Evaluation of an error between a (coarse) solution and a reference solution and adaptivity. More...

#include <adapt.h>

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

Classes
struct	ElementReference
	A reference to an element. More...

class	MatrixFormVolError
	Matrix forms for error calculation. More...

Public Member Functions
	Adapt (Hermes::vector< Space< Scalar > * > spaces, Hermes::vector< ProjNormType > proj_norms=Hermes::vector< ProjNormType >())

	Adapt (Space< Scalar > *space, ProjNormType proj_norm=HERMES_UNSET_NORM)

virtual	~Adapt ()
	Destructor. Deallocates allocated private data.

void	set_error_form (int i, int j, MatrixFormVolError *form)
	Sets user defined bilinear form which is used to calculate error. More...

void	set_error_form (MatrixFormVolError *form)
	i = j = 0

void	set_norm_form (int i, int j, MatrixFormVolError *form)

void	set_norm_form (MatrixFormVolError *form)
	i = j = 0

double	calc_err_est (Solution< Scalar > sln, Solution< Scalar > rsln, bool solutions_for_adapt=true, unsigned int error_flags=HERMES_TOTAL_ERROR_REL\|HERMES_ELEMENT_ERROR_REL)

double	calc_err_est (Hermes::vector< Solution< Scalar > * > slns, Hermes::vector< Solution< Scalar > * > rslns, Hermes::vector< double > *component_errors=NULL, bool solutions_for_adapt=true, unsigned int error_flags=HERMES_TOTAL_ERROR_REL\|HERMES_ELEMENT_ERROR_REL)

double	calc_err_exact (Solution< Scalar > sln, Solution< Scalar > rsln, bool solutions_for_adapt=true, unsigned int error_flags=HERMES_TOTAL_ERROR_REL\|HERMES_ELEMENT_ERROR_REL)

double	calc_err_exact (Hermes::vector< Solution< Scalar > * > slns, Hermes::vector< Solution< Scalar > * > rslns, Hermes::vector< double > *component_errors=NULL, bool solutions_for_adapt=true, unsigned int error_flags=HERMES_TOTAL_ERROR_REL\|HERMES_ELEMENT_ERROR_REL)

bool	adapt (Hermes::vector< RefinementSelectors::Selector< Scalar > * > refinement_selectors, double thr, int strat=0, int regularize=-1, double to_be_processed=0.0)
	Refines elements based on results from calc_err_est(). More...

bool	adapt (RefinementSelectors::Selector< Scalar > *refinement_selector, double thr, int strat=0, int regularize=-1, double to_be_processed=0.0)
	Refines elements based on results from calc_err_est(). More...

double	get_element_error_squared (int component, int id) const
	Returns a squared error of an element. More...

Protected Member Functions
const Hermes::vector < ElementReference > &	get_regular_queue () const
	Returns regular queue of elements. More...

void	apply_refinement (const ElementToRefine &elem_ref)
	Apply a single refinement. More...

virtual void	apply_refinements (std::vector< ElementToRefine > &elems_to_refine)
	Apply a vector of refinements. More...

const std::vector < ElementToRefine > &	get_last_refinements () const
	Returns a vector of refinements generated during the last execution of the method adapt(). More...

void	fix_shared_mesh_refinements (Mesh meshes, std::vector< ElementToRefine > &elems_to_refine, int idx, RefinementSelectors::Selector< Scalar > ***refinement_selectors)
	Fixes refinements of a mesh which is shared among multiple components of a multimesh. More...

void	homogenize_shared_mesh_orders (Mesh **meshes)
	Enforces the same order to an element of a mesh which is shared among multiple components. More...

virtual double	calc_err_internal (Hermes::vector< Solution< Scalar > * > slns, Hermes::vector< Solution< Scalar > * > rslns, Hermes::vector< double > *component_errors, bool solutions_for_adapt, unsigned int error_flags)
	Calculates error between a coarse solution and a reference solution and sorts components according to the error. More...

virtual double	calc_err_internal (Solution< Scalar > sln, Solution< Scalar > rsln, Hermes::vector< double > *component_errors, bool solutions_for_adapt, unsigned int error_flags)
	One Space version.

virtual double	eval_error (MatrixFormVolError form, MeshFunction< Scalar > sln1, MeshFunction< Scalar > sln2, MeshFunction< Scalar > rsln1, MeshFunction< Scalar > *rsln2)
	Evaluates a square of an absolute error of an active element among a given pair of components. More...

virtual double	eval_error_norm (MatrixFormVolError form, MeshFunction< Scalar > rsln1, MeshFunction< Scalar > *rsln2)
	Evaluates the square of a norm of an active element in the reference solution among a given pair of components. More...

virtual void	fill_regular_queue (const Mesh **meshes)
	Builds an ordered queue of elements that are be examined. More...

Protected Attributes
Exceptions::Exception *	caughtException

std::queue< ElementReference >	priority_queue
	A queue of priority elements. Elements in this queue are processed before the elements in the Adapt::regular_queue.

Hermes::vector< ElementReference >	regular_queue
	A queue of elements which should be processes. The queue had to be filled by the method fill_regular_queue().

std::vector< ElementToRefine >	last_refinements
	A vector of refinements generated during the last finished execution of the method adapt().

int	num
	Number of solution components (as in wf->neq).

Hermes::vector< Space< Scalar > * >	spaces
	Spaces.

bool **	own_forms

int	num_act_elems
	A total number of active elements across all provided meshes.

Solution< Scalar > *	sln [H2D_MAX_COMPONENTS]
	Coarse solution.

Solution< Scalar > *	rsln [H2D_MAX_COMPONENTS]
	Reference solutions.

bool	have_errors
	True if errors of elements were calculated.

bool	have_coarse_solutions
	True if the coarse solutions were set.

bool	have_reference_solutions
	True if the reference solutions were set.

double *	errors [H2D_MAX_COMPONENTS]
	method calc_errors_internal() was calls. Initialized in the method calc_errors_internal(). More...

double	errors_squared_sum
	Sum of errors in the array Adapt::errors_squared. Used by a method adapt() in some strategies.

double	error_time
	Time needed to calculate the error.

MatrixFormVolError *	error_form [H2D_MAX_COMPONENTS][H2D_MAX_COMPONENTS]
	Bilinear forms to calculate error.

MatrixFormVolError *	norm_form [H2D_MAX_COMPONENTS][H2D_MAX_COMPONENTS]
	Bilinear forms to calculate norm (set to error_form by default).

Static Protected Attributes
static const unsigned char	HERMES_TOTAL_ERROR_MASK = 0x0F
	A mask which masks-out total error type. Used by Adapt::calc_err_internal().

static const unsigned char	HERMES_ELEMENT_ERROR_MASK = 0xF0
	A mask which masks-out element error type. Used by Adapt::calc_err_internal().

Detailed Description

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

Evaluation of an error between a (coarse) solution and a reference solution and adaptivity.

The class provides basic functionality necessary to adaptively refine elements. Given a reference solution and a coarse solution, it calculates error estimates and it acts as a container for the calculated errors.

Definition at line 57 of file adapt.h.

Constructor & Destructor Documentation

template<typename Scalar >

Hermes::Hermes2D::Adapt< Scalar >::Adapt	(	Hermes::vector< Space< Scalar > * >	spaces,
		Hermes::vector< ProjNormType >	proj_norms = `Hermes::vector<ProjNormType>()`
	)

Constructor. Suitable for problems where various solution components belong to different spaces (L2, H1, Hcurl, Hdiv). If proj_norms are not specified, they are defined according to the spaces.

Definition at line 34 of file adapt.cpp.

Member Function Documentation

template<typename Scalar >

bool Hermes::Hermes2D::Adapt< Scalar >::adapt	(	Hermes::vector< RefinementSelectors::Selector< Scalar > * >	refinement_selectors,
		double	thr,
		int	strat = `0`,
		int	regularize = `-1`,
		double	to_be_processed = `0.0`
	)

Refines elements based on results from calc_err_est().

Parameters

[in]	refinement_selectors	Vector of selectors.
[in]	thr	A threshold. The meaning of the threshold is defined by the parameter strat.
[in]	strat	A strategy. It specifies a stop condition which quits processing elements in the Adapt::regular_queue. Possible values are 0, 1, 2, and 3.
[in]	regularize	Regularizing of a mesh.
[in]	same_order	True if all element have to have same orders after all refinements are applied.
[in]	to_be_processed	Error which has to be processed. Used in strategy number 3.

Returns: True if no element was refined. In usual case, this indicates that adaptivity is not able to refine anything and the adaptivity loop should end.

Definition at line 158 of file adapt.cpp.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::adapt(), and Hermes::Hermes2D::KellyTypeAdapt< Scalar >::adapt().

template<typename Scalar >

bool Hermes::Hermes2D::Adapt< Scalar >::adapt	(	RefinementSelectors::Selector< Scalar > *	refinement_selector,
		double	thr,
		int	strat = `0`,
		int	regularize = `-1`,
		double	to_be_processed = `0.0`
	)

Refines elements based on results from calc_err_est().

Parameters

[in]	refinement_selector	A pointer to a selector which will select a refinement.
[in]	thr	A threshold. The meaning of the threshold is defined by the parameter strat.
[in]	strat	A strategy. It specifies a stop condition which quits processing elements in the Adapt::regular_queue. Possible values are 0, 1, 2, and 3.
[in]	regularize	Regularizing of a mesh.
[in]	same_order	True if all element have to have same orders after all refinements are applied.
[in]	to_be_processed	Error which has to be processed. Used in strategy number 3.

Returns: True if no element was refined. In usual case, this indicates that adaptivity is not able to refine anything and the adaptivity loop should end.

Definition at line 688 of file adapt.cpp.

template<typename Scalar >

void Hermes::Hermes2D::Adapt< Scalar >::apply_refinement ( const ElementToRefine & elem_ref )

protected

Apply a single refinement.

Parameters

[in] A refinement to apply.

Definition at line 828 of file adapt.cpp.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::apply_refinements().

template<typename Scalar >

void Hermes::Hermes2D::Adapt< Scalar >::apply_refinements ( std::vector< ElementToRefine > & elems_to_refine )

protectedvirtual

Apply a vector of refinements.

Parameters

[in] A vector of refinements to apply.

Definition at line 820 of file adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::calc_err_est	(	Solution< Scalar > *	sln,
		Solution< Scalar > *	rsln,
		bool	solutions_for_adapt = `true`,
		unsigned int	error_flags = `HERMES_TOTAL_ERROR_REL \| HERMES_ELEMENT_ERROR_REL`
	)

Type-safe version of calc_err_est() for one solution.

Parameters

[in] solutions_for_adapt - if sln and rsln are the solutions error of which is used in the function adapt().

Definition at line 601 of file adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::calc_err_est	(	Hermes::vector< Solution< Scalar > * >	slns,
		Hermes::vector< Solution< Scalar > * >	rslns,
		Hermes::vector< double > *	component_errors = `NULL`,
		bool	solutions_for_adapt = `true`,
		unsigned int	error_flags = `HERMES_TOTAL_ERROR_REL \| HERMES_ELEMENT_ERROR_REL`
	)

Calculates the error of the solution. 'n' must be the same as 'num' in the constructor. After that, n coarse solution pointers are passed, followed by n fine solution pointers.

Parameters

[in] solutions_for_adapt - if slns and rslns are the solutions error of which is used in the function adapt().

Definition at line 614 of file adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::calc_err_exact	(	Solution< Scalar > *	sln,
		Solution< Scalar > *	rsln,
		bool	solutions_for_adapt = `true`,
		unsigned int	error_flags = `HERMES_TOTAL_ERROR_REL \| HERMES_ELEMENT_ERROR_REL`
	)

Type-safe version of calc_err_exact() for one solution.

Parameters

[in] solutions_for_adapt - if sln and rsln are the solutions error of which is used in the function adapt().

Definition at line 630 of file adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::calc_err_exact	(	Hermes::vector< Solution< Scalar > * >	slns,
		Hermes::vector< Solution< Scalar > * >	rslns,
		Hermes::vector< double > *	component_errors = `NULL`,
		bool	solutions_for_adapt = `true`,
		unsigned int	error_flags = `HERMES_TOTAL_ERROR_REL \| HERMES_ELEMENT_ERROR_REL`
	)

Calculates the error of the solution.

Parameters

[in] solutions_for_adapt - if slns and rslns are the solutions error of which is used in the function adapt().

Definition at line 652 of file adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::calc_err_internal	(	Hermes::vector< Solution< Scalar > * >	slns,
		Hermes::vector< Solution< Scalar > * >	rslns,
		Hermes::vector< double > *	component_errors,
		bool	solutions_for_adapt,
		unsigned int	error_flags
	)

protectedvirtual

Calculates error between a coarse solution and a reference solution and sorts components according to the error.

If overridden, this method has to initialize errors (Array::errors), sum of errors (Array::error_sum), norms of components (Array::norm), number of active elements (Array::num_act_elems). Also, it has to fill the regular queue through the method fill_regular_queue().

Parameters

[in] error_flags Flags which calculates the error. It can be a combination of HERMES_TOTAL_ERROR_REL, HERMES_TOTAL_ERROR_ABS, HERMES_ELEMENT_ERROR_REL, HERMES_ELEMENT_ERROR_ABS.

Returns: The total error. Interpretation of the error is specified by the parameter error_flags.

Definition at line 1028 of file adapt.cpp.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::calc_err_est(), Hermes::Hermes2D::Adapt< Scalar >::calc_err_exact(), and Hermes::Hermes2D::Adapt< Scalar >::calc_err_internal().

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::eval_error	(	MatrixFormVolError *	form,
		MeshFunction< Scalar > *	sln1,
		MeshFunction< Scalar > *	sln2,
		MeshFunction< Scalar > *	rsln1,
		MeshFunction< Scalar > *	rsln2
	)

protectedvirtual

Evaluates a square of an absolute error of an active element among a given pair of components.

The method uses a bilinear forms to calculate the error. This is done by supplying a differences (f1 - v1) and (f2 - v2) at integration points to the bilinear form, where f1 and f2 are values of (coarse) solutions of the first and the second component respectively, v1 and v2 are values of reference solutions of the first and the second component respectively.

Parameters

[in]	form	A bilinear form.
[in]	sln1	A (coarse) solution corresponding to the first component.
[in]	sln2	A (coarse) solution corresponding to the second component.
[in]	rsln1	A reference solution corresponding to the first component.
[in]	rsln2	A reference solution corresponding to the second component.
[in]	rv1	A reference map of a (coarse) solution sln1.
[in]	rv2	A reference map of a (coarse) solution sln2.
[in]	rrv1	A reference map of a reference solution rsln1.
[in]	rrv2	A reference map of a reference solution rsln2.

Returns: A square of an absolute error.

Definition at line 904 of file adapt.cpp.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::calc_err_internal().

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::eval_error_norm	(	MatrixFormVolError *	form,
		MeshFunction< Scalar > *	rsln1,
		MeshFunction< Scalar > *	rsln2
	)

protectedvirtual

Evaluates the square of a norm of an active element in the reference solution among a given pair of components.

The method uses a bilinear forms to calculate the norm. This is done by supplying a v1 and v2 at integration points to the bilinear form, where v1 and v2 are values of reference solutions of the first and the second component respectively.

Parameters

[in]	form	A bilinear form.
[in]	rsln1	A reference solution corresponding to the first component.
[in]	rsln2	A reference solution corresponding to the second component.
[in]	rrv1	A reference map of a reference solution rsln1.
[in]	rrv2	A reference map of a reference solution rsln2.

Returns: A square of a norm.

Definition at line 971 of file adapt.cpp.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::calc_err_internal().

template<typename Scalar >

void Hermes::Hermes2D::Adapt< Scalar >::fill_regular_queue ( const Mesh ** meshes )

protectedvirtual

Builds an ordered queue of elements that are be examined.

The method fills Adapt::standard_queue by elements sorted accordin to their error descending. The method assumes that Adapt::errors_squared contains valid values. If a special order of elements is requested, this method has to be overridden. /param[in] meshes An array of pointers to meshes of a (coarse) solution. An index into the array is an index of a component. /param[in] meshes An array of pointers to meshes of a reference solution. An index into the array is an index of a component.

Definition at line 1242 of file adapt.cpp.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::calc_err_internal().

template<typename Scalar >

void Hermes::Hermes2D::Adapt< Scalar >::fix_shared_mesh_refinements	(	Mesh **	meshes,
		std::vector< ElementToRefine > &	elems_to_refine,
		int **	idx,
		RefinementSelectors::Selector< Scalar > ***	refinement_selectors
	)

protected

Fixes refinements of a mesh which is shared among multiple components of a multimesh.

If a mesh is shared among components, it has to be refined similarly in order to avoid inconsistency.

Parameters

[in]	meshes	An array of meshes of components.
[in]	elems_to_refine	A vector of refinements.
[in]	idx	A 2D array that translates a pair (a component index, an element id) to an index of a refinement in the vector of refinements. If the index is below zero, a given element was not refined.
[in]	refinement_selector	A selected used by the adaptivity. The selector is used to correct orders of modified refinements using RefinementSelectors::Selector::update_shared_mesh_orders().

Definition at line 699 of file adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::Adapt< Scalar >::get_element_error_squared	(	int	component,
		int	id
	)		const

Returns a squared error of an element.

Parameters

[in]	A	component index.
[in]	An	element index.

Returns: Squared error. Meaning of the error depends on parameters of the function calc_errors_internal().

Definition at line 776 of file adapt.cpp.

template<typename Scalar >

const std::vector< ElementToRefine > & Hermes::Hermes2D::Adapt< Scalar >::get_last_refinements ( ) const

protected

Returns a vector of refinements generated during the last execution of the method adapt().

Returns: A vector of refinements generated during the last execution of the method adapt(). The returned vector might change or become invalid after the next execution of the method adadpt(). Returns last refinements.

Definition at line 814 of file adapt.cpp.

template<typename Scalar >

const Hermes::vector< typename Adapt< Scalar >::ElementReference > & Hermes::Hermes2D::Adapt< Scalar >::get_regular_queue ( ) const

protected

Returns regular queue of elements.

Returns: A regular queue.

Definition at line 784 of file adapt.cpp.

template<typename Scalar >

void Hermes::Hermes2D::Adapt< Scalar >::homogenize_shared_mesh_orders ( Mesh ** meshes )

protected

Enforces the same order to an element of a mesh which is shared among multiple components.

Parameters

[in] meshes An array of meshes of components.

Definition at line 790 of file adapt.cpp.

template<typename Scalar >

void Hermes::Hermes2D::Adapt< Scalar >::set_error_form	(	int	i,
		int	j,
		MatrixFormVolError *	form
	)

Sets user defined bilinear form which is used to calculate error.

By default, all inherited class should set default bilinear forms for each element (i.e. i = j). This method can change it or set forms that can combine components (e.g. energy error).

Parameters

[in]	i	The first component index.
[in]	j	The second component index.
[in]	bi_form	A bilinear form which calculates value.
[in]	bi_ord	A bilinear form which calculates order.

Member Data Documentation

template<typename Scalar >

double* Hermes::Hermes2D::Adapt< Scalar >::errors[H2D_MAX_COMPONENTS]

protected

method calc_errors_internal() was calls. Initialized in the method calc_errors_internal().

Errors of elements. Meaning of the error depeds on flags used when the

Definition at line 237 of file adapt.h.

Referenced by Hermes::Hermes2D::Adapt< Scalar >::Adapt(), Hermes::Hermes2D::Adapt< Scalar >::calc_err_internal(), and Hermes::Hermes2D::Adapt< Scalar >::get_element_error_squared().

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

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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