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Reference documentation for deal.II version 8.1.0
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#include <mapping_q1.h>
Public Member Functions | |
InternalData (const unsigned int n_shape_functions) | |
double | shape (const unsigned int qpoint, const unsigned int shape_nr) const |
double & | shape (const unsigned int qpoint, const unsigned int shape_nr) |
Tensor< 1, dim > | derivative (const unsigned int qpoint, const unsigned int shape_nr) const |
Tensor< 1, dim > & | derivative (const unsigned int qpoint, const unsigned int shape_nr) |
Tensor< 2, dim > | second_derivative (const unsigned int qpoint, const unsigned int shape_nr) const |
Tensor< 2, dim > & | second_derivative (const unsigned int qpoint, const unsigned int shape_nr) |
virtual std::size_t | memory_consumption () const |
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InternalDataBase () | |
virtual | ~InternalDataBase () |
UpdateFlags | current_update_flags () const |
bool | is_first_cell () const |
virtual void | clear_first_cell () |
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Subscriptor () | |
Subscriptor (const Subscriptor &) | |
virtual | ~Subscriptor () |
Subscriptor & | operator= (const Subscriptor &) |
void | subscribe (const char *identifier=0) const |
void | unsubscribe (const char *identifier=0) const |
unsigned int | n_subscriptions () const |
void | list_subscribers () const |
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.") | |
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1) | |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
Public Attributes | |
std::vector< double > | shape_values |
std::vector< Tensor< 1, dim > > | shape_derivatives |
std::vector< Tensor< 2, dim > > | shape_second_derivatives |
std::vector< DerivativeForm < 1, dim, spacedim > > | covariant |
std::vector< DerivativeForm < 1, dim, spacedim > > | contravariant |
std::vector< std::vector < Tensor< 1, dim > > > | unit_tangentials |
std::vector< std::vector < Tensor< 1, spacedim > > > | aux |
std::vector< Point< spacedim > > | mapping_support_points |
Triangulation< dim, spacedim > ::cell_iterator | cell_of_current_support_points |
bool | is_mapping_q1_data |
unsigned int | n_shape_functions |
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UpdateFlags | update_flags |
UpdateFlags | update_once |
UpdateFlags | update_each |
std::vector< double > | volume_elements |
std::vector< Point< spacedim > > | support_point_values |
std::vector< Tensor < 2, spacedim > > | support_point_gradients |
std::vector< Tensor < 2, spacedim > > | support_point_inverse_gradients |
Storage for internal data of d-linear transformation.
Definition at line 186 of file mapping_q1.h.
MappingQ1< dim, spacedim >::InternalData::InternalData | ( | const unsigned int | n_shape_functions | ) |
Constructor. Pass the number of shape functions.
double MappingQ1< dim, spacedim >::InternalData::shape | ( | const unsigned int | qpoint, |
const unsigned int | shape_nr | ||
) | const |
Shape function at quadrature point. Shape functions are in tensor product order, so vertices must be reordered to obtain transformation.
double& MappingQ1< dim, spacedim >::InternalData::shape | ( | const unsigned int | qpoint, |
const unsigned int | shape_nr | ||
) |
Shape function at quadrature point. See above.
Tensor<1,dim> MappingQ1< dim, spacedim >::InternalData::derivative | ( | const unsigned int | qpoint, |
const unsigned int | shape_nr | ||
) | const |
Gradient of shape function in quadrature point. See above.
Tensor<1,dim>& MappingQ1< dim, spacedim >::InternalData::derivative | ( | const unsigned int | qpoint, |
const unsigned int | shape_nr | ||
) |
Gradient of shape function in quadrature point. See above.
Tensor<2,dim> MappingQ1< dim, spacedim >::InternalData::second_derivative | ( | const unsigned int | qpoint, |
const unsigned int | shape_nr | ||
) | const |
Second derivative of shape function in quadrature point. See above.
Tensor<2,dim>& MappingQ1< dim, spacedim >::InternalData::second_derivative | ( | const unsigned int | qpoint, |
const unsigned int | shape_nr | ||
) |
Second derivative of shape function in quadrature point. See above.
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virtual |
Return an estimate (in bytes) or the memory consumption of this object.
Reimplemented from Mapping< dim, spacedim >::InternalDataBase.
Reimplemented in MappingQ< dim, spacedim >::InternalData.
std::vector<double> MappingQ1< dim, spacedim >::InternalData::shape_values |
Values of shape functions. Access by function shape
.
Computed once.
Definition at line 259 of file mapping_q1.h.
std::vector<Tensor<1,dim> > MappingQ1< dim, spacedim >::InternalData::shape_derivatives |
Values of shape function derivatives. Access by function derivative
.
Computed once.
Definition at line 268 of file mapping_q1.h.
std::vector<Tensor<2,dim> > MappingQ1< dim, spacedim >::InternalData::shape_second_derivatives |
Values of shape function second derivatives. Access by function second_derivative
.
Computed once.
Definition at line 278 of file mapping_q1.h.
std::vector<DerivativeForm<1,dim, spacedim > > MappingQ1< dim, spacedim >::InternalData::covariant |
Tensors of covariant transformation at each of the quadrature points. The matrix stored is the Jacobian * G^{-1}, where G = Jacobian^{t} * Jacobian, is the first fundamental form of the map; if dim=spacedim then it reduces to the transpose of the inverse of the Jacobian matrix, which itself is stored in the contravariant
field of this structure.
Computed on each cell.
Definition at line 299 of file mapping_q1.h.
std::vector< DerivativeForm<1,dim,spacedim> > MappingQ1< dim, spacedim >::InternalData::contravariant |
Tensors of contravariant transformation at each of the quadrature points. The contravariant matrix is the Jacobian of the transformation, i.e. .
Computed on each cell.
Definition at line 312 of file mapping_q1.h.
std::vector<std::vector<Tensor<1,dim> > > MappingQ1< dim, spacedim >::InternalData::unit_tangentials |
Unit tangential vectors. Used for the computation of boundary forms and normal vectors.
This vector has (dim-1)GeometryInfo::faces_per_cell entries. The first GeometryInfo::faces_per_cell contain the vectors in the first tangential direction for each face; the second set of GeometryInfo::faces_per_cell entries contain the vectors in the second tangential direction (only in 3d, since there we have 2 tangential directions per face), etc.
Filled once.
Definition at line 336 of file mapping_q1.h.
std::vector<std::vector<Tensor<1,spacedim> > > MappingQ1< dim, spacedim >::InternalData::aux |
Auxiliary vectors for internal use.
Definition at line 341 of file mapping_q1.h.
std::vector<Point<spacedim> > MappingQ1< dim, spacedim >::InternalData::mapping_support_points |
Stores the support points of the mapping shape functions on the cell_of_current_support_points
.
Definition at line 348 of file mapping_q1.h.
Triangulation<dim,spacedim>::cell_iterator MappingQ1< dim, spacedim >::InternalData::cell_of_current_support_points |
Stores the cell of which the mapping_support_points
are stored.
Definition at line 355 of file mapping_q1.h.
bool MappingQ1< dim, spacedim >::InternalData::is_mapping_q1_data |
Default value of this flag is true
. If *this
is an object of a derived class, this flag is set to false
.
Definition at line 364 of file mapping_q1.h.
unsigned int MappingQ1< dim, spacedim >::InternalData::n_shape_functions |
Number of shape functions. If this is a Q1 mapping, then it is simply the number of vertices per cell. However, since also derived classes use this class (e.g. the Mapping_Q() class), the number of shape functions may also be different.
Definition at line 379 of file mapping_q1.h.