A framework for explicit aposteriori error estimators. More...

#include <kelly_type_adapt.h>

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

Classes
class	ErrorEstimatorForm

Public Member Functions
	KellyTypeAdapt (Hermes::vector< Space< Scalar > * > spaces, bool ignore_visited_segments=true, Hermes::vector< const InterfaceEstimatorScalingFunction * > interface_scaling_fns_=Hermes::vector< const InterfaceEstimatorScalingFunction * >(), Hermes::vector< ProjNormType > norms_=Hermes::vector< ProjNormType >())

	KellyTypeAdapt (Space< Scalar > space, bool ignore_visited_segments=true, const InterfaceEstimatorScalingFunction interface_scaling_fn_=NULL, ProjNormType norm_=HERMES_UNSET_NORM)

virtual	~KellyTypeAdapt ()
	Destructor.

Mesh::ElementMarkersConversion *	get_element_markers_conversion ()

Mesh::BoundaryMarkersConversion *	get_boundary_markers_conversion ()

void	add_error_estimator_vol (ErrorEstimatorForm *form)

void	add_error_estimator_surf (ErrorEstimatorForm *form)

double	calc_err_est (Solution< Scalar > *sln, unsigned int error_flags=HERMES_TOTAL_ERROR_REL\|HERMES_ELEMENT_ERROR_REL)

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

bool	adapt (double thr, int strat=0, int regularize=-1, double to_be_processed=0.0)

void	disable_aposteriori_interface_scaling ()

void	set_volumetric_scaling_const (double C)

void	set_boundary_scaling_const (double C)

Public Member Functions inherited from Hermes::Hermes2D::Adapt< Scalar >
	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
double	eval_volumetric_estimator (typename KellyTypeAdapt::ErrorEstimatorForm err_est_form, RefMap rm)

double	eval_boundary_estimator (typename KellyTypeAdapt::ErrorEstimatorForm err_est_form, RefMap rm, SurfPos *surf_pos)

double	eval_interface_estimator (typename KellyTypeAdapt::ErrorEstimatorForm err_est_form, RefMap rm, SurfPos surf_pos, LightArray< NeighborSearch< Scalar > > &neighbor_searches, int neighbor_index)

double	eval_solution_norm (typename Adapt< Scalar >::MatrixFormVolError form, RefMap rm, MeshFunction< Scalar > *sln)

virtual double	calc_err_internal (Hermes::vector< Solution< Scalar > * > slns, Hermes::vector< double > *component_errors, unsigned int error_flags)

Protected Member Functions inherited from Hermes::Hermes2D::Adapt< Scalar >
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
DiscreteProblem< Scalar >	dp

Hermes::vector< typename KellyTypeAdapt::ErrorEstimatorForm * >	error_estimators_vol

Hermes::vector< typename KellyTypeAdapt::ErrorEstimatorForm * >	error_estimators_surf

Mesh::ElementMarkersConversion	element_markers_conversion

Mesh::BoundaryMarkersConversion	boundary_markers_conversion

Hermes::vector< const InterfaceEstimatorScalingFunction * >	interface_scaling_fns

bool	use_aposteriori_interface_scaling

double	interface_scaling_const
	Constant scaling of the boundary error estimates. More...

double	volumetric_scaling_const
	Constant scaling of the volumetric error estimates (like the residual norm).

double	boundary_scaling_const
	Constant scaling of the boundary error estimates.

bool	ignore_visited_segments

Protected Attributes inherited from Hermes::Hermes2D::Adapt< Scalar >
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).

Additional Inherited Members
Static Protected Attributes inherited from Hermes::Hermes2D::Adapt< Scalar >
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::KellyTypeAdapt< Scalar >

A framework for explicit aposteriori error estimators.

Explicit error estimators estimate the error of approximate solution on an element by evaluating element residuals and jumps of the solution across element edges ([2]). A typical example is the Kelly error estimator ([1]) where a sum of the L2 norms of element residual and jumps of solution gradients across the element boundaries defines the element error.

References: [1] Kelly D. W., Gago O. C., Zienkiewicz O. C., Babuska I.: A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis. Int. J. Numer. Methods Engng. 1983;19:1593–619. [2] Gratsch T., Bathe K. J.: A posteriori error estimation techniques in practical finite element analysis. Computers and Structures 83 (2005) 235–265. [3] Zienkiewicz O. C., Taylor R. L., Zhu J. Z.: The finite element method: its basis and fundamentals (Section 13.7.1). 6th ed. (2005), Elsevier.

Definition at line 65 of file kelly_type_adapt.h.

Constructor & Destructor Documentation

template<typename Scalar >

Hermes::Hermes2D::KellyTypeAdapt< Scalar >::KellyTypeAdapt	(	Hermes::vector< Space< Scalar > * >	spaces,
		bool	ignore_visited_segments = `true`,
		Hermes::vector< const InterfaceEstimatorScalingFunction * >	interface_scaling_fns_ = `Hermes::vector<const InterfaceEstimatorScalingFunction*>()`,
		Hermes::vector< ProjNormType >	norms_ = `Hermes::vector<ProjNormType>()`
	)

Constructor.

Parameters

[in]	spaces_	Approximation space of each solution component.
[in]	ignore_visited_segments_	If true, error estimator for each inner edge will be evaluated only once. It will be added to the total error estimate for both the active element and its neighbors across that edge, after possibly being scaled by `interface_scaling_fns_` for the current component (with the diameter of the appropriate element). This saves duplicate evaluations with same results when the estimator is given e.g. by the jumps of the solution.

If false, error estimator for each surface of each element will be evaluated, regardless of whether the neighbor side of the interface has already been processed.

Note that if interface_scaling_fns_ is empty (or unspecified) then the default scaling by element diameter will be always performed unless it is switched off by a call to disable_aposteriori_interface_scaling.

Parameters

[in]	interface_scaling_fns_	Specifies functions used for scaling the interface error estimator for each component. The scale is defined as a real function of the element diameter (and possibly equation coefficients associated to the element) and multiplies the result of the interface estimators. It may thus be already present in the interface estimator forms themselves, in which case call `disable_aposteriori_interface_scaling`. In this case, it may also be required that `ignore_visited_segments` be false in order to always ensure that the diameter belongs to the element whose error is being calculated.
[in]	norms_	Norms used for making relative error estimates. If not specified, they are defined according to the spaces.

Definition at line 35 of file kelly_type_adapt.cpp.

Member Function Documentation

template<typename Scalar >

bool Hermes::Hermes2D::KellyTypeAdapt< Scalar >::adapt	(	double	thr,
		int	strat = `0`,
		int	regularize = `-1`,
		double	to_be_processed = `0.0`
	)

Refines the elements selected by the

RefinementSelectors::HOnlySelector

according to the errors calculated by

calc_err_est

.

Definition at line 81 of file kelly_type_adapt.cpp.

template<typename Scalar >

void Hermes::Hermes2D::KellyTypeAdapt< Scalar >::add_error_estimator_surf ( ErrorEstimatorForm * form )

Append boundary or interface error estimator form.

Interface form is defined by form::area == H2D_DG_INNER_EDGE . The effective types for u_ext, u and e (three of the obligatory parameters of form::value() and form::ord()) will then be, respectively DiscontinuousFunc*[], DiscontinuousFunc* and InterfaceGeom*.

Definition at line 102 of file kelly_type_adapt.cpp.

template<typename Scalar >

void Hermes::Hermes2D::KellyTypeAdapt< Scalar >::add_error_estimator_vol ( ErrorEstimatorForm * form )

Append volumetric error estimator form.

For example, element residual norms may be represented by such a form.

Parameters

[in] form ... object representing the form. A class derived from KellyTypeAdapt::ErrorEstimatorForm defines its datatype.

Definition at line 92 of file kelly_type_adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::KellyTypeAdapt< Scalar >::calc_err_est	(	Solution< Scalar > *	sln,
		unsigned int	error_flags = `HERMES_TOTAL_ERROR_REL \| HERMES_ELEMENT_ERROR_REL`
	)

inline

The following two methods calculate the error of the given sln, using

calc_err_internal

.

Definition at line 268 of file kelly_type_adapt.h.

template<typename Scalar >

double Hermes::Hermes2D::KellyTypeAdapt< Scalar >::calc_err_internal	(	Hermes::vector< Solution< Scalar > * >	slns,
		Hermes::vector< double > *	component_errors,
		unsigned int	error_flags
	)

protectedvirtual

Calculates error estimates for each solution component, the total error estimate, and possibly also their normalizations. If called with a pair of solutions, the version from Adapt is used (this is e.g. done when comparing approximate solution to the exact one - in this case, we do not want to compute the Kelly estimator value, but rather the ordinary difference between the solutions).

Definition at line 112 of file kelly_type_adapt.cpp.

template<typename Scalar >

double Hermes::Hermes2D::KellyTypeAdapt< Scalar >::eval_volumetric_estimator	(	typename KellyTypeAdapt< Scalar >::ErrorEstimatorForm *	err_est_form,
		RefMap *	rm
	)

protected

Functions used for evaluating the actual error estimator forms for an active element or edge segment.

Definition at line 529 of file kelly_type_adapt.cpp.

Member Data Documentation

template<typename Scalar >

Hermes::vector<typename KellyTypeAdapt::ErrorEstimatorForm *> Hermes::Hermes2D::KellyTypeAdapt< Scalar >::error_estimators_vol

protected

Linear forms used to calculate the error estimator value for each component.

Definition at line 147 of file kelly_type_adapt.h.

Referenced by Hermes::Hermes2D::KellyTypeAdapt< Scalar >::KellyTypeAdapt().

template<typename Scalar >

bool Hermes::Hermes2D::KellyTypeAdapt< Scalar >::ignore_visited_segments

protected

Specifies whether the interface error estimator will be evaluated from each side of each interface (when ignore_visited_segments == false ), or only once for each interface (ignore_visited_segments == true).

Definition at line 170 of file kelly_type_adapt.h.

Referenced by Hermes::Hermes2D::KellyTypeAdapt< Scalar >::KellyTypeAdapt().

template<typename Scalar >

double Hermes::Hermes2D::KellyTypeAdapt< Scalar >::interface_scaling_const

protected

Constant scaling of the boundary error estimates.

Constant scaling. Reserved for the derived classes, not to be used by the user explicitly.

Definition at line 163 of file kelly_type_adapt.h.

Referenced by Hermes::Hermes2D::KellyTypeAdapt< Scalar >::KellyTypeAdapt().

template<typename Scalar >

Hermes::vector<const InterfaceEstimatorScalingFunction*> Hermes::Hermes2D::KellyTypeAdapt< Scalar >::interface_scaling_fns

protected

Scaling of the interface error estimates. May be specified by the user during construction.

Definition at line 155 of file kelly_type_adapt.h.

Referenced by Hermes::Hermes2D::KellyTypeAdapt< Scalar >::KellyTypeAdapt().

template<typename Scalar >

bool Hermes::Hermes2D::KellyTypeAdapt< Scalar >::use_aposteriori_interface_scaling

protected

 Specifies whether the interface error estimators for each

component will be multiplied by interface_scaling_fns after being evaluated.

Definition at line 156 of file kelly_type_adapt.h.

Referenced by Hermes::Hermes2D::KellyTypeAdapt< Scalar >::KellyTypeAdapt().

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

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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