Dune::ScalarLocalToGlobalBasisAdaptor< LocalBasis, Geometry > Class Template Reference

Convert a simple scalar local basis into a global basis. More...

#include <dune/localfunctions/common/localtoglobaladaptors.hh>

Public Member Functions
	ScalarLocalToGlobalBasisAdaptor (const LocalBasis &localBasis_, const Geometry &geometry_)
	construct a ScalarLocalToGlobalBasisAdaptor More...
std::size_t	order () const
	return maximum polynomial order of the base function More...
void	evaluateFunction (const Traits::DomainType &in, std::vector< Traits::RangeType > &out) const
	Evaluate all shape functions at given position.
void	evaluateJacobian (const Traits::DomainType &in, std::vector< Traits::Jacobian > &out) const
	Evaluate Jacobian of all shape functions at given position.
void	partial (const std::array< unsigned int, Traits::dimDomain > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
	Evaluate partial derivatives of any order of all shape functions. More...

Detailed Description

template<class LocalBasis, class Geometry>
class Dune::ScalarLocalToGlobalBasisAdaptor< LocalBasis, Geometry >

Convert a simple scalar local basis into a global basis.

The local basis must be scalar, i.e. LocalBasis::Traits::dimRange must be

1. It's values are not transformed.

For scalar function \(f\), the gradient is equivalent to the transposed Jacobian \(\nabla f|_x = J_f^T(x)\). The Jacobian is thus transformed using

\[ \nabla f|_{\mu(\hat x)} = \hat J_\mu^{-T}(\hat x) \cdot \hat\nabla\hat f|_{\hat x} \]

Here the hat \(\hat{\phantom x}\) denotes local quantities and \(\mu\) denotes the local-to-global map of the geometry.

Template Parameters

LocalBasis	Type of the local basis to adapt.
Geometry	Type of the local-to-global transformation.

Constructor & Destructor Documentation

ScalarLocalToGlobalBasisAdaptor()

template<class LocalBasis , class Geometry >

Dune::ScalarLocalToGlobalBasisAdaptor< LocalBasis, Geometry >::ScalarLocalToGlobalBasisAdaptor ( const LocalBasis &  localBasis_, const Geometry &  geometry_  )

inline

construct a ScalarLocalToGlobalBasisAdaptor

Parameters

localBasis_	The local basis object to adapt.
geometry_	The geometry object to use for adaption.

Note

This class stores the references passed here. Any use of this class after these references have become invalid results in undefined behaviour. The exception is that the destructor of this class may still be called.

Member Function Documentation

order()

template<class LocalBasis , class Geometry >

std::size_t Dune::ScalarLocalToGlobalBasisAdaptor< LocalBasis, Geometry >::order ( ) const

inline

return maximum polynomial order of the base function

This is to determine the required quadrature order. For an affine geometry this is the same order as for the local basis. For other geometries this returns the order of the local basis plus the global dimension minus 1. The assumption for non-affine geometries is that they are still multi-linear.

References Dune::Geometry< mydim, cdim, GridImp, GeometryImp >::affine().

partial()

void Dune::BasisInterface::partial ( const std::array< unsigned int, Traits::dimDomain > &  order, const typename Traits::DomainType &  in, std::vector< typename Traits::RangeType > &  out  ) const

inherited

Evaluate partial derivatives of any order of all shape functions.

Parameters

	order	Order of the partial derivatives, in the classic multi-index notation
	in	Position where to evaluate the derivatives
[out]	out	Return value: the desired partial derivatives

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

• dune/localfunctions/common/localtoglobaladaptors.hh