Function integral info class. More...

#include <function_integral_info.hpp>

Public Types
typedef DataType_	DataType
	the underlying scalar data type More...

typedef GradientType_	GradientType
	the function gradient type More...

typedef HessianType_	HessianType
	the function hessian type More...

typedef ValueType_	ValueType
	the function value type More...

Public Member Functions
	FunctionIntegralInfo ()
	Constructor. More...

template<int m_, int n_, int sm_, int sn_>
void	add_grad (DataType omega, const Tiny::Matrix< DataType, m_, n_, sm_, sn_ > &g)
	Assembly helper function: adds another function gradient. More...

template<int n_, int sn_>
void	add_grad (DataType omega, const Tiny::Vector< DataType, n_, sn_ > &g)
	Assembly helper function: adds another function gradient. More...

template<int m_, int n_, int sm_, int sn_>
void	add_hess (DataType omega, const Tiny::Matrix< DataType, m_, n_, sm_, sn_ > &h)
	Assembly helper function: adds another function hessian. More...

template<int l_, int m_, int n_, int sl_, int sm_, int sn_>
void	add_hess (DataType omega, const Tiny::Tensor3< DataType, l_, m_, n_, sl_, sm_, sn_ > &h)
	Assembly helper function: adds another function hessian. More...

void	add_value (DataType omega, const DataType &v)
	Assembly helper function: adds another function value. More...

template<int n_, int sn_>
void	add_value (DataType omega, const Tiny::Vector< DataType, n_, sn_ > &v)
	Assembly helper function: adds another function value. More...

void	format ()
	Formats the local values. More...

String	print_field_info (int precision=0, std::size_t pad_size=15u, char pad_char='.') const
	Prints the additional field information to a formatted string and returns it. More...

String	print_norms (int precision=0, std::size_t pad_size=15u, char pad_char='.') const
	Prints all (computed) norms to a formatted string and returns it. More...

void	push (const FunctionIntegralInfo &other)
	Assembly helper function: adds another info object. More...

void	synchronize (const Dist::Comm &comm)
	Synchronizes the function integral information over a communicator. More...

Public Attributes
DataType	divergence_l2_sqr
	squared L2-norm of the vector field divergence More...

GradientType_	grad
	Integral of the function gradient. More...

HessianType_	hess
	Integral of the function hessian. More...

int	max_der
	the maximum derivative for which the integrals have been computed More...

DataType_	norm_h0_sqr
	squared H0-norm (aka L2-norm) of the function More...

ValueType_	norm_h0_sqr_comp
	the component-wise squared H0-norm (only for vector fields) More...

DataType_	norm_h1_sqr
	squared H1-semi-norm of the function More...

ValueType_	norm_h1_sqr_comp
	the component-wise squared H1-semi-norm (only for vector fields) More...

DataType_	norm_h2_sqr
	squared H2-semi-norm of the function More...

ValueType_	norm_h2_sqr_comp
	the component-wise squared H2-semi-norm (only for vector fields) More...

DataType_	norm_l1
	L1-norm of the function. More...

ValueType_	norm_l1_comp
	the component-wise L1-norm (only for vector fields) More...

DataType_	norm_lmax
	Lmax-norm of the function. More...

ValueType_	norm_lmax_comp
	the component-wise Lmax-norm (only for vector fields) More...

ValueType_	value
	Integral of the function value. More...

DataType	vorticity_l2_sqr
	squared L2-norm of the vector field vorticity More...

Detailed Description

template<typename DataType_, typename ValueType_, typename GradientType_, typename HessianType_>
class FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >

Function integral info class.

This class is used to store and manage the results of a AnalyticFunctionIntegralJob, DiscreteFunctionIntegralJob or ErrorFunctionIntegralJob. It contains all the integral values as well as a bunch of auxiliary helper functions which are used during the assembly process.

Template Parameters

DataType_	The scalar datatype used during the assembly.
ValueType	The type of a function value. This corresponds to DataType_ for scalar functions and to Tiny::Vector<DataType_,...> for (blocked) vector fields.
GradientType	The type of a function gradient. This corresponds to Tiny::Vector<DataType_,...> for scalar functions and to Tiny::Matrix<DataType_, ...> for (blocked) vector fields.
HessianType	The type of a function hessian. This corresponds to Tiny::Matrix<DataType_,...> for scalar functions and to Tiny::Tensor3<DataType_, ...> for (blocked) vector fields.

Author: Peter Zajac

Definition at line 44 of file function_integral_info.hpp.

Member Typedef Documentation

◆ DataType

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

typedef DataType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::DataType

the underlying scalar data type

Definition at line 48 of file function_integral_info.hpp.

◆ GradientType

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

typedef GradientType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::GradientType

the function gradient type

Definition at line 52 of file function_integral_info.hpp.

◆ HessianType

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

typedef HessianType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::HessianType

the function hessian type

Definition at line 54 of file function_integral_info.hpp.

◆ ValueType

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

typedef ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::ValueType

the function value type

Definition at line 50 of file function_integral_info.hpp.

Constructor & Destructor Documentation

◆ FunctionIntegralInfo()

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::FunctionIntegralInfo ( )

inline

Constructor.

Definition at line 317 of file function_integral_info.hpp.

Member Function Documentation

◆ add_grad() [1/2]

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

template<int m_, int n_, int sm_, int sn_>

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad	(	DataType	omega,
		const Tiny::Matrix< DataType, m_, n_, sm_, sn_ > &	g
	)

inline

Assembly helper function: adds another function gradient.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in]	omega	The cubature weight.
[in]	g	The function gradient in the cubature point.

Definition at line 466 of file function_integral_info.hpp.

References FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::divergence_l2_sqr, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::grad, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h1_sqr, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h1_sqr_comp, FEAT::Math::sqr(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::trace(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::vorticity_l2_sqr.

◆ add_grad() [2/2]

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

template<int n_, int sn_>

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad	(	DataType	omega,
		const Tiny::Vector< DataType, n_, sn_ > &	g
	)

inline

Assembly helper function: adds another function gradient.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in]	omega	The cubature weight.
[in]	g	The function gradient in the cubature point.

Definition at line 448 of file function_integral_info.hpp.

References FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::grad, FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_sqr(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h1_sqr.

◆ add_hess() [1/2]

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

template<int m_, int n_, int sm_, int sn_>

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_hess	(	DataType	omega,
		const Tiny::Matrix< DataType, m_, n_, sm_, sn_ > &	h
	)

inline

Assembly helper function: adds another function hessian.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in]	omega	The cubature weight.
[in]	h	The function hessian in the cubature point.

Definition at line 495 of file function_integral_info.hpp.

References FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::hess, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h2_sqr, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_hessian_sqr().

◆ add_hess() [2/2]

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

template<int l_, int m_, int n_, int sl_, int sm_, int sn_>

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_hess	(	DataType	omega,
		const Tiny::Tensor3< DataType, l_, m_, n_, sl_, sm_, sn_ > &	h
	)

inline

Assembly helper function: adds another function hessian.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in]	omega	The cubature weight.
[in]	h	The function hessian in the cubature point.

Definition at line 513 of file function_integral_info.hpp.

References FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::hess, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h2_sqr, and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h2_sqr_comp.

◆ add_value() [1/2]

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value	(	DataType	omega,
		const DataType &	v
	)

inline

Assembly helper function: adds another function value.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in]	omega	The cubature weight.
[in]	v	The function value in the cubature point.

Definition at line 398 of file function_integral_info.hpp.

References FEAT::Math::abs(), FEAT::Math::max(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h0_sqr, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_l1, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_lmax, FEAT::Math::sqr(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::value.

◆ add_value() [2/2]

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

template<int n_, int sn_>

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value	(	DataType	omega,
		const Tiny::Vector< DataType, n_, sn_ > &	v
	)

inline

Assembly helper function: adds another function value.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in]	omega	The cubature weight.
[in]	v	The function value in the cubature point.

Definition at line 420 of file function_integral_info.hpp.

References FEAT::Math::abs(), FEAT::Math::max(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h0_sqr, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h0_sqr_comp, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_l1, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_l1_comp, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_lmax, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_lmax_comp, FEAT::Math::sqr(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::value.

◆ format()

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format ( )

inline

Formats the local values.

Definition at line 340 of file function_integral_info.hpp.

◆ print_field_info()

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

String FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_field_info	(	int	precision = `0`,
		std::size_t	pad_size = `15u`,
		char	pad_char = `'.'`
	)		const

inline

Prints the additional field information to a formatted string and returns it.

This function prints the kinetic energy, the vorticity and the divergence.

Parameters

[in]	precision	The number of digits to print. Default to 0, which prints a default number of digits.
[in]	pad_size	The number of characters for the padding. Should be >= 9 to enable a vertically aligned output.
[in]	pad_char	The character used for padding. Defaults to a dot.

Returns: A formatted multi-line string that contains all the additional field information.

Definition at line 647 of file function_integral_info.hpp.

References FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::divergence_l2_sqr, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::max_der, FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h0_sqr, FEAT::String::pad_back(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::vorticity_l2_sqr.

◆ print_norms()

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

String FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms	(	int	precision = `0`,
		std::size_t	pad_size = `15u`,
		char	pad_char = `'.'`
	)		const

inline

Prints all (computed) norms to a formatted string and returns it.

Parameters

[in]	precision	The number of digits to print. Defaults to 0, which prints a default number of digits.
[in]	pad_size	The number of characters for the padding. Should be >= 9 to enable a vertically aligned output.
[in]	pad_char	The character used for padding. Defaults to a dot.

Note: This function does not print the divergence or vorticity, even if these have been computed; call print_field_info() to have these printed.

Returns: A formatted multi-line string that contains all the computed norms.

Definition at line 612 of file function_integral_info.hpp.

◆ push()

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push ( const FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ > & other )

inline

Assembly helper function: adds another info object.

This function is used by the assembly and is not meant to be used elsewhere.

Parameters

[in] other The other integral info that is to be incorporated into this one.

Definition at line 368 of file function_integral_info.hpp.

◆ synchronize()

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

void FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize ( const Dist::Comm & comm )

inline

Synchronizes the function integral information over a communicator.

This function sums up the function integral information of all patches in a parallel simulation to obtain the information for the global mesh.

Parameters

[in] comm The transient communicator over which to synchronize.

Definition at line 533 of file function_integral_info.hpp.

Member Data Documentation

◆ divergence_l2_sqr

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::divergence_l2_sqr

squared L2-norm of the vector field divergence

This entry stores the squared L2-norm of the divergence of the vector field:

\[ \| \nabla \cdot u\|_{\mathcal{L}^2}^2 = \Big(\int_\Omega \big(\sum_{i=1}^d \partial_i u_i\big)^2\Big)^{\frac{1}{2}}\]

Note: This entry is only meaningful if u is a vector field from R^n to R^n with n=2 or n=3.

Definition at line 153 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_field_info(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ grad

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

GradientType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::grad

Integral of the function gradient.

This entry stores the integral of the function gradient if max_der >= 1, i.e. it is

\[g \in\mathbb{R}^n;\quad g_i := \int_\Omega \partial_i u(x)~dx \]

Definition at line 73 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ hess

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

HessianType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::hess

Integral of the function hessian.

This entry stores the integral of the function gradient if max_der >= 2, i.e. it is

\[h \in\mathbb{R}^{n\times n};\quad h_{ij} := \int_\Omega \partial_i\partial_j u(x)~dx \]

Definition at line 81 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_hess(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ max_der

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

int FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::max_der

the maximum derivative for which the integrals have been computed

Definition at line 57 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_field_info(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms().

◆ norm_h0_sqr

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h0_sqr

squared H0-norm (aka L2-norm) of the function

This entry stores the squared H0-norm of the function if max_der >= 0, i.e. it is

\[|u|_{H^0} := \int_\Omega (u(x))^2~dx \]

For vector fields, this is simply the sum of all component-wise H0-norms.

Definition at line 91 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_field_info(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_h0_sqr_comp

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h0_sqr_comp

the component-wise squared H0-norm (only for vector fields)

Definition at line 134 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_h1_sqr

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h1_sqr

squared H1-semi-norm of the function

This entry stores the squared H1-semi-norm of the function if max_der >= 1, i.e. it is

\[|u|_{H^1} := \sum_{1\leq i\leq n}\int_\Omega (\partial_i u(x))^2~dx \]

For vector fields, this is simply the sum of all component-wise H1-semi-norms.

Definition at line 101 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_h1_sqr_comp

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h1_sqr_comp

the component-wise squared H1-semi-norm (only for vector fields)

Definition at line 136 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_h2_sqr

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h2_sqr

squared H2-semi-norm of the function

This entry stores the squared H2-semi-norm of the function if max_der >= 2, i.e. it is

\[|u|_{H^2} := \sum_{1\leq i,j\leq n}\int_\Omega (\partial_i \partial_j u(x))^2~dx \]

For vector fields, this is simply the sum of all component-wise H2-semi-norms.

Definition at line 111 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_hess(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_h2_sqr_comp

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_h2_sqr_comp

the component-wise squared H2-semi-norm (only for vector fields)

Definition at line 138 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_hess(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_l1

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_l1

L1-norm of the function.

This entry stores the L1-norm of the function if max_der >= 0, i.e. it is

\[|u|_{L^1} := \int_\Omega |u(x)|~dx \]

For vector fields, this is simply the sum of all component-wise L1-norms.

Definition at line 121 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_l1_comp

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_l1_comp

the component-wise L1-norm (only for vector fields)

Definition at line 140 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_lmax

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_lmax

Lmax-norm of the function.

This entry stores the Lmax-norm of the function if max_der >= 0, i.e. it is

\[|u|_{L^\infty} := \max_{x\in\Omega} |u(x)| \]

For vector fields, this is simply the sum of all component-wise Lmax-norms.

Definition at line 131 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ norm_lmax_comp

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::norm_lmax_comp

the component-wise Lmax-norm (only for vector fields)

Definition at line 142 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_norms(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ value

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

ValueType_ FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::value

Integral of the function value.

This entry stores the integral of the function value if max_der >= 0, i.e. it is

\[v \in\mathbb{R};\quad v := \int_\Omega u(x)~dx \]

Definition at line 65 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_value(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

◆ vorticity_l2_sqr

template<typename DataType_ , typename ValueType_ , typename GradientType_ , typename HessianType_ >

DataType FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::vorticity_l2_sqr

squared L2-norm of the vector field vorticity

This entry stores the squared L2-norm of the curl of the vector field:

\[ \| \nabla \times u\|_{\mathcal{L}^2}^2 \]

Note: This entry is only meaningful if u is a vector field from R^n to R^n with n=2 or n=3.

Definition at line 164 of file function_integral_info.hpp.

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::format(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::print_field_info(), FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::push(), and FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::synchronize().

The documentation for this class was generated from the following file:

kernel/assembly/function_integral_info.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ DataType

◆ GradientType

◆ HessianType

◆ ValueType

Constructor & Destructor Documentation

◆ FunctionIntegralInfo()

Member Function Documentation

◆ add_grad() [1/2]

◆ add_grad() [2/2]

◆ add_hess() [1/2]

◆ add_hess() [2/2]

◆ add_value() [1/2]

◆ add_value() [2/2]

◆ format()

◆ print_field_info()

◆ print_norms()

◆ push()

◆ synchronize()

Member Data Documentation

◆ divergence_l2_sqr

◆ grad

◆ hess

◆ max_der

◆ norm_h0_sqr

◆ norm_h0_sqr_comp

◆ norm_h1_sqr

◆ norm_h1_sqr_comp

◆ norm_h2_sqr

◆ norm_h2_sqr_comp

◆ norm_l1

◆ norm_l1_comp

◆ norm_lmax

◆ norm_lmax_comp

◆ value

◆ vorticity_l2_sqr