void LaplaceSystem::init_context(DiffContext &context)
{
FEMContext &c = libmesh_cast_ref<FEMContext&>(context);
// Get finite element object
FEGenericBase<RealGradient>* fe;
c.get_element_fe<RealGradient>( u_var, fe );
// We should prerequest all the data
// we will need to build the linear system.
fe->get_JxW();
fe->get_phi();
fe->get_dphi();
fe->get_xyz();
FEGenericBase<RealGradient>* side_fe;
c.get_side_fe<RealGradient>( u_var, side_fe );
side_fe->get_JxW();
side_fe->get_phi();
}
bool LaplaceSystem::element_time_derivative (bool request_jacobian,
DiffContext &context)
{
FEMContext &c = libmesh_cast_ref<FEMContext&>(context);
// Get finite element object
FEGenericBase<RealGradient>* fe = NULL;
c.get_element_fe<RealGradient>( u_var, fe );
// 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 = fe->get_JxW();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<RealGradient> >& phi = fe->get_phi();
// The velocity shape function gradients at interior
// quadrature points.
const std::vector<std::vector<RealTensor> >& grad_phi = fe->get_dphi();
const std::vector<Point>& qpoint = fe->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = c.dof_indices_var[u_var].size();
DenseSubMatrix<Number> &Kuu = *c.elem_subjacobians[u_var][u_var];
DenseSubVector<Number> &Fu = *c.elem_subresiduals[u_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.
const unsigned int n_qpoints = (c.get_element_qrule())->n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
Tensor grad_u;
c.interior_gradient( u_var, qp, grad_u );
// Value of the forcing function at this quadrature point
RealGradient f = this->forcing(qpoint[qp]);
// First, an i-loop over the velocity degrees of freedom.
// We know that n_u_dofs == n_v_dofs so we can compute contributions
// for both at the same time.
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) += ( grad_u.contract(grad_phi[i][qp]) - f*phi[i][qp] )*JxW[qp];
if (request_jacobian)
{
// Matrix contributions for the uu and vv couplings.
for (unsigned int j=0; j != n_u_dofs; j++)
{
Kuu(i,j) += grad_phi[j][qp].contract(grad_phi[i][qp])*JxW[qp];
}
}
}
} // end of the quadrature point qp-loop
return request_jacobian;
}
bool CurlCurlSystem::element_time_derivative (bool request_jacobian,
DiffContext &context)
{
FEMContext &c = cast_ref<FEMContext&>(context);
// Get finite element object
FEGenericBase<RealGradient>* fe = NULL;
c.get_element_fe<RealGradient>( u_var, fe );
// 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 = fe->get_JxW();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<RealGradient> >& phi = fe->get_phi();
// The velocity shape function gradients at interior
// quadrature points.
const std::vector<std::vector<RealGradient> >& curl_phi = fe->get_curl_phi();
const std::vector<Point>& qpoint = fe->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();
DenseSubMatrix<Number> &Kuu = c.get_elem_jacobian(u_var,u_var);
DenseSubVector<Number> &Fu = c.get_elem_residual(u_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.
const unsigned int n_qpoints = c.get_element_qrule().n_points();
// Loop over quadrature points
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
Gradient u;
Gradient curl_u;
c.interior_value( u_var, qp, u );
c.interior_curl( u_var, qp, curl_u );
// Value of the forcing function at this quadrature point
RealGradient f = this->forcing(qpoint[qp]);
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) += ( curl_u*curl_phi[i][qp] + u*phi[i][qp] - f*phi[i][qp] )*JxW[qp];
if (request_jacobian)
{
// Matrix contributions for the uu and vv couplings.
for (unsigned int j=0; j != n_u_dofs; j++)
{
Kuu(i,j) += ( curl_phi[j][qp]*curl_phi[i][qp] +
phi[j][qp]*phi[i][qp] )*JxW[qp];
}
}
}
} // end of the quadrature point qp-loop
return request_jacobian;
}
