dune-localfunctions
2.2.1
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Convert a simple scalar local basis into a global basis. More...
#include <dune/localfunctions/common/localtoglobaladaptors.hh>
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typedef LocalToGlobalBasisAdaptorTraits < typename LocalBasis::Traits, Geometry::coorddimension > | Traits |
Public Member Functions | |
ScalarLocalToGlobalBasisAdaptor (const LocalBasis &localBasis_, const Geometry &geometry_) | |
construct a ScalarLocalToGlobalBasisAdaptor More... | |
std::size_t | size () const |
std::size_t | order () const |
return maximum polynomial order of the base function More... | |
void | evaluateFunction (const typename Traits::DomainLocal &in, std::vector< typename Traits::Range > &out) const |
void | evaluateJacobian (const typename Traits::DomainLocal &in, std::vector< typename Traits::Jacobian > &out) const |
void | evaluateFunction (const Traits::DomainLocal &in, std::vector< Traits::Range > &out) const |
Evaluate all shape functions at given position. More... | |
void | evaluateJacobian (const Traits::DomainLocal &in, std::vector< Traits::Jacobian > &out) const |
Evaluate Jacobian of all shape functions at given position. More... | |
void | evaluate (const array< std::size_t, Traits::dimDomainGlobal > &directions, const Traits::DomainLocal &in, std::vector< Traits::Range > &out) const |
Evaluate derivatives of all shape functions at given position. More... | |
Convert a simple scalar local basis into a global basis.
The local basis must be scalar, i.e. LocalBasis::Traits::dimRange must be
For scalar function , the gradient is equivalent to the transposed Jacobian
. The Jacobian is thus transformed using
Here the hat denotes local quantities and
denotes the local-to-global map of the geometry.
LocalBasis | Type of the local basis to adapt. |
Geometry | Type of the local-to-global transformation. |
typedef LocalToGlobalBasisAdaptorTraits<typename LocalBasis::Traits, Geometry::coorddimension> Dune::ScalarLocalToGlobalBasisAdaptor< LocalBasis, Geometry >::Traits |
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construct a ScalarLocalToGlobalBasisAdaptor
localBasis_ | The local basis object to adapt. |
geometry_ | The geometry object to use for adaption. |
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inherited |
Evaluate derivatives of all shape functions at given position.
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inherited |
Evaluate all shape functions at given position.
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Referenced by Dune::EdgeS0_5Basis< Geometry, RF >::EdgeS0_5Basis().
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inherited |
Evaluate Jacobian of all shape functions at given position.
Note: Only required for Traits::diffOrder >= 1
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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 assumtion for non-affine geometries is that they are still multi-linear.
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