ptems::DoerflerMarking Struct Reference

Functor object that can be passed to FEMesh::Adapt(Func, bool) to perform Dörfler marking [2] for refinement of elements based on an error indicator. More...

#include <ptems/refinements.hpp>

Public Member Functions
template<typename Estimators >
	DoerflerMarking (const Estimators &estimators, double refineThreshold, double coarsenThreshold=0)
	Create a functor for performing Dörfler marking. More...
AdaptationType	operator() (std::size_t element) const
	Functor operator to compute the adaptation type for the specifeid element. More...

Detailed Description

Functor object that can be passed to FEMesh::Adapt(Func, bool) to perform Dörfler marking [2] for refinement of elements based on an error indicator.

Given a mesh \(\mathcal{T}_h\) and per-element error indicators, \(\eta_K\), \(K\in\mathcal{T}_h\) Dörfler marking constructs the smallest set \(\mathcal{A}\) such that

\[ \sum_{K\in\mathcal{A}} \eta_K^2 \geq \theta_R \sum_{K\in\mathcal{T}_h} \eta_K^2, \]

where \(\theta_R\in(0,1)\) is a threshold parameter, and marks the elements in the set \(\mathcal{A}\) for refinement.

Optionally, we can also construct the largest set \(\mathcal{B}\) such that

\[ \sum_{K\in\mathcal{B}} \eta_K^2 \leq \theta_C \sum_{K\in\mathcal{T}_h} \eta_K^2, \]

where \(\theta_C\in[0,1)\) is a threshold parameter, and marks the elements in the set \(\mathcal{B}\) for coarsening.

Constructor & Destructor Documentation

DoerflerMarking()

template<typename Estimators >

ptems::DoerflerMarking::DoerflerMarking ( const Estimators &  estimators, double  refineThreshold, double  coarsenThreshold = 0  )

inline

Create a functor for performing Dörfler marking.

Exceptions

std::invalid_argument	If estimators.empty() is true
std::invalid_argument	If refineThreshold is not in \([0,1]\)
std::invalid_argument	If coarsenThreshold is not in \((0,1)\)
std::invalid_argument	If refineThreshold+coarsenThreshold is greater than 1.

Template Parameters

Estimators

Type of the list of estimators. Must by an STL-like container supporting empty(), size(), begin(), end(), and operator[](std::size_t)

Parameters

estimators	List of error indicators \(\eta_K\) (one per element) to use for Dörfler marking.
refineThreshold	The constant \(\theta_R\) denoting the percentage of the total error the sum of the indicators for the elements that should be marked for refinement should be greater than. Must be in range \((0,1)\).
coarsenThreshold	The constant \(\theta_C\) denoting the percentage of the total error the sum of the indicators of the elements that should be marked for coarsening should be less than. Must be in range \([0,1)\) and refineThreshold+coarsenThreshold must be less than 1.

Member Function Documentation

operator()()

AdaptationType ptems::DoerflerMarking::operator() ( std::size_t  element ) const

inline

Functor operator to compute the adaptation type for the specifeid element.

Parameters

element

Index of the element to get the adaptation type for

Returns

Adaptation type (Refine, coarsen, or none)

---

The documentation for this struct was generated from the following file:

• ptems/refinements.hpp