nonlinear-heat_transfer_with_AD_NOX.h File Reference

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Typedefs
using	ADHelper = Differentiation::AD::ResidualLinearization<Differentiation::AD::NumberTypes::sacado_dfad,double>
using	ADNumberType = typename ADHelper::ad_type

Functions
*  *  FEFaceValues< 2 >	fe_face_values (fe, face_quadrature_formula, update_values|update_quadrature_points| *  update_normal_vectors|update_JxW_values)
*  *  Vector< double >	cell_rhs (dofs_per_cell)
*  *  *  std::vector< double >	consol (n_q_points)
*	for (const auto &cell:dof_handler.active_cell_iterators()) *
*  *	for (const types::global_dof_index i:DoFTools::extract_boundary_dofs(dof_handler, t_mask,{1})) *  residual(i)=0

Variables
*  const unsigned int	dofs_per_cell = fe.dofs_per_cell
*  const unsigned int	n_q_points = quadrature_formula.size()
*  const unsigned int	n_q_f_points = face_quadrature_formula.size()
*  *  const FEValuesExtractors::Scalar t *
*  *  ComponentMask	t_mask = fe.component_mask(t)
*  *	residual = 0.0

Typedef Documentation

ADHelper

using ADHelper = Differentiation::AD::ResidualLinearization<Differentiation::AD::NumberTypes::sacado_dfad,double>

  * Here we define the type of Number we want to use to define our variables   * so that they are suitable for automatic differentiation.  

Definition at line 1398 of file nonlinear-heat_transfer_with_AD_NOX.h.

ADNumberType

using ADNumberType = typename ADHelper::ad_type

Definition at line 1399 of file nonlinear-heat_transfer_with_AD_NOX.h.

Function Documentation

fe_face_values()

*  *  FEFaceValues< 2 > fe_face_values	(	fe	,
		face_quadrature_formula	,
		update_values|update_quadrature_points| *  update_normal_vectors|	update_JxW_values )

cell_rhs()

*  *  Vector< double > cell_rhs

(

dofs_per_cell

)

  * cell_rhs holds the local rhs. That is the residual evaluated at the   * #evaluation_point.   Defining a local (residual) vector

consol()

*  *  *  std::vector< double > consol

(

n_q_points

)

  * consol now holds the #converged_solution at the Gauss points of a current cell. These are of the double type i.e., regular numbers.  

for() [1/2]

*  for

(

const auto &cell:dof_handler.

active_cell_iterators()

)

  * It is in the following line, we say that the #evalaution_point needs to be substituted in   * place of the #old_solution (or #old_solution_grad) to get the residual (in numerical form).  

  * In the following steps, consol and #consol_grad are used to grab value of the #converged_solution   * and its gradient at the gauss points, respectively.  

  * residual_ad is defined and initialized in its symbolic form.  

  * We here define the entire residual using all intermediate variables, which are also of the type ADNumberType.  

  * The following lines, apply the Newmann boundary conditions to the right hand side.  

  * The Newumann boundary condition (-10) is applied to the right edge, with boundary id 3.  

  * Here, we tell the ad_helper that the residual (in its symbolic form) is given by #residual_ad.  

  * Here, the residual is calculated at the values given by #evaluation_point.   * Note that the residual does not have the -ve sign as in the regular way of solving.   * This is because, the NOX solvers, only needs the actual reisdual.  

Definition at line 1430 of file nonlinear-heat_transfer_with_AD_NOX.h.

for() [2/2]

*  *  for ( const types::global_dof_index i:DoFTools::extract_boundary_dofsdof_handler, t_mask,{1} )

pure virtual

Variable Documentation

dofs_per_cell

*   const unsigned int dofs_per_cell = fe.dofs_per_cell

Number of degree of freedom per cell

Definition at line 1385 of file nonlinear-heat_transfer_with_AD_NOX.h.

n_q_points

*   const unsigned int n_q_points = quadrature_formula.size()

Number of quadrature points over the domain of the finite element

Definition at line 1386 of file nonlinear-heat_transfer_with_AD_NOX.h.

n_q_f_points

*   const unsigned int n_q_f_points = face_quadrature_formula.size()

Number of quadrature point over the boundary of a finite element

Definition at line 1387 of file nonlinear-heat_transfer_with_AD_NOX.h.

 

*   std::vector<Tensor<1, 2,ADNumberType> > old_solution_grad *

  * The FEValuesExtractors is used as usual to get the degree of freedom we are interested in.   * For this single variable problem, this may not be needed. We still use it to show   * how it needs to be declared, when multiple variables exist and when we want to define component mask   * to define boundary conditions for specific variables.  

Local to Global Degree of freedom indices

  * #concol_grad now holds the #converged_solution at the Gauss points of the current cell. These are regular numbers.  

Definition at line 1406 of file nonlinear-heat_transfer_with_AD_NOX.h.

t_mask

*  *   ComponentMask t_mask = fe.component_mask(t)

Definition at line 1425 of file nonlinear-heat_transfer_with_AD_NOX.h.

residual

*  *   residual = 0.0

  * Actual, numerical residual.  

Definition at line 1429 of file nonlinear-heat_transfer_with_AD_NOX.h.