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Reference documentation for deal.II version 8.1.0
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#include <derivative_form.h>
Public Member Functions | |
DerivativeForm () | |
DerivativeForm (const Tensor< 2, dim > &) | |
Tensor< order, dim > & | operator[] (const unsigned int i) |
const Tensor< order, dim > & | operator[] (const unsigned int i) const |
DerivativeForm & | operator= (const DerivativeForm< order, dim, spacedim > &) |
DerivativeForm & | operator= (const Tensor< 2, dim > &) |
DerivativeForm & | operator= (const Tensor< 1, dim > &) |
operator Tensor< 2, dim > () const | |
operator Tensor< 1, dim > () const | |
DerivativeForm< 1, spacedim, dim > | transpose () const |
double | determinant () const |
DerivativeForm< 1, dim, spacedim > | covariant_form () const |
DeclException1 (ExcInvalidTensorIndex, int,<< "Invalid DerivativeForm index "<< arg1) | |
Static Public Member Functions | |
static std::size_t | memory_consumption () |
Private Member Functions | |
DerivativeForm< 1, dim, spacedim > | times_T_t (Tensor< 2, dim > T) const |
Private Attributes | |
Tensor< order, dim > | tensor [spacedim] |
Related Functions | |
(Note that these are not member functions.) | |
template<int spacedim, int dim> | |
Tensor< 1, spacedim > | apply_transformation (const DerivativeForm< 1, dim, spacedim > &DF, const Tensor< 1, dim > &T) |
template<int spacedim, int dim> | |
DerivativeForm< 1, spacedim, dim > | apply_transformation (const DerivativeForm< 1, dim, spacedim > &DF, const Tensor< 2, dim > &T) |
template<int spacedim, int dim> | |
Tensor< 2, spacedim > | apply_transformation (const DerivativeForm< 1, dim, spacedim > &DF1, const DerivativeForm< 1, dim, spacedim > &DF2) |
template<int dim, int spacedim> | |
DerivativeForm< 1, spacedim, dim > | transpose (const DerivativeForm< 1, dim, spacedim > &DF) |
This class represents the (tangential) derivatives of a function . Such functions are always used to map the reference dim-dimensional cell into spacedim-dimensional space. For such objects, the first derivative of the function is a linear map from
to
, the second derivative a bilinear map from
to
and so on.
In deal.II we represent these derivaties using objects of type DerivativeForm<1,dim,spacedim>, DerivativeForm<2,dim,spacedim> and so on.
Definition at line 41 of file derivative_form.h.
DerivativeForm< order, dim, spacedim >::DerivativeForm | ( | ) |
Constructor. Initialize all entries to zero.
DerivativeForm< order, dim, spacedim >::DerivativeForm | ( | const Tensor< 2, dim > & | ) |
Constructor from a second order tensor.
Tensor<order,dim>& DerivativeForm< order, dim, spacedim >::operator[] | ( | const unsigned int | i | ) |
Read-Write access operator.
const Tensor<order,dim>& DerivativeForm< order, dim, spacedim >::operator[] | ( | const unsigned int | i | ) | const |
Read-only access operator.
DerivativeForm& DerivativeForm< order, dim, spacedim >::operator= | ( | const DerivativeForm< order, dim, spacedim > & | ) |
Assignment operator.
DerivativeForm& DerivativeForm< order, dim, spacedim >::operator= | ( | const Tensor< 2, dim > & | ) |
Assignment operator.
DerivativeForm& DerivativeForm< order, dim, spacedim >::operator= | ( | const Tensor< 1, dim > & | ) |
Assignment operator.
DerivativeForm< order, dim, spacedim >::operator Tensor< 2, dim > | ( | ) | const |
Converts a DerivativeForm <1,dim, dim> to Tensor<2,dim>. If the derivative is the Jacobian of F, then Tensor[i] = grad(F^i).
DerivativeForm< order, dim, spacedim >::operator Tensor< 1, dim > | ( | ) | const |
Converts a DerivativeForm <1, dim, 1> to Tensor<1,dim>.
DerivativeForm<1, spacedim, dim> DerivativeForm< order, dim, spacedim >::transpose | ( | ) | const |
Return the transpose of a rectangular DerivativeForm, that is to say viewed as a two dimensional matrix.
double DerivativeForm< order, dim, spacedim >::determinant | ( | ) | const |
Computes the volume element associated with the jacobian of the tranformation F. That is to say if is square, it computes
, in case DF is not square returns
.
DerivativeForm<1, dim, spacedim> DerivativeForm< order, dim, spacedim >::covariant_form | ( | ) | const |
Assuming (*this) stores the jacobian of the mapping F, it computes its covariant matrix, namely , where
. If
is square, covariant from gives
.
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static |
Determine an estimate for the memory consumption (in bytes) of this object.
DerivativeForm< order, dim, spacedim >::DeclException1 | ( | ExcInvalidTensorIndex | , |
int | , | ||
<< "Invalid DerivativeForm< order, dim, spacedim > index "<< | arg1 | ||
) |
Exception.
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private |
Auxiliary function that computes (*this) * T^{t}
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related |
One of the uses of DerivativeForm is to apply it as a transformation. This is what this function does.
If T
is DerivativeForm<1,dim,1> it computes , if
T
is DerivativeForm<1,dim,rank> it computes .
Definition at line 409 of file derivative_form.h.
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related |
Similar to previous apply_transformation. It computes
Definition at line 430 of file derivative_form.h.
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related |
Similar to previous apply_transformation. It computes
Definition at line 450 of file derivative_form.h.
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related |
Transpose of a rectangular DerivativeForm DF, mostly for compatibility reasons.
Definition at line 471 of file derivative_form.h.
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private |
Array of tensors holding the subelements.
Definition at line 151 of file derivative_form.h.