Reference documentation for deal.II version 9.1.1
\(\newcommand{\dealcoloneq}{\mathrel{\vcenter{:}}=}\)
Public Types | List of all members
Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType > Class Template Reference

#include <deal.II/differentiation/ad/ad_helpers.h>

Inheritance diagram for Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >:
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Public Types

using scalar_type = typename HelperBase< ADNumberTypeCode, ScalarType >::scalar_type
 
using ad_type = typename HelperBase< ADNumberTypeCode, ScalarType >::ad_type
 
- Public Types inherited from Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >
using scalar_type = typename HelperBase< ADNumberTypeCode, ScalarType >::scalar_type
 
using ad_type = typename HelperBase< ADNumberTypeCode, ScalarType >::ad_type
 
- Public Types inherited from Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >
using scalar_type = typename AD::NumberTraits< ScalarType, ADNumberTypeCode >::scalar_type
 
using ad_type = typename AD::NumberTraits< ScalarType, ADNumberTypeCode >::ad_type
 

Public Member Functions

Constructor / destructor
 ResidualLinearization (const unsigned int n_independent_variables, const unsigned int n_dependent_variables)
 
virtual ~ResidualLinearization ()=default
 
Dependent variables
void register_residual_vector (const std::vector< ad_type > &residual)
 
virtual void compute_residual (Vector< scalar_type > &residual) const override
 
virtual void compute_linearization (FullMatrix< scalar_type > &linearization) const override
 
- Public Member Functions inherited from Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >
 CellLevelBase (const unsigned int n_independent_variables, const unsigned int n_dependent_variables)
 
virtual ~CellLevelBase ()=default
 
void register_dof_values (const std::vector< scalar_type > &dof_values)
 
template<typename VectorType >
void register_dof_values (const VectorType &values, const std::vector<::types::global_dof_index > &local_dof_indices)
 
const std::vector< ad_type > & get_sensitive_dof_values () const
 
void set_dof_values (const std::vector< scalar_type > &dof_values)
 
template<typename VectorType >
void set_dof_values (const VectorType &values, const std::vector<::types::global_dof_index > &local_dof_indices)
 
- Public Member Functions inherited from Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >
 HelperBase (const unsigned int n_independent_variables, const unsigned int n_dependent_variables)
 
virtual ~HelperBase ()=default
 
std::size_t n_independent_variables () const
 
std::size_t n_dependent_variables () const
 
void print (std::ostream &stream) const
 
void print_values (std::ostream &stream) const
 
void print_tape_stats (const typename Types< ad_type >::tape_index tape_index, std::ostream &stream) const
 
virtual void reset (const unsigned int n_independent_variables=::numbers::invalid_unsigned_int, const unsigned int n_dependent_variables=::numbers::invalid_unsigned_int, const bool clear_registered_tapes=true)
 
bool is_recording () const
 
Types< ad_type >::tape_index active_tape_index () const
 
bool is_registered_tape (const typename Types< ad_type >::tape_index tape_index) const
 
void set_tape_buffer_sizes (const typename Types< ad_type >::tape_buffer_sizes obufsize=64 *1024 *1024, const typename Types< ad_type >::tape_buffer_sizes lbufsize=64 *1024 *1024, const typename Types< ad_type >::tape_buffer_sizes vbufsize=64 *1024 *1024, const typename Types< ad_type >::tape_buffer_sizes tbufsize=64 *1024 *1024)
 
bool start_recording_operations (const typename Types< ad_type >::tape_index tape_index, const bool overwrite_tape=false, const bool keep_independent_values=true)
 
void stop_recording_operations (const bool write_tapes_to_file=false)
 
void activate_recorded_tape (const typename Types< ad_type >::tape_index tape_index)
 
bool recorded_tape_requires_retaping (const typename Types< ad_type >::tape_index tape_index) const
 
bool active_tape_requires_retaping () const
 
void clear_active_tape ()
 

Additional Inherited Members

- Static Public Member Functions inherited from Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >
static void configure_tapeless_mode (const unsigned int n_independent_variables, const bool ensure_persistent_setting=true)
 
- Protected Member Functions inherited from Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >
void activate_tape (const typename Types< ad_type >::tape_index tape_index, const bool read_mode)
 
void reset_registered_independent_variables ()
 
void set_sensitivity_value (const unsigned int index, const scalar_type &value)
 
void mark_independent_variable (const unsigned int index, ad_type &out) const
 
void finalize_sensitive_independent_variables () const
 
void initialize_non_sensitive_independent_variable (const unsigned int index, ad_type &out) const
 
unsigned int n_registered_independent_variables () const
 
void reset_registered_dependent_variables (const bool flag=false)
 
unsigned int n_registered_dependent_variables () const
 
void register_dependent_variable (const unsigned int index, const ad_type &func)
 
- Protected Attributes inherited from Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >
TapedDrivers< ad_type, scalar_type > taped_driver
 
TapelessDrivers< ad_type, scalar_type > tapeless_driver
 
std::vector< scalar_type > independent_variable_values
 
std::vector< ad_type > independent_variables
 
std::vector< bool > registered_independent_variable_values
 
std::vector< bool > registered_marked_independent_variables
 
std::vector< ad_type > dependent_variables
 
std::vector< bool > registered_marked_dependent_variables
 

Detailed Description

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType = double>
class Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >

A helper class that facilitates the evaluation and automated linearization of a vector of functions that represents a residual vector (as computed from some corresponding local degree of freedom values). This class would typically be used to compute the linearization of a residual vector defined on the level of a cell, or for local nonlinear equations.

An example of its usage in the case of a residual linearization might be as follows (in this case we'll compute the linearization of a finite-strain magneto-elastic solid from the residual, as constructed from the Piola-Kirchoff stress and magnetic induction assuming the magnetic scalar potential formulation):

// Existing data structures:
Vector<double> solution (...); // Or another vector type
std::vector<types::global_dof_index> local_dof_indices (...);
const FEValuesExtractors::Vector u_fe (...);
const FEValuesExtractors::Scalar msp_fe (...);
const unsigned int u_block (...);
const unsigned int msp_block (...);
FEValues<dim> fe_values (...);
const unsigned int n_q_points (...);
FullMatrix<double> cell_matrix (...);
Vector<double> cell_rhs (...);
// Assembly loop:
for (auto & cell : ...)
{
cell->get_dof_indices(local_dof_indices);
const unsigned int n_independent_variables
= local_dof_indices.size();
const unsigned int n_dependent_variables
= local_dof_indices.size();
// Create some aliases for the AD helper.
// In this example, we strictly assume that we're using tapeless
// AD types, and so the AD_typecode used in the template argument
// must refer to one of these types. See the example for the
// EnergyFunctional for details on how to extend
// support to taped AD numbers.
using ADHelper = AD::ResidualLinearization<...>;
using ADNumberType = typename ADHelper::ad_type;
// Create and initialize an instance of the helper class.
ADHelper ad_helper(n_independent_variables,n_dependent_variables);
// Initialize the local data structures for assembly.
// This is also taken care of by the ADHelper, so this step could
// be skipped.
cell_rhs.reinit(n_dependent_variables);
cell_matrix.reinit(n_independent_variables,n_dependent_variables);
// This next code block corresponds to the "recording" phase, where
// the operations performed with the AD numbers are tracked and
// differentiation is performed.
{
// First, we set the values for all DoFs.
ad_helper.register_dof_values(solution, local_dof_indices);
// Then we get the complete set of degree of freedom values as
// represented by auto-differentiable numbers. The operations
// performed with these variables are tracked by the AD library
// from this point until stop_recording_operations() is called.
const std::vector<ADNumberType> dof_values_ad
= ad_helper.get_sensitive_dof_values();
// Then we do some problem specific tasks, the first being to
// compute all values, gradients, etc. based on sensitive AD DoF
// values. Here we are fetching the displacement gradients at each
// quadrature point, as well as the gradients of the magnetic
// scalar potential field.
std::vector<Tensor<2, dim, ADNumberType>> Grad_u(
n_q_points, Tensor<2, dim, ADNumberType>());
std::vector<Tensor<1, dim, ADNumberType>> Grad_msp(
n_q_points, Tensor<1, dim, ADNumberType>());
fe_values[u_fe].get_function_gradients_from_local_dof_values(
dof_values_ad, Grad_u);
fe_values[msp_fe].get_function_gradients_from_local_dof_values(
dof_values_ad, Grad_msp);
// This variable stores the cell residual vector contributions.
// IMPORTANT: Note that each entry is hand-initialized with a value
// of zero. This is a highly recommended practise, as some AD
// numbers appear not to safely initialize their internal data
// structures.
std::vector<ADNumberType> residual_ad (
n_dependent_variables, ADNumberType(0.0));
// Compute the cell total residual
// = (internal + external) contributions
for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
{
// Calculate the deformation gradient and magnetic field at this
// quadrature point
const Tensor<2, dim, ADNumberType> F =
unit_symmetric_tensor<dim>() + Grad_u[q_point];
const Tensor<1, dim, ADNumberType> H = -Grad_msp[q_point];
Assert(numbers::value_is_greater_than(determinant(F), 0.0),
ExcMessage("Negative determinant of the deformation "
"gradient detected!"));
// Extract some configuration dependent variables from our
// nonlinear constitutive law for the current quadrature point.
// In this way they only have to be computed once per quadrature
// point.
const SymmetricTensor<2,dim,ad_type> S = get_S(F,H);
const Tensor<1,dim,ad_type> B = get_B(F,H);
// Define some position-dependent aliases, to make the assembly
// process easier to follow.
const double JxW = fe_values.JxW(q_point);
// Add contribution of the internal forces:
// Note that we assemble the residual contribution directly
// as it is this vector that is to be automatically linearized.
for (unsigned int I = 0; I < n_dofs_per_cell; ++I)
{
// Determine the component and block associated with
// the I'th local degree of freedom.
const unsigned int block_I =
fe.system_to_base_index(I).first.first;
if (block_I == u_block) // u-terms
{
// Variation of the Green-Lagrange strain tensor
// associated with the I'th vector-valued basis function.
const SymmetricTensor<2,dim,double> dE_I
= symmetrize(transpose(F)
* fe_values[u_fe].gradient(I,q_point));
residual_ad[I] += (dE_I*S) * JxW;
}
else if (block_I == msp_block)
{
// Variation of the magnetic field vector associated with
// the I'th scalar-valued basis function
const Tensor<1,dim,double> dH_I
= -fe_values[msp_fe].gradient(I, q_point);
residual_ad[I] -= (dH_I*B) * JxW;
}
}
}
// Add contribution from external sources. If these contributions
// are also solution dependent then they will also be consistently
// linearized.
// Loop over faces and accumulate external contributions into the
// cell total residual.
for (unsigned int face : ...)
if (cell->face(face)->at_boundary())
residual_ad[I] += ...
// Register the definition of the cell residual
ad_helper.register_residual_vector(residual_ad);
}
// Compute the residual values and their Jacobian at the
// evaluation point
ad_helper.compute_residual(cell_rhs);
cell_rhs *= -1.0; // RHS = - residual
ad_helper.compute_linearization(cell_matrix);
}

In most use cases, and in particular in the code example shown above, both the number of independent and dependent variables equals the number of dofs_per_cell for the used finite element.

Warning
ADOL-C does not support the standard threading models used by deal.II, so this class should not be embedded within a multithreaded function when using ADOL-C number types. It is, however, suitable for use in both serial and MPI routines.
Author
Jean-Paul Pelteret, 2016, 2017, 2018

Definition at line 1539 of file ad_helpers.h.

Member Typedef Documentation

◆ scalar_type

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType = double>
using Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::scalar_type = typename HelperBase<ADNumberTypeCode, ScalarType>::scalar_type

Type definition for the floating point number type that is used in, and results from, all computations.

Definition at line 1548 of file ad_helpers.h.

◆ ad_type

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType = double>
using Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::ad_type = typename HelperBase<ADNumberTypeCode, ScalarType>::ad_type

Type definition for the auto-differentiation number type that is used in all computations.

Definition at line 1555 of file ad_helpers.h.

Constructor & Destructor Documentation

◆ ResidualLinearization()

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType >
Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::ResidualLinearization ( const unsigned int  n_independent_variables,
const unsigned int  n_dependent_variables 
)

The constructor for the class.

Parameters
[in]n_independent_variablesThe number of independent variables that will be used in the definition of the functions that it is desired to compute the sensitivities of. In the computation of $\mathbf{r}(\mathbf{X})$, this will be the number of inputs $\mathbf{X}$, i.e., the dimension of the domain space.
[in]n_dependent_variablesThe number of scalar functions to be defined that will have a sensitivity to the given independent variables. In the computation of $\mathbf{r}(\mathbf{X})$, this will be the number of outputs $\mathbf{r}$, i.e., the dimension of the image space.

Definition at line 1015 of file ad_helpers.cc.

◆ ~ResidualLinearization()

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType = double>
virtual Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::~ResidualLinearization ( )
virtualdefault

Destructor

Member Function Documentation

◆ register_residual_vector()

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType >
void Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::register_residual_vector ( const std::vector< ad_type > &  residual)

Register the definition of the cell residual vector $\mathbf{r}(\mathbf{X})$.

Parameters
[in]residualA vector of recorded functions that defines the residual. The components of this vector represents the dependent variables.
Note
For this class that expects only vector fields of dependent variables, this function must only be called once per tape.
For taped AD numbers, this operation is only valid in recording mode.

Definition at line 1027 of file ad_helpers.cc.

◆ compute_residual()

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType >
void Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::compute_residual ( Vector< scalar_type > &  residual) const
overridevirtual

Evaluation of the residual for a chosen set of degree of freedom values. This corresponds to the computation of the residual vector, i.e.

\[ \mathbf{r}(\mathbf{X}) \vert_{\mathbf{X}} \]

The values at the evaluation point $\mathbf{X}$ are obtained by calling CellLevelBase::set_dof_values().

Parameters
[out]residualA Vector object, for which the value for each entry represents the residual value for the corresponding local degree of freedom. The output residual vector has a length corresponding to n_dependent_variables.

Implements Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >.

Definition at line 1041 of file ad_helpers.cc.

◆ compute_linearization()

template<enum AD::NumberTypes ADNumberTypeCode, typename ScalarType >
void Differentiation::AD::ResidualLinearization< ADNumberTypeCode, ScalarType >::compute_linearization ( FullMatrix< scalar_type > &  linearization) const
overridevirtual

Compute the linearization of the residual vector around a chosen set of degree of freedom values. Underlying this is the computation of the gradient (first derivative) of the residual vector $\mathbf{r}$ with respect to all independent variables, i.e.

\[ \frac{\partial\mathbf{r}(\mathbf{X})}{\partial\mathbf{X}} \]

The values at the evaluation point $\mathbf{X}$ are obtained by calling CellLevelBase::set_dof_values().

Parameters
[out]linearizationA FullMatrix representing the linearization of the residual vector. The output linearization matrix has dimensions corresponding to n_dependent_variables $\times$n_independent_variables.

Implements Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >.

Definition at line 1095 of file ad_helpers.cc.

The documentation for this class was generated from the following files:
Physics::Elasticity::Kinematics::F
Tensor< 2, dim, Number > F(const Tensor< 2, dim, Number > &Grad_u)
SymmetricTensor
Definition: mpi.h:92
FEValuesExtractors::Scalar
Definition: fe_values_extractors.h:95
determinant
Number determinant(const SymmetricTensor< 2, dim, Number > &)
Definition: symmetric_tensor.h:2688
transpose
SymmetricTensor< rank_, dim, Number > transpose(const SymmetricTensor< rank_, dim, Number > &t)
Definition: symmetric_tensor.h:3247
LocalIntegrators::Advection::cell_matrix
void cell_matrix(FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, const ArrayView< const std::vector< double >> &velocity, const double factor=1.)
Definition: advection.h:80
FEValues< dim >
Differentiation::AD::HelperBase::n_independent_variables
std::size_t n_independent_variables() const
Definition: ad_helpers.cc:245
FEValuesExtractors::Vector
Definition: fe_values_extractors.h:150
symmetrize
SymmetricTensor< 2, dim, Number > symmetrize(const Tensor< 2, dim, Number > &t)
Definition: symmetric_tensor.h:3556
StandardExceptions::ExcMessage
static ::ExceptionBase & ExcMessage(std::string arg1)
Tensor
Definition: mpi.h:90
Assert
#define Assert(cond, exc)
Definition: exceptions.h:1407
Differentiation::AD::HelperBase::n_dependent_variables
std::size_t n_dependent_variables() const
Definition: ad_helpers.cc:266
FullMatrix< double >
numbers::value_is_greater_than
bool value_is_greater_than(const Number1 &value_1, const Number2 &value_2)
Definition: numbers.h:901
Vector< double >
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