get_elem_jacobian(T_var, T_var);
DenseSubVector<Number> & F = c.get_elem_residual(T_var);
// Now we will build the element Jacobian and residual.
// Constructing the residual requires the solution and its
// gradient from the previous timestep. This must be
// calculated at each quadrature point by summing the
// solution degree-of-freedom values by the appropriate
// weight functions.
unsigned int n_qpoints = c.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution gradient at the Newton iterate
Gradient grad_T = c.interior_gradient(T_var, qp);
const Number k = _k[dim];
const Point & p = xyz[qp];
// solution + laplacian depend on problem dimension
const Number u_exact = (mesh_dim == 2) ?
std::sin(libMesh::pi*p(0)) * std::sin(libMesh::pi*p(1)) :
std::sin(libMesh::pi*p(0)) * std::sin(libMesh::pi*p(1)) *
std::sin(libMesh::pi*p(2));
// Only apply forcing to interior elements
const Number forcing = (dim == mesh_dim) ?
-k * u_exact * (dim * libMesh::pi * libMesh::pi) : 0;
const Number JxWxNK = JxW[qp] * -k;
for (unsigned int i=0; i != n_T_dofs; i++)
F(i) += JxWxNK * (grad_T * dphi[i][qp] + forcing * phi[i][qp]);
if (request_jacobian)
{
const Number JxWxNKxD = JxWxNK *
context.get_elem_solution_derivative();
for (unsigned int i=0; i != n_T_dofs; i++)
for (unsigned int j=0; j != n_T_dofs; ++j)
K(i,j) += JxWxNKxD * (dphi[i][qp] * dphi[j][qp]);
}
} // end of the quadrature point qp-loop
return request_jacobian;
}