Hermes2D  3.0
Hermes::Hermes2D::Function< Scalar > Class Template Referenceabstract

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

#include <function.h>

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

Public Member Functions

 Function ()
 Default constructor.
 
virtual ~Function ()
 
unsigned char get_num_components () const
 Returns the number of components of the function being represented by the class.
 
virtual const Scalar * get_fn_values (int component=0) const
 Returns function values. More...
 
virtual const Scalar * get_dx_values (int component=0) const
 Returns the x partial derivative. More...
 
virtual const Scalar * get_dy_values (int component=0) const
 Returns the y partial derivative. More...
 
Scalar * deep_copy_array (int component=0, int item=0) const
 Returns function values. More...
 
Quad2Dget_quad_2d () const
 Returns the current quadrature points.
 
void set_quad_order (unsigned short order, unsigned short mask=H2D_FN_DEFAULT)
 
virtual const Scalar * get_values (int component, int item) const
 
virtual int get_fn_order () const
 Returns the polynomial degree of the function being represented by the class.
 
virtual void push_transform (int son)
 
virtual void pop_transform ()
 
virtual void set_active_element (Element *e)
 Sets the active element.
 
virtual void set_transform (uint64_t idx)
 
- Public Member Functions inherited from Hermes::Hermes2D::Transformable
Elementget_active_element () const
 
uint64_t get_transform () const
 

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 reset_transform ()
 Empties the stack, loads identity transform.
 
virtual void force_transform (uint64_t sub_idx, Trf *ctm)
 For internal use only.
 
virtual void free ()=0
 Frees all precalculated tables.
 
virtual int get_edge_fn_order (unsigned char edge) const
 Returns the polynomial degree of the function at given edge. To be overridden in derived classes. More...
 
virtual void precalculate (unsigned short order, unsigned short mask)
 precalculates the current function at the current integration points.
 
void invalidate_values ()
 
- Protected Member Functions inherited from Hermes::Hermes2D::Transformable
double get_transform_jacobian () const
 
Trfget_ctm () const
 
unsigned int get_depth () const
 

Protected Attributes

Scalar values [H2D_MAX_SOLUTION_COMPONENTS][H2D_NUM_FUNCTION_VALUES][H2D_MAX_INTEGRATION_POINTS_COUNT]
 The data.
 
bool values_valid
 Flag that the data are not 'dirty'.
 
int order
 Current function polynomial order.
 
unsigned char num_components
 Number of vector components.
 
Quad2Dquads [H2D_MAX_QUADRATURES]
 List of available quadratures.
 
int cur_quad
 Active quadrature (index into 'quads')
 
- Protected Attributes inherited from Hermes::Hermes2D::Transformable
Elementelement
 The active element.
 
Trfctm
 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 [H2D_NUM_FUNCTION_VALUES][2]
 Index to mask table. More...
 
- Static Protected Attributes inherited from Hermes::Hermes2D::Transformable
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
 
template<typename T >
class DiscontinuousFunc
 
template<typename T >
class DiscreteProblem
 
class CurvMap
 
template<typename T >
class Func
 
template<typename T >
class Filter
 
template<typename T >
class SimpleFilter
 
template<typename T >
class DXDYFilter
 
class ComplexFilter
 
class VonMisesFilter
 
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)
 

Additional Inherited Members

- Static Public Attributes inherited from Hermes::Hermes2D::Transformable
static const unsigned int H2D_MAX_TRN_LEVEL = 15
 If this changes, NeighborSearch::H2D_MAX_NEIGHBORS must change too.
 
- 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)
 

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 106 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 42 of file function.cpp.

Member Function Documentation

template<typename Scalar >
Scalar * Hermes::Hermes2D::Function< Scalar >::deep_copy_array ( int  component = 0,
int  item = 0 
) const

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 212 of file function.cpp.

template<typename Scalar >
const Scalar * Hermes::Hermes2D::Function< Scalar >::get_dx_values ( int  component = 0) const
virtual

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.

Reimplemented in Hermes::Hermes2D::PrecalcShapesetAssembling.

Definition at line 175 of file function.cpp.

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

template<typename Scalar >
const Scalar * Hermes::Hermes2D::Function< Scalar >::get_dy_values ( int  component = 0) const
virtual

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.

Reimplemented in Hermes::Hermes2D::PrecalcShapesetAssembling.

Definition at line 182 of file function.cpp.

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

template<typename Scalar >
int Hermes::Hermes2D::Function< Scalar >::get_edge_fn_order ( unsigned char  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 53 of file function.cpp.

template<typename Scalar >
const Scalar * Hermes::Hermes2D::Function< Scalar >::get_fn_values ( int  component = 0) const
virtual
template<typename Scalar >
void Hermes::Hermes2D::Function< Scalar >::invalidate_values ( )
protected

With changed sub-element mapping, or an element, or anything else there comes the need for a change of the current values. This invalidates the current values. See values_valid

Definition at line 135 of file function.cpp.

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::PrecalcShapeset, Hermes::Hermes2D::Filter< Scalar >, Hermes::Hermes2D::Filter< double >, and Hermes::Hermes2D::Filter< std::complex< double > >.

Definition at line 79 of file function.cpp.

Referenced by Hermes::Hermes2D::PrecalcShapeset::set_quad_2d(), and Hermes::Hermes2D::UExtFunction< Scalar >::UExtFunction().

template<typename Scalar >
void Hermes::Hermes2D::Function< Scalar >::set_quad_order ( unsigned short  order,
unsigned short  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, ...

Definition at line 59 of file function.cpp.

Referenced by Hermes::Hermes2D::RefinementSelectors::ProjBasedSelector< Scalar >::calc_projection_errors(), Hermes::Hermes2D::CurvMapStatic::calculate_bubble_projection_matrix(), and Hermes::Hermes2D::init_fn_preallocated().

template<typename Scalar >
void Hermes::Hermes2D::Function< Scalar >::set_transform ( uint64_t  idx)
virtual

Sets the current transform at once as if it was created by multiple calls to push_transform().

Parameters
idx[in]The number of the sub-element, as returned by get_transform().

Reimplemented from Hermes::Hermes2D::Transformable.

Definition at line 155 of file function.cpp.

Referenced by Hermes::Hermes2D::NeighborSearch< Scalar >::init_ext_fn(), and Hermes::Hermes2D::CurvMap::update_refmap_coeffs().

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 },
}

Index to mask table.

Definition at line 231 of file function.h.


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