Represents an arbitrary function defined on an element. More...

#include <function.h>

Inheritance diagram for Hermes::Hermes2D::Function< Scalar >:

Classes
struct	Node

Public Member Functions
	Function ()
	Default constructor.

virtual	~Function ()

int	get_num_components () const
	Returns the number of components of the function being represented by the class.

Scalar *	get_fn_values (int component=0)
	Returns function values. More...

Scalar *	get_dx_values (int component=0)
	Returns the x partial derivative. More...

Scalar *	get_dy_values (int component=0)
	Returns the y partial derivative. More...

void	get_dx_dy_values (Scalar &dx, Scalar &dy, int component=0)
	Returns both x and y partial derivatives. This function provides the both often-used dx and dy values in one call. More...

Scalar *	get_dxx_values (int component=0)
	Returns the second x partial derivative. More...

Scalar *	get_dyy_values (int component=0)
	Returns the second y partial derivative. More...

Scalar *	get_dxy_values (int component=0)
	Returns the second mixed derivative. More...

Quad2D *	get_quad_2d () const
	Returns the current quadrature points.

void	set_quad_order (unsigned int order, int mask=H2D_FN_DEFAULT)

Scalar *	get_values (int a, int b)

int	get_fn_order () const
	Returns the polynomial degree of the function being represented by the class.

Public Member Functions inherited from Hermes::Hermes2D::Transformable
Element *	get_active_element () const

void	set_transform (uint64_t idx)

uint64_t	get_transform () const

virtual void	push_transform (int son)

Protected Member Functions
virtual void	set_quad_2d (Quad2D *quad_2d)
	Selects the quadrature points in which the function will be evaluated. More...

virtual void	free ()=0
	Frees all precalculated tables.

virtual int	get_edge_fn_order (int edge) const
	Returns the polynomial degree of the function at given edge. To be overridden in derived classes. More...

virtual void	precalculate (int order, int mask)=0
	precalculates the current function at the current integration points.

void	update_nodes_ptr ()

void	force_transform (uint64_t sub_idx, Trf *ctm)
	For internal use only.

Node *	new_node (int mask, int num_points)
	allocates a new Node structure

virtual void	handle_overflow_idx ()=0

void	replace_cur_node (Node *node)

Protected Member Functions inherited from Hermes::Hermes2D::Transformable
virtual void	set_active_element (Element *e)

virtual void	pop_transform ()

void	reset_transform ()
	Empties the stack, loads identity transform.

double	get_transform_jacobian () const

Trf *	get_ctm () const

unsigned int	get_depth () const

Static Protected Member Functions
static void	check_params (int component, Node *cur_node, int num_components)

static void	check_table (int component, Node cur_node, int n, const char msg)

Static Protected Member Functions inherited from Hermes::Hermes2D::Transformable
static void	push_transforms (std::set< Transformable * > &transformables, int son)

static void	pop_transforms (std::set< Transformable * > &transformables)

Protected Attributes
int	order
	current function polynomial order

int	num_components
	number of vector components

std::map< uint64_t, LightArray < Node * > * > *	sub_tables
	Table of Node tables, for each possible transformation there can be a different Node table.

LightArray< Node * > *	nodes
	Table of nodes.

Node *	cur_node
	Current Node.

LightArray< Node * > *	overflow_nodes
	Nodes for the overflow sub-element transformation.

Quad2D *	quads [8]
	list of available quadratures

int	cur_quad
	active quadrature (index into 'quads')

int	total_mem
	total memory in bytes used by the tables

int	max_mem
	peak memory usage

Protected Attributes inherited from Hermes::Hermes2D::Transformable
Element *	element
	The active element.

Trf *	ctm
	Current sub-element transformation matrix.

uint64_t	sub_idx
	Sub-element transformation index.

Trf	stack [21]
	Transformation matrix stack.

unsigned int	top
	Stack top.

Static Protected Attributes
static int	idx2mask [6][2]
	index to mask table More...

Static Protected Attributes inherited from Hermes::Hermes2D::Transformable
static const unsigned int	H2D_MAX_TRN_LEVEL = 15

static const uint64_t	H2D_MAX_IDX = (1ULL << 3 * H2D_MAX_TRN_LEVEL) - 1

Friends
template<typename T >
class	KellyTypeAdapt

template<typename T >
class	RefinementSelectors::H1ProjBasedSelector

template<typename T >
class	RefinementSelectors::L2ProjBasedSelector

template<typename T >
class	RefinementSelectors::HcurlProjBasedSelector

template<typename T >
class	Adapt

class	Views::Orderizer

class	Views::Vectorizer

class	Views::Linearizer

template<typename T >
class	DiscontinuousFunc

template<typename T >
class	DiscreteProblem

template<typename T >
class	DiscreteProblemLinear

template<typename T >
class	Global

class	CurvMap

template<typename T >
class	Func

template<typename T >
class	Geom

template<typename T >
class	Filter

template<typename T >
class	SimpleFilter

template<typename T >
class	DXDYFilter

class	ComplexFilter

class	VonMisesFilter

HERMES_API Geom< double > *	init_geom_vol (RefMap *rm, const int order)
	Init element geometry for volumetric integrals.

HERMES_API Geom< double > *	init_geom_surf (RefMap rm, SurfPos surf_pos, const int order)

HERMES_API Func< double > *	init_fn (PrecalcShapeset fu, RefMap rm, const int order)
	Init the shape function for the evaluation of the volumetric/surface integral (transformation of values).

template<typename T >
HERMES_API Func< T > *	init_fn (MeshFunction< T > *fu, const int order)

Detailed Description

template<typename Scalar>
class Hermes::Hermes2D::Function< Scalar >

Represents an arbitrary function defined on an element.

The Function class is an abstraction of a function defined in integration points on an element. You first specify what quadrature tables you want to use (set_quad_2d()) and select an element (Transformable::set_active_element()). Then you select concrete integration points (set_quad_order()) and obtain the function values by calling one of the functions get_fn_values(), get_dx_values(), etc.

This class is a template for RealFunction and ScalarFunction, depending of which type the function values are. For example, shape functions are always Real (see PrecalcShapeset), while the solution can be complex (see Solution).

The design goal for this class is to define a single common interface for functions used as integrands in the weak formulation. It should not matter whether you are integrating a shape function or, for example, a previous solution of the PDE in time-dependent problems. Ideally, you should also be able to apply the bilinear form not only to shape functions during assembling, but also to the solution when calculating energy norms etc. The last feature is unfortunately limited to Real code, because a PDE solution can be complex (hence Solution inherits from ScalarFunction), but shape functions are Real and for efficiency the bilinear form only takes RealFunction arguments.

Since this class inherits from Transformable, you can obtain function values in integration points transformed to sub-areas of the current element (see push_transform(), pop_transform()).

Definition at line 98 of file function.h.

Constructor & Destructor Documentation

template<typename Scalar >

Hermes::Hermes2D::Function< Scalar >::~Function ( )

virtual

Default destructor. Added to delete Function::sub_tables.

Definition at line 53 of file function.cpp.

Member Function Documentation

template<typename Scalar>

void Hermes::Hermes2D::Function< Scalar >::get_dx_dy_values	(	Scalar *&	dx,
		Scalar *&	dy,
		int	component = `0`
	)

Returns both x and y partial derivatives. This function provides the both often-used dx and dy values in one call.

Parameters

dx[out]	Variable which receives the pointer to the first partial derivatives by x
dy[out]	Variable which receives the pointer to the first partial derivatives by y
component[in]	The component of the function (0 or 1).

Definition at line 116 of file function.cpp.

Referenced by Hermes::Hermes2D::VonMisesFilter::precalculate().

template<typename Scalar >

Scalar * Hermes::Hermes2D::Function< Scalar >::get_dx_values ( int component = 0 )

Returns the x partial derivative.

Parameters

component[in] The component of the function (0 or 1).

Returns: The x partial derivative of the function at all points of the current integration rule.

Definition at line 102 of file function.cpp.

Referenced by Hermes::Hermes2D::init_fn(), Hermes::Hermes2D::RefinementSelectors::H1ProjBasedSelector< Scalar >::precalc_ref_solution(), and Hermes::Hermes2D::RefinementSelectors::HcurlProjBasedSelector< Scalar >::precalc_ref_solution().

template<typename Scalar >

Scalar * Hermes::Hermes2D::Function< Scalar >::get_dxx_values ( int component = 0 )

Returns the second x partial derivative.

Parameters

component[in] The component of the function (0 or 1).

Returns: The x second partial derivative of the function at all points of the current integration rule.

Definition at line 124 of file function.cpp.

Referenced by Hermes::Hermes2D::init_fn().

template<typename Scalar >

Scalar * Hermes::Hermes2D::Function< Scalar >::get_dxy_values ( int component = 0 )

Returns the second mixed derivative.

Parameters

component[in] The component of the function (0 or 1).

Returns: The second mixed derivative of the function at all points of the current integration rule.

Definition at line 138 of file function.cpp.

Referenced by Hermes::Hermes2D::init_fn().

template<typename Scalar >

Scalar * Hermes::Hermes2D::Function< Scalar >::get_dy_values ( int component = 0 )

Returns the y partial derivative.

Parameters

component[in] The component of the function (0 or 1).

Returns: The y partial derivative of the function at all points of the current integration rule.

Definition at line 109 of file function.cpp.

Referenced by Hermes::Hermes2D::init_fn(), Hermes::Hermes2D::RefinementSelectors::H1ProjBasedSelector< Scalar >::precalc_ref_solution(), and Hermes::Hermes2D::RefinementSelectors::HcurlProjBasedSelector< Scalar >::precalc_ref_solution().

template<typename Scalar >

Scalar * Hermes::Hermes2D::Function< Scalar >::get_dyy_values ( int component = 0 )

Returns the second y partial derivative.

Parameters

component[in] The component of the function (0 or 1).

Returns: The y second partial derivative of the function at all points of the current integration rule.

Definition at line 131 of file function.cpp.

Referenced by Hermes::Hermes2D::init_fn().

template<typename Scalar >

int Hermes::Hermes2D::Function< Scalar >::get_edge_fn_order ( int edge ) const

protectedvirtual

Returns the polynomial degree of the function at given edge. To be overridden in derived classes.

Parameters

edge[in] Edge at which the order should be evaluated. (0-3)

Definition at line 64 of file function.cpp.

template<typename Scalar >

Scalar * Hermes::Hermes2D::Function< Scalar >::get_fn_values ( int component = 0 )

Returns function values.

Parameters

component[in] The component of the function (0 or 1).

Returns: The values of the function at all points of the current integration rule.

Definition at line 95 of file function.cpp.

Referenced by Hermes::Hermes2D::init_fn(), Hermes::Hermes2D::RefinementSelectors::L2ProjBasedSelector< Scalar >::precalc_ref_solution(), Hermes::Hermes2D::RefinementSelectors::H1ProjBasedSelector< Scalar >::precalc_ref_solution(), Hermes::Hermes2D::RefinementSelectors::HcurlProjBasedSelector< Scalar >::precalc_ref_solution(), Hermes::Hermes2D::DXDYFilter< Scalar >::precalculate(), and Hermes::Hermes2D::VonMisesFilter::precalculate().

template<typename Scalar >

void Hermes::Hermes2D::Function< Scalar >::set_quad_2d ( Quad2D * quad_2d )

protectedvirtual

Selects the quadrature points in which the function will be evaluated.

It is possible to switch back and forth between different quadrature points: no precalculated values are freed. The standard quadrature is always selected by default already.

Parameters

quad_2d[in] The quadrature points.

Reimplemented in Hermes::Hermes2D::ComplexFilter, Hermes::Hermes2D::MeshFunction< Scalar >, Hermes::Hermes2D::MeshFunction< double >, Hermes::Hermes2D::MeshFunction< std::complex< double > >, Hermes::Hermes2D::Filter< Scalar >, Hermes::Hermes2D::Filter< double >, and Hermes::Hermes2D::Filter< std::complex< double > >.

Definition at line 151 of file function.cpp.

Referenced by Hermes::Hermes2D::MeshFunction< Scalar >::set_quad_2d().

template<typename Scalar >

void Hermes::Hermes2D::Function< Scalar >::set_quad_order	(	unsigned int	order,
		int	mask = `H2D_FN_DEFAULT`
	)

Activates an integration rule of the specified order. Subsequent calls to get_values(), get_dx_values() etc. will be returning function values at these points.

Parameters

order[in]	Integration rule order.
mask[in]	A combination of one or more of the constants H2D_FN_VAL, H2D_FN_DX, H2D_FN_DY, H2D_FN_DXX, H2D_FN_DYY, H2D_FN_DXY specifying the values which should be precalculated. The default is H2D_FN_VAL \| H2D_FN_DX \| H2D_FN_DY. You can also use H2D_FN_ALL to precalculate everything.

Definition at line 76 of file function.cpp.

Referenced by Hermes::Hermes2D::RefinementSelectors::ProjBasedSelector< Scalar >::calc_projection_errors(), Hermes::Hermes2D::init_fn(), and Hermes::Hermes2D::VonMisesFilter::precalculate().

template<typename Scalar >

void Hermes::Hermes2D::Function< Scalar >::update_nodes_ptr ( )

protected

With changed sub-element mapping, there comes the need for a change of the current Node table nodes.

Definition at line 217 of file function.cpp.

Referenced by Hermes::Hermes2D::MeshFunction< Scalar >::pop_transform(), and Hermes::Hermes2D::MeshFunction< Scalar >::push_transform().

Member Data Documentation

template<typename Scalar>

int Hermes::Hermes2D::Function< Scalar >::idx2mask

staticprotected

Initial value:

=
    {
      { H2D_FN_VAL_0, H2D_FN_VAL_1 }, { H2D_FN_DX_0,  H2D_FN_DX_1  }, { H2D_FN_DY_0,  H2D_FN_DY_1  },
      { H2D_FN_DXX_0, H2D_FN_DXX_1 }, { H2D_FN_DYY_0, H2D_FN_DYY_1 }, { H2D_FN_DXY_0, H2D_FN_DXY_1 }
    }

index to mask table

Definition at line 240 of file function.h.

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

Classes

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

template<typename Scalar> class Hermes::Hermes2D::Function< Scalar >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename Scalar>
class Hermes::Hermes2D::Function< Scalar >