Represents the solution of a PDE.
More...

#include <solution.h>

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

Public Member Functions
	Solution (MeshSharedPtr mesh)

	Solution (SpaceSharedPtr< Scalar > s, Vector< Scalar > *coeff_vec)

	Solution (SpaceSharedPtr< Scalar > s, Scalar *coeff_vec)

virtual bool	isOkay () const
	State querying helpers.

virtual std::string	getClassName () const

virtual void	copy (const MeshFunction< Scalar > *sln)
	Copy from sln to this instance.

void	set_dirichlet_lift (SpaceSharedPtr< Scalar > space)
	Sets solution equal to Dirichlet lift only, solution vector = 0.

virtual void	save (const char *filename) const

void	load (const char *filename, SpaceSharedPtr< Scalar > space)

Scalar	get_ref_value (Element *e, double xi1, double xi2, int component=0, int item=0)

Scalar	get_ref_value_transformed (Element *e, double xi1, double xi2, int a, int b)

Scalar **	get_ref_values_transformed (Element *e, double x, double y)

virtual Func< Scalar > *	get_pt_value (double x, double y, bool use_MeshHashGrid=false, Element *e=nullptr)

virtual void	add (MeshFunctionSharedPtr< Scalar > &other_mesh_function, SpaceSharedPtr< Scalar > target_space)

virtual void	multiply (Scalar coef)
	Multiplies the function represented by this class by the given coefficient.

SolutionType	get_type () const
	Returns solution type.

SpaceType	get_space_type () const

virtual void	set_active_element (Element *e)
	Internal.

virtual MeshFunction< Scalar > *	clone () const

void	set_type (SolutionType type)

virtual void	free ()
	Frees all precalculated tables.

template<>
	Solution (MeshSharedPtr mesh)

template<>
	Solution (MeshSharedPtr mesh)

template<>
	Solution (SpaceSharedPtr< double > s, Vector< double > *coeff_vec)

template<>
	Solution (SpaceSharedPtr< std::complex< double > > s, Vector< std::complex< double > > *coeff_vec)

template<>
	Solution (SpaceSharedPtr< double > s, double *coeff_vec)

template<>
	Solution (SpaceSharedPtr< std::complex< double > > s, std::complex< double > *coeff_vec)

template<>
void	save (const char *filename) const

template<>
void	save (const char *filename) const

template<>
void	load (const char *filename, SpaceSharedPtr< double > space)

template<>
void	load (const char *filename, SpaceSharedPtr< std::complex< double > > space)

Public Member Functions inherited from Hermes::Hermes2D::MeshFunction< Scalar >
	MeshFunction ()
	Empty constructor.

	MeshFunction (MeshSharedPtr mesh)
	Constructor.

virtual	~MeshFunction ()
	Destructor.

MeshSharedPtr	get_mesh () const
	Return the mesh.

virtual void	copy (MeshFunctionSharedPtr< Scalar > sln)

RefMap *	get_refmap (bool update=true)
	Return the reference mapping.

virtual Scalar	get_approx_max_value (int item=H2D_FN_VAL_0)
	Return the approximate maximum value of this instance.

virtual Scalar	get_approx_min_value (int item=H2D_FN_VAL_0)
	Return the approximate minimum value of this instance.

std::string	getClassName () const
	Internal.

virtual void	reinit ()
	Internal.

virtual void	set_quad_2d (Quad2D *quad_2d)

virtual int	get_edge_fn_order (int edge)
	Returns the order of the edge number edge of the current active element.

template<>
double	get_approx_max_value (int item_)

template<>
std::complex< double >	get_approx_max_value (int item_)

template<>
double	get_approx_min_value (int item_)

template<>
std::complex< double >	get_approx_min_value (int item_)

Public Member Functions inherited from Hermes::Hermes2D::Function< Scalar >
	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...

Quad2D *	get_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_transform (uint64_t idx)

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

uint64_t	get_transform () const

Public Member Functions inherited from Hermes::Hermes2D::Mixins::XMLParsing
	XMLParsing ()
	Constructor.

void	set_validation (bool to_set)
	Set to validate / not to validate.

Static Public Member Functions
static void	make_dx_coeffs (int mode, int o, Scalar mono, Scalar result)

static void	make_dy_coeffs (int mode, int o, Scalar mono, Scalar result)

static void	set_static_verbose_output (bool verbose)

static void	vector_to_solutions (const Scalar *solution_vector, std::vector< SpaceSharedPtr< Scalar > > spaces, std::vector< MeshFunctionSharedPtr< Scalar > > solutions, std::vector< bool > add_dir_lift=std::vector< bool >(), std::vector< int > start_indices=std::vector< int >())
	Passes solution components calculated from solution vector as Solutions.

static void	vector_to_solution (const Scalar *solution_vector, SpaceSharedPtr< Scalar > space, MeshFunctionSharedPtr< Scalar > solution, bool add_dir_lift=true, int start_index=0)

static void	vector_to_solution (const Scalar solution_vector, SpaceSharedPtr< Scalar > space, Solution< Scalar > solution, bool add_dir_lift=true, int start_index=0)

static void	vector_to_solutions (const Vector< Scalar > *vec, std::vector< SpaceSharedPtr< Scalar > > spaces, std::vector< MeshFunctionSharedPtr< Scalar > > solutions, std::vector< bool > add_dir_lift=std::vector< bool >(), std::vector< int > start_indices=std::vector< int >())

static void	vector_to_solutions_common_dir_lift (const Vector< Scalar > *vec, std::vector< SpaceSharedPtr< Scalar > > spaces, std::vector< MeshFunctionSharedPtr< Scalar > > solutions, bool add_dir_lift=false)

static void	vector_to_solutions_common_dir_lift (const Scalar *solution_vector, std::vector< SpaceSharedPtr< Scalar > > spaces, std::vector< MeshFunctionSharedPtr< Scalar > > solutions, bool add_dir_lift=false)

static void	vector_to_solution (const Vector< Scalar > *vec, SpaceSharedPtr< Scalar > space, MeshFunctionSharedPtr< Scalar > solution, bool add_dir_lift=true, int start_index=0)

Public Attributes
Scalar *	mono_coeffs
	Monomial coefficient array.

int *	elem_orders

Static Public Attributes
static bool	static_verbose_output = false

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.

Protected Member Functions
void	enable_transform (bool enable=true)

virtual void	init ()
	Internal.

virtual void	set_coeff_vector (SpaceSharedPtr< Scalar > space, const Vector< Scalar > *vec, bool add_dir_lift, int start_index)
	Converts a coefficient vector into a Solution.

virtual void	set_coeff_vector (SpaceSharedPtr< Scalar > space, const Scalar *coeffs, bool add_dir_lift, int start_index)

void	transform_values (int order, int mask, int np)

virtual void	precalculate (unsigned short order, unsigned short mask)
	precalculates the current function at the current integration points.

double **	calc_mono_matrix (int mode, unsigned char o)

void	init_dxdy_buffer ()

void	check_space_type_compliance (const char *space_type_to_check) const
	Internal, checks the compliance of the passed space type and owned space type.

void	load_exact_solution (int number_of_components, SpaceSharedPtr< Scalar > space, bool complexness, double x_real, double y_real, double x_complex, double y_complex)
	Special internal method for loading exact solutions.

template<>
void	load_exact_solution (int number_of_components, SpaceSharedPtr< double > space, bool complexness, double x_real, double y_real, double x_complex, double y_complex)

template<>
void	load_exact_solution (int number_of_components, SpaceSharedPtr< std::complex< double > > space, bool complexness, double x_real, double y_real, double x_complex, double y_complex)

Protected Member Functions inherited from Hermes::Hermes2D::MeshFunction< Scalar >
void	update_refmap ()

Protected Member Functions inherited from Hermes::Hermes2D::Function< Scalar >
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 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...

void	invalidate_values ()

Protected Member Functions inherited from Hermes::Hermes2D::Transformable
double	get_transform_jacobian () const

Trf *	get_ctm () const

unsigned int	get_depth () const

Protected Attributes
SolutionType	sln_type

SpaceType	space_type

bool	transform

int *	elem_coeffs [H2D_MAX_SOLUTION_COMPONENTS]
	array of pointers into mono_coeffs

int	num_coeffs

int	num_elems

int	num_dofs

Scalar *	dxdy_coeffs [H2D_MAX_SOLUTION_COMPONENTS][H2D_NUM_FUNCTION_VALUES]

Scalar *	dxdy_buffer

Scalar	x [H2D_MAX_INTEGRATION_POINTS_COUNT]
	Utility.

Scalar	y [H2D_MAX_INTEGRATION_POINTS_COUNT]

Scalar	tx [H2D_MAX_INTEGRATION_POINTS_COUNT]

Protected Attributes inherited from Hermes::Hermes2D::MeshFunction< Scalar >
ElementMode2D	mode

MeshSharedPtr	mesh

RefMap	refmap

Protected Attributes inherited from Hermes::Hermes2D::Function< Scalar >
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.

Quad2D *	quads [H2D_MAX_QUADRATURES]
	List of available quadratures.

int	cur_quad
	Active quadrature (index into 'quads')

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.

Protected Attributes inherited from Hermes::Hermes2D::Mixins::XMLParsing
bool	validate
	Internal.

Friends
class	RefMap

template<typename T >
class	KellyTypeAdapt

template<typename T >
class	Views::BaseView

template<typename T >
class	Views::VectorBaseView

template<typename T >
class	OGProjectionNOX

template<typename T >
class	Adapt

template<typename T >
class	Func

template<typename T >
class	DiscontinuousFunc

template<typename T >
class	DiscreteProblem

template<typename T >
class	DiscreteProblemIntegrationOrderCalculator

template<typename T >
class	NeighborSearch

template<typename T >
class	RefinementSelectors::ProjBasedSelector

template<typename T >
class	RefinementSelectors::H1ProjBasedSelector

template<typename T >
class	RefinementSelectors::L2ProjBasedSelector

template<typename T >
class	RefinementSelectors::HcurlProjBasedSelector

Additional Inherited Members
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)

Static Protected Attributes inherited from Hermes::Hermes2D::Function< Scalar >
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

Detailed Description

template<typename Scalar>
singleton Hermes::Hermes2D::Solution< Scalar >

Represents the solution of a PDE.

The Solution class represents the solution of a PDE. Given a space and a solution vector, it calculates the appropriate linear combination of basis functions at the specified element and integration points.

The higher-order solution on elements is best calculated not as a linear combination of shape functions (the usual approach), but as a linear combination of monomials. This has the advantage that no shape function table calculation and look-ups are necessary (except for the conversion of the solution coefficients), which means that visualization and multi-mesh calculations are much faster (all the push_transforms and table searches take the most time when evaluating the solution).

The linear combination of monomials can be calculated using the Horner's scheme, which requires the same number of multiplications as the calculation of the linear combination of shape functions. However, sub-element transforms are trivial and cheap. Moreover, after the solution on all elements is expressed as a combination of monomials, the Space can be forgotten. This is comfortable for the user, since the Solution class acts as a self-contained unit, internally containing just a copy of the mesh and a table of monomial coefficients. It is also very straight-forward to obtain all derivatives of a solution defined in this way. Finally, it is possible to store the solution on the disk easily (no need to store the Space, which is difficult).

The following is an example of the set of monomials for a cubic quad and a cubic triangle. (Note that these are actually the definitions of the polynomial spaces on these elements.)

[ x^3*y^3 x^2*y^3 x*y^3 y^3 ] [ y^3 ] [ x^3*y^2 x^2*y^2 x*y^2 y^2 ] [ x*y^2 y^2 ] [ x^3*y x^2*y x*y y ] [ x^2*y x*y y ] [ x^3 x^2 x 1 ] [ x^3 x^2 x 1 ]

The number of monomials is (p + 1)^2 for quads and (p + 1)*(p + 2)/2 for triangles, where 'p' is the polynomial degree.

Definition at line 35 of file api2d.h.

Member Function Documentation

template<typename Scalar>

void Hermes::Hermes2D::Solution< Scalar >::add	(	MeshFunctionSharedPtr< Scalar > &	other_mesh_function,
		SpaceSharedPtr< Scalar >	target_space
	)

virtual

Adds another mesh function on the given space. See method of parent class.

Reimplemented from Hermes::Hermes2D::MeshFunction< Scalar >.

Definition at line 628 of file solution.cpp.

template<typename Scalar >

MeshFunction< Scalar > * Hermes::Hermes2D::Solution< Scalar >::clone ( ) const

virtual

Cloning function - for parallel OpenMP blocks. Designed to return an identical clone of this instance.

Implements Hermes::Hermes2D::MeshFunction< Scalar >.

Reimplemented in Hermes::Hermes2D::ExactSolutionEggShell, Hermes::Hermes2D::ZeroSolutionVector< Scalar >, Hermes::Hermes2D::ConstantSolutionVector< Scalar >, Hermes::Hermes2D::ZeroSolution< Scalar >, Hermes::Hermes2D::ConstantSolution< Scalar >, Hermes::Hermes2D::ExactSolutionConstantArray< Scalar, ValueType >, Hermes::Hermes2D::ExactSolution< Scalar >, and Hermes::Hermes2D::ExactSolution< double >.

Definition at line 220 of file solution.cpp.

Referenced by Hermes::Hermes2D::ConstantSolution< Scalar >::clone(), Hermes::Hermes2D::ZeroSolution< Scalar >::clone(), Hermes::Hermes2D::ConstantSolutionVector< Scalar >::clone(), and Hermes::Hermes2D::ZeroSolutionVector< Scalar >::clone().

template<typename Scalar >

void Hermes::Hermes2D::Solution< Scalar >::enable_transform ( bool enable = true )

protected

Enables or disables transformation of the solution derivatives (H1 case) or values (vector (Hcurl) case). This means H2D_FN_DX_0 and H2D_FN_DY_0 or H2D_FN_VAL_0 and H2D_FN_VAL_1 will or will not be returned premultiplied by the reference mapping matrix. The default is enabled (true).

Definition at line 620 of file solution.cpp.

Referenced by Hermes::Hermes2D::RefinementSelectors::ProjBasedSelector< Scalar >::calc_projection_errors().

template<typename Scalar >

Func< Scalar > * Hermes::Hermes2D::Solution< Scalar >::get_pt_value	(	double	x,
		double	y,
		bool	use_MeshHashGrid = `false`,
		Element *	e = `nullptr`
	)

virtual

Returns solution value or derivatives at the physical domain point (x, y). 'item' controls the returned value: H2D_FN_VAL_0, H2D_FN_VAL_1, H2D_FN_DX_0, H2D_FN_DX_1, H2D_FN_DY_0, .... NOTE: This function should be used for postprocessing only, it is not effective enough for calculations. Since it searches for an element sequentinally, it is extremelly slow. Prefer Solution::get_ref_value if possible.

Implements Hermes::Hermes2D::MeshFunction< Scalar >.

Definition at line 1837 of file solution.cpp.

template<typename Scalar >

Scalar Hermes::Hermes2D::Solution< Scalar >::get_ref_value	(	Element *	e,
		double	xi1,
		double	xi2,
		int	component = `0`,
		int	item = `0`
	)

Returns solution value or derivatives at element e, in its reference domain point (xi1, xi2). 'item' controls the returned value: 0 = value, 1 = dx, 2 = dy, 3 = dxx, 4 = dyy, 5 = dxy. NOTE: This function should be used for postprocessing only, it is not effective enough for calculations.

Definition at line 1678 of file solution.cpp.

template<typename Scalar >

Scalar Hermes::Hermes2D::Solution< Scalar >::get_ref_value_transformed	(	Element *	e,
		double	xi1,
		double	xi2,
		int	a,
		int	b
	)

Returns solution value or derivatives (correctly transformed) at element e, in its reference domain point (xi1, xi2). 'item' controls the returned value: 0 = value, 1 = dx, 2 = dy, 3 = dxx, 4 = dyy, 5 = dxy. NOTE: This function should be used for postprocessing only, it is not effective enough for calculations.

Definition at line 1700 of file solution.cpp.

template<typename Scalar >

Scalar ** Hermes::Hermes2D::Solution< Scalar >::get_ref_values_transformed	(	Element *	e,
		double	x,
		double	y
	)

Returns solution value and derivatives (correctly transformed) at element e, in its REAL COORDINATES domain point (xi1, xi2). The values are returned. NOTE: This function should be used for postprocessing only, it is not effective enough for calculations.

Definition at line 1777 of file solution.cpp.

template<typename Scalar>

void Hermes::Hermes2D::Solution< Scalar >::load	(	const char *	filename,
		SpaceSharedPtr< Scalar >	space
	)

Loads the solution from a file previously created by Solution::save(). This completely restores the solution in the memory.

template<typename Scalar>

virtual void Hermes::Hermes2D::Solution< Scalar >::save ( const char * filename ) const

virtual

Saves the complete solution (i.e., including the internal copy of the mesh and element orders) to an XML file.

Reimplemented in Hermes::Hermes2D::ConstantSolutionVector< Scalar >, Hermes::Hermes2D::ConstantSolutionVector< Scalar >, Hermes::Hermes2D::ConstantSolutionVector< Scalar >, Hermes::Hermes2D::ConstantSolution< Scalar >, Hermes::Hermes2D::ConstantSolution< Scalar >, Hermes::Hermes2D::ConstantSolution< Scalar >, Hermes::Hermes2D::ExactSolution< Scalar >, and Hermes::Hermes2D::ExactSolution< double >.

Referenced by Hermes::Hermes2D::ExactSolution< Scalar >::save(), Hermes::Hermes2D::ConstantSolution< Scalar >::save(), and Hermes::Hermes2D::ConstantSolutionVector< Scalar >::save().

Member Data Documentation

template<typename Scalar>

int* Hermes::Hermes2D::Solution< Scalar >::elem_orders

Stored element orders in the mathematical sense. The polynomial degree of the highest basis function + increments due to the element shape, etc. .

Definition at line 161 of file solution.h.

Referenced by Hermes::Hermes2D::Solution< Scalar >::copy().

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

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

template<typename Scalar> singleton Hermes::Hermes2D::Solution< Scalar >

Member Function Documentation

Member Data Documentation

template<typename Scalar>
singleton Hermes::Hermes2D::Solution< Scalar >