void AssemblyA0::interior_assembly(FEMContext & c)
{
const unsigned int n_components = rb_sys.n_vars();
// make sure we have three components
libmesh_assert_equal_to (n_components, 3);
const unsigned int u_var = rb_sys.u_var;
const unsigned int v_var = rb_sys.v_var;
const unsigned int w_var = rb_sys.w_var;
FEBase * elem_fe = libmesh_nullptr;
c.get_element_fe(u_var, elem_fe);
const std::vector<Real> & JxW = elem_fe->get_JxW();
// The velocity shape function gradients at interior
// quadrature points.
const std::vector<std::vector<RealGradient>> & dphi = elem_fe->get_dphi();
// Now we will build the affine operator
unsigned int n_qpoints = c.get_element_qrule().n_points();
std::vector<unsigned int> n_var_dofs(n_components);
n_var_dofs[u_var] = c.get_dof_indices(u_var).size();
n_var_dofs[v_var] = c.get_dof_indices(v_var).size();
n_var_dofs[w_var] = c.get_dof_indices(w_var).size();
for (unsigned int C_i = 0; C_i < n_components; C_i++)
{
unsigned int C_j = 0;
for (unsigned int C_k = 0; C_k < n_components; C_k++)
for (unsigned int C_l = 1; C_l < n_components; C_l++)
{
Real C_ijkl = elasticity_tensor(C_i, C_j, C_k, C_l);
for (unsigned int qp=0; qp<n_qpoints; qp++)
for (unsigned int i=0; i<n_var_dofs[C_i]; i++)
for (unsigned int j=0; j<n_var_dofs[C_k]; j++)
(c.get_elem_jacobian(C_i,C_k))(i,j) +=
JxW[qp]*(C_ijkl * dphi[i][qp](C_j)*dphi[j][qp](C_l));
}
}
for (unsigned int C_i = 0; C_i < n_components; C_i++)
for (unsigned int C_j = 1; C_j < n_components; C_j++)
for (unsigned int C_k = 0; C_k < n_components; C_k++)
{
unsigned int C_l = 0;
Real C_ijkl = elasticity_tensor(C_i, C_j, C_k, C_l);
for (unsigned int qp=0; qp<n_qpoints; qp++)
for (unsigned int i=0; i<n_var_dofs[C_i]; i++)
for (unsigned int j=0; j<n_var_dofs[C_k]; j++)
(c.get_elem_jacobian(C_i,C_k))(i,j) +=
JxW[qp]*(C_ijkl * dphi[i][qp](C_j)*dphi[j][qp](C_l));
}
}
AutoPtr<DiffContext> FEMSystem::build_context ()
{
FEMContext* fc = new FEMContext(*this);
AutoPtr<DiffContext> ap(fc);
DifferentiablePhysics* phys = this->get_physics();
libmesh_assert (phys);
// If we are solving a moving mesh problem, tell that to the Context
fc->set_mesh_system(phys->get_mesh_system());
fc->set_mesh_x_var(phys->get_mesh_x_var());
fc->set_mesh_y_var(phys->get_mesh_y_var());
fc->set_mesh_z_var(phys->get_mesh_z_var());
ap->set_deltat_pointer( &deltat );
// If we are solving the adjoint problem, tell that to the Context
ap->is_adjoint() = this->get_time_solver().is_adjoint();
return ap;
}
void InnerProductAssembly::interior_assembly(FEMContext & c)
{
const unsigned int u_var = rb_sys.u_var;
const unsigned int v_var = rb_sys.v_var;
const unsigned int w_var = rb_sys.w_var;
FEBase * elem_fe = libmesh_nullptr;
c.get_element_fe(u_var, elem_fe);
const std::vector<Real> & JxW = elem_fe->get_JxW();
// The velocity shape function gradients at interior
// quadrature points.
const std::vector<std::vector<RealGradient> >& dphi = elem_fe->get_dphi();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();
const unsigned int n_v_dofs = c.get_dof_indices(v_var).size();
const unsigned int n_w_dofs = c.get_dof_indices(w_var).size();
// Now we will build the affine operator
unsigned int n_qpoints = c.get_element_qrule().n_points();
DenseSubMatrix<Number> & Kuu = c.get_elem_jacobian(u_var, u_var);
DenseSubMatrix<Number> & Kvv = c.get_elem_jacobian(v_var, v_var);
DenseSubMatrix<Number> & Kww = c.get_elem_jacobian(w_var, w_var);
for (unsigned int qp=0; qp<n_qpoints; qp++)
{
for (unsigned int i=0; i<n_u_dofs; i++)
for (unsigned int j=0; j<n_u_dofs; j++)
Kuu(i,j) += JxW[qp]*(dphi[i][qp]*dphi[j][qp]);
for (unsigned int i=0; i<n_v_dofs; i++)
for (unsigned int j=0; j<n_v_dofs; j++)
Kvv(i,j) += JxW[qp]*(dphi[i][qp]*dphi[j][qp]);
for (unsigned int i=0; i<n_w_dofs; i++)
for (unsigned int j=0; j<n_w_dofs; j++)
Kww(i,j) += JxW[qp]*(dphi[i][qp]*dphi[j][qp]);
}
}
void FEMSystem::numerical_jacobian (TimeSolverResPtr res,
FEMContext &context)
{
// Logging is done by numerical_elem_jacobian
// or numerical_side_jacobian
DenseVector<Number> original_residual(context.elem_residual);
DenseVector<Number> backwards_residual(context.elem_residual);
DenseMatrix<Number> numerical_jacobian(context.elem_jacobian);
#ifdef DEBUG
DenseMatrix<Number> old_jacobian(context.elem_jacobian);
#endif
Real numerical_point_h = 0.;
if (_mesh_sys == this)
numerical_point_h = numerical_jacobian_h * context.elem->hmin();
for (unsigned int j = 0; j != context.dof_indices.size(); ++j)
{
// Take the "minus" side of a central differenced first derivative
Number original_solution = context.elem_solution(j);
context.elem_solution(j) -= numerical_jacobian_h;
// Make sure to catch any moving mesh terms
// FIXME - this could be less ugly
Real *coord = NULL;
if (_mesh_sys == this)
{
if (_mesh_x_var != libMesh::invalid_uint)
for (unsigned int k = 0;
k != context.dof_indices_var[_mesh_x_var].size(); ++k)
if (context.dof_indices_var[_mesh_x_var][k] ==
context.dof_indices[j])
coord = &(const_cast<Elem*>(context.elem)->point(k)(0));
if (_mesh_y_var != libMesh::invalid_uint)
for (unsigned int k = 0;
k != context.dof_indices_var[_mesh_y_var].size(); ++k)
if (context.dof_indices_var[_mesh_y_var][k] ==
context.dof_indices[j])
coord = &(const_cast<Elem*>(context.elem)->point(k)(1));
if (_mesh_z_var != libMesh::invalid_uint)
for (unsigned int k = 0;
k != context.dof_indices_var[_mesh_z_var].size(); ++k)
if (context.dof_indices_var[_mesh_z_var][k] ==
context.dof_indices[j])
coord = &(const_cast<Elem*>(context.elem)->point(k)(2));
}
if (coord)
{
// We have enough information to scale the perturbations
// here appropriately
context.elem_solution(j) = original_solution - numerical_point_h;
*coord = libmesh_real(context.elem_solution(j));
}
context.elem_residual.zero();
((*time_solver).*(res))(false, context);
#ifdef DEBUG
libmesh_assert_equal_to (old_jacobian, context.elem_jacobian);
#endif
backwards_residual = context.elem_residual;
// Take the "plus" side of a central differenced first derivative
context.elem_solution(j) = original_solution + numerical_jacobian_h;
if (coord)
{
context.elem_solution(j) = original_solution + numerical_point_h;
*coord = libmesh_real(context.elem_solution(j));
}
context.elem_residual.zero();
((*time_solver).*(res))(false, context);
#ifdef DEBUG
libmesh_assert_equal_to (old_jacobian, context.elem_jacobian);
#endif
context.elem_solution(j) = original_solution;
if (coord)
{
*coord = libmesh_real(context.elem_solution(j));
for (unsigned int i = 0; i != context.dof_indices.size(); ++i)
{
numerical_jacobian(i,j) =
(context.elem_residual(i) - backwards_residual(i)) /
2. / numerical_point_h;
}
}
else
{
for (unsigned int i = 0; i != context.dof_indices.size(); ++i)
{
numerical_jacobian(i,j) =
(context.elem_residual(i) - backwards_residual(i)) /
2. / numerical_jacobian_h;
}
}
}
context.elem_residual = original_residual;
context.elem_jacobian = numerical_jacobian;
}