libMesh::TensorTools Namespace Reference

Classes
struct	DecrementRank
struct	DecrementRank< TensorValue< T > >
struct	DecrementRank< TypeNTensor< N, T > >
struct	DecrementRank< TypeTensor< T > >
struct	DecrementRank< TypeVector< T > >
struct	DecrementRank< VectorValue< T > >
struct	IncrementRank
struct	IncrementRank< TensorValue< T > >
struct	IncrementRank< TypeNTensor< N, T > >
struct	IncrementRank< TypeTensor< T > >
struct	IncrementRank< TypeVector< T > >
struct	IncrementRank< VectorValue< T > >
struct	MakeBaseNumber
struct	MakeBaseNumber< T, typename std::enable_if< ScalarTraits< T >::value >::type >
struct	MakeBaseNumber< Wrapper< T >, typename std::enable_if< MathWrapperTraits< Wrapper< T > >::value >::type >
struct	MakeNumber
struct	MakeNumber< std::complex< T > >
struct	MakeNumber< TensorValue< T > >
struct	MakeNumber< TypeNTensor< N, T > >
struct	MakeNumber< TypeTensor< T > >
struct	MakeNumber< TypeVector< T > >
struct	MakeNumber< VectorValue< T > >
struct	MakeReal
struct	MakeReal< std::complex< T > >
struct	MakeReal< TensorValue< T > >
struct	MakeReal< TypeNTensor< N, T > >
struct	MakeReal< TypeTensor< T > >
struct	MakeReal< TypeVector< T > >
struct	MakeReal< VectorValue< T > >
struct	MathWrapperTraits
	This helper structure is used to determine whether a template class is one of our mathematical structures, like TypeVector, TypeTensor and their descendents. More...
struct	MathWrapperTraits< TensorValue< T > >
struct	MathWrapperTraits< TypeNTensor< N, T > >
struct	MathWrapperTraits< TypeTensor< T > >
struct	MathWrapperTraits< TypeVector< T > >
struct	MathWrapperTraits< VectorValue< T > >
struct	TensorTraits
struct	TensorTraits< T, typename std::enable_if< ScalarTraits< T >::value >::type >
struct	TensorTraits< TensorValue< T > >
struct	TensorTraits< TypeNTensor< N, T > >
struct	TensorTraits< TypeTensor< T > >
struct	TensorTraits< TypeVector< T > >
struct	TensorTraits< VectorValue< T > >

Functions
template<typename T , typename T2 >
LIBMESH_DEVICE_INLINE std::enable_if< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typenameCompareTypes< T, T2 >::supertype >::type	inner_product (const T &a, const T2 &b)
template<typename T , typename T2 >
LIBMESH_DEVICE_INLINE CompareTypes< T, T2 >::supertype	inner_product (const TypeVector< T > &a, const TypeVector< T2 > &b)
template<typename T , typename T2 >
LIBMESH_DEVICE_INLINE CompareTypes< T, T2 >::supertype	inner_product (const TypeTensor< T > &a, const TypeTensor< T2 > &b)
template<unsigned int N, typename T , typename T2 >
LIBMESH_DEVICE_INLINE CompareTypes< T, T2 >::supertype	inner_product (const TypeNTensor< N, T > &a, const TypeNTensor< N, T2 > &b)
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm (const T &a)
template<typename T >
LIBMESH_DEVICE_INLINE T	norm (std::complex< T > a)
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm (const TypeVector< T > &a) -> decltype(TensorTools::norm(T()))
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm (const VectorValue< T > &a) -> decltype(TensorTools::norm(T()))
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm (const TypeTensor< T > &a) -> decltype(TensorTools::norm(T()))
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm (const TensorValue< T > &a) -> decltype(TensorTools::norm(T()))
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm_sq (const T &a)
template<typename T >
LIBMESH_DEVICE_INLINE T	norm_sq (std::complex< T > a)
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm_sq (const TypeVector< T > &a)
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm_sq (const VectorValue< T > &a)
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm_sq (const TypeTensor< T > &a)
template<typename T >
LIBMESH_DEVICE_INLINE auto	norm_sq (const TensorValue< T > &a)
template<typename T >
LIBMESH_DEVICE_INLINE bool	is_zero (const T &a)
Number	curl_from_grad (const VectorValue< Number > &)
VectorValue< Number >	curl_from_grad (const TensorValue< Number > &grad)
	Computes the curl of a vector given the gradient of that vector.
TensorValue< Number >	curl_from_grad (const TypeNTensor< 3, Number > &grad)
Number	div_from_grad (const VectorValue< Number > &grad)
	Dummy. Divergence of a scalar not defined, but is needed for ExactSolution to compile.
Number	div_from_grad (const TensorValue< Number > &grad)
	Computes the divergence of a vector given the gradient of that vector.
VectorValue< Number >	div_from_grad (const TypeNTensor< 3, Number > &grad)

Function Documentation

curl_from_grad() [1/3]

VectorValue< Number > libMesh::TensorTools::curl_from_grad

(

const TensorValue< Number > &

grad

)

Computes the curl of a vector given the gradient of that vector.

Definition at line 33 of file tensor_tools.C.

{
  const Number duz_dy = grad(2,1);
  const Number duy_dz = grad(1,2);
  const Number dux_dz = grad(0,2);
  const Number duz_dx = grad(2,0);
  const Number duy_dx = grad(1,0);
  const Number dux_dy = grad(0,1);
 
  return VectorValue<Number>(duz_dy - duy_dz,
                             dux_dz - duz_dx,
                             duy_dx - dux_dy);
}

curl_from_grad() [2/3]

TensorValue< Number > libMesh::TensorTools::curl_from_grad

(

const TypeNTensor< 3, Number > &

grad

)

Place holder needed for ExactSolution to compile. Will compute the curl of a tensor given the gradient of that tensor.

Definition at line 48 of file tensor_tools.C.

{
  libmesh_not_implemented();
}

curl_from_grad() [3/3]

Number libMesh::TensorTools::curl_from_grad

(

const VectorValue< Number > &

)

Definition at line 28 of file tensor_tools.C.

{
  libmesh_error_msg("Operation not defined for scalar quantities.");
}

Referenced by libMesh::ExactSolution::_compute_error().

div_from_grad() [1/3]

Number libMesh::TensorTools::div_from_grad

(

const TensorValue< Number > &

grad

)

Computes the divergence of a vector given the gradient of that vector.

Definition at line 59 of file tensor_tools.C.

{
  const Number dux_dx = grad(0,0);
  const Number duy_dy = grad(1,1);
  const Number duz_dz = grad(2,2);
 
  return dux_dx + duy_dy + duz_dz;
}

div_from_grad() [2/3]

VectorValue< Number > libMesh::TensorTools::div_from_grad

(

const TypeNTensor< 3, Number > &

grad

)

Place holder needed for ExactSolution to compile. Will compute the divergence of a tensor given the gradient of that tensor.

Definition at line 69 of file tensor_tools.C.

{
  libmesh_not_implemented();
}

div_from_grad() [3/3]

Number libMesh::TensorTools::div_from_grad

(

const VectorValue< Number > &

grad

)

Dummy. Divergence of a scalar not defined, but is needed for ExactSolution to compile.

Definition at line 54 of file tensor_tools.C.

{
  libmesh_error_msg("Operation not defined for scalar quantities.");
}

Referenced by libMesh::ExactSolution::_compute_error().

inner_product() [1/4]

template<typename T , typename T2 >

LIBMESH_DEVICE_INLINE std::enable_if< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typenameCompareTypes< T, T2 >::supertype >::type libMesh::TensorTools::inner_product	(	const T &	a,
		const T2 &	b
	)

Definition at line 51 of file tensor_tools.h.

{ return a * b; }

References b.

Referenced by libMesh::FEGenericBase< OutputType >::coarsened_dof_values(), libMesh::FEGenericBase< OutputType >::compute_periodic_constraints(), libMesh::FEGenericBase< OutputType >::compute_proj_constraints(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubProjector::construct_projection().

inner_product() [2/4]

template<unsigned int N, typename T , typename T2 >

LIBMESH_DEVICE_INLINE CompareTypes< T, T2 >::supertype libMesh::TensorTools::inner_product	(	const TypeNTensor< N, T > &	a,
		const TypeNTensor< N, T2 > &	b
	)

Definition at line 69 of file tensor_tools.h.

{ return a.contract(b); }

References b, and libMesh::TypeNTensor< N, T >::contract().

inner_product() [3/4]

template<typename T , typename T2 >

LIBMESH_DEVICE_INLINE CompareTypes< T, T2 >::supertype libMesh::TensorTools::inner_product	(	const TypeTensor< T > &	a,
		const TypeTensor< T2 > &	b
	)

Definition at line 63 of file tensor_tools.h.

{ return a.contract(b); }

References b, and libMesh::TypeTensor< T >::contract().

inner_product() [4/4]

template<typename T , typename T2 >

LIBMESH_DEVICE_INLINE CompareTypes< T, T2 >::supertype libMesh::TensorTools::inner_product	(	const TypeVector< T > &	a,
		const TypeVector< T2 > &	b
	)

Definition at line 57 of file tensor_tools.h.

{ return a * b; }

References b.

is_zero()

template<typename T >

LIBMESH_DEVICE_INLINE bool libMesh::TensorTools::is_zero

(

const T &

a

)

Definition at line 134 of file tensor_tools.h.

{ return a.is_zero();}

norm() [1/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm

(

const T &

a

)

Definition at line 74 of file tensor_tools.h.

{ using std::abs; return abs(a); }

Referenced by norm_sq().

norm() [2/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm

(

const TensorValue< T > &

a

)

-> decltype(TensorTools::norm(T()))

Definition at line 98 of file tensor_tools.h.

{return a.norm();}

norm() [3/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm

(

const TypeTensor< T > &

a

)

-> decltype(TensorTools::norm(T()))

Definition at line 93 of file tensor_tools.h.

{return a.norm();}

norm() [4/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm

(

const TypeVector< T > &

a

)

-> decltype(TensorTools::norm(T()))

Definition at line 83 of file tensor_tools.h.

{return a.norm();}

norm() [5/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm

(

const VectorValue< T > &

a

)

-> decltype(TensorTools::norm(T()))

Definition at line 88 of file tensor_tools.h.

{return a.norm();}

norm() [6/6]

template<typename T >

LIBMESH_DEVICE_INLINE T libMesh::TensorTools::norm

(

std::complex< T >

a

)

Definition at line 79 of file tensor_tools.h.

{ using std::abs; return abs(a); }

norm_sq() [1/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm_sq

(

const T &

a

)

Definition at line 104 of file tensor_tools.h.

{ return a * libmesh_conj(a); }

References libMesh::libmesh_conj().

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::KellyErrorEstimator::internal_side_integration(), libMesh::DenseSubVector< T >::l2_norm(), libMesh::DenseVector< T >::l2_norm(), libMesh::DistributedVector< T >::l2_norm(), libMesh::DenseSubVector< T >::linfty_norm(), libMesh::Kokkos::vector_ref< ViewType >::norm_sq(), libMesh::Kokkos::tensor_ref< ViewType >::norm_sq(), libMesh::TypeTensor< T >::norm_sq(), libMesh::TypeVector< T >::norm_sq(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), and libMesh::HPCoarsenTest::select_refinement().

norm_sq() [2/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm_sq

(

const TensorValue< T > &

a

)

Definition at line 128 of file tensor_tools.h.

{return a.norm_sq();}

References libMesh::TypeTensor< T >::norm_sq().

norm_sq() [3/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm_sq

(

const TypeTensor< T > &

a

)

Definition at line 123 of file tensor_tools.h.

{return a.norm_sq();}

References libMesh::TypeTensor< T >::norm_sq().

norm_sq() [4/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm_sq

(

const TypeVector< T > &

a

)

Definition at line 113 of file tensor_tools.h.

{return a.norm_sq();}

References libMesh::TypeVector< T >::norm_sq().

norm_sq() [5/6]

template<typename T >

LIBMESH_DEVICE_INLINE auto libMesh::TensorTools::norm_sq

(

const VectorValue< T > &

a

)

Definition at line 118 of file tensor_tools.h.

{return a.norm_sq();}

References libMesh::TypeVector< T >::norm_sq().

norm_sq() [6/6]

template<typename T >

LIBMESH_DEVICE_INLINE T libMesh::TensorTools::norm_sq

(

std::complex< T >

a

)

Definition at line 109 of file tensor_tools.h.

{ using std::norm; return norm(a); }

References std::norm(), and norm().