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Reference documentation for deal.II version 9.5.1
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#include <deal.II/base/derivative_form.h>
Public Member Functions | |
DerivativeForm ()=default | |
DerivativeForm (const Tensor< order+1, dim, Number > &) | |
DerivativeForm (const Tensor< 1, spacedim, Tensor< order, dim, Number > > &) | |
Tensor< order, dim, Number > & | operator[] (const unsigned int i) |
const Tensor< order, dim, Number > & | operator[] (const unsigned int i) const |
DerivativeForm & | operator= (const Tensor< order+1, dim, Number > &) |
DerivativeForm & | operator= (const Tensor< order, spacedim, Tensor< 1, dim, Number > > &) |
DerivativeForm & | operator= (const Tensor< 1, dim, Number > &) |
template<typename OtherNumber > | |
DerivativeForm & | operator= (const DerivativeForm< order, dim, spacedim, OtherNumber > &df) |
operator Tensor< order+1, dim, Number > () const | |
operator Tensor< 1, dim, Number > () const | |
DerivativeForm< 1, spacedim, dim, Number > | transpose () const |
numbers::NumberTraits< Number >::real_type | norm () const |
Number | determinant () const |
DerivativeForm< 1, dim, spacedim, Number > | covariant_form () const |
Static Public Member Functions | |
static std::size_t | memory_consumption () |
static ::ExceptionBase & | ExcInvalidTensorIndex (int arg1) |
Private Member Functions | |
DerivativeForm< 1, dim, spacedim, Number > | times_T_t (const Tensor< 2, dim, Number > &T) const |
Private Attributes | |
Tensor< order, dim, Number > | tensor [spacedim] |
Related Symbols | |
(Note that these are not member symbols.) | |
template<int spacedim, int dim, typename Number1 , typename Number2 > | |
Tensor< 1, spacedim, typename ProductType< Number1, Number2 >::type > | apply_transformation (const DerivativeForm< 1, dim, spacedim, Number1 > &grad_F, const Tensor< 1, dim, Number2 > &d_x) |
template<int spacedim, int dim, typename Number1 , typename Number2 > | |
DerivativeForm< 1, spacedim, dim, typename ProductType< Number1, Number2 >::type > | apply_transformation (const DerivativeForm< 1, dim, spacedim, Number1 > &grad_F, const Tensor< 2, dim, Number2 > &D_X) |
template<int dim, typename Number1 , typename Number2 > | |
Tensor< 2, dim, typename ProductType< Number1, Number2 >::type > | apply_transformation (const DerivativeForm< 1, dim, dim, Number1 > &grad_F, const Tensor< 2, dim, Number2 > &D_X) |
template<int spacedim, int dim, int n_components, typename Number1 , typename Number2 > | |
Tensor< 1, n_components, Tensor< 1, spacedim, typename ProductType< Number1, Number2 >::type > > | apply_transformation (const DerivativeForm< 1, dim, spacedim, Number1 > &grad_F, const Tensor< 1, n_components, Tensor< 1, dim, Number2 > > &D_X) |
template<int spacedim, int dim, typename Number1 , typename Number2 > | |
Tensor< 2, spacedim, typename ProductType< Number1, Number2 >::type > | apply_transformation (const DerivativeForm< 1, dim, spacedim, Number1 > &DF1, const DerivativeForm< 1, dim, spacedim, Number2 > &DF2) |
template<int dim, int spacedim, typename Number > | |
DerivativeForm< 1, spacedim, dim, Number > | transpose (const DerivativeForm< 1, dim, spacedim, Number > &DF) |
This class represents the (tangential) derivatives of a function
i.e., one needs to be able to multiply the matrix
Similarly, the second derivative is a bilinear map from
In deal.II we represent these derivatives using objects of type DerivativeForm<1,dim,spacedim,Number>, DerivativeForm<2,dim,spacedim,Number> and so on.
Definition at line 58 of file derivative_form.h.
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default |
Constructor. Initialize all entries to zero.
DerivativeForm< order, dim, spacedim, Number >::DerivativeForm | ( | const Tensor< order+1, dim, Number > & | ) |
Constructor from a tensor.
DerivativeForm< order, dim, spacedim, Number >::DerivativeForm | ( | const Tensor< 1, spacedim, Tensor< order, dim, Number > > & | ) |
Tensor< order, dim, Number > & DerivativeForm< order, dim, spacedim, Number >::operator[] | ( | const unsigned int | i | ) |
Read-Write access operator.
const Tensor< order, dim, Number > & DerivativeForm< order, dim, spacedim, Number >::operator[] | ( | const unsigned int | i | ) | const |
Read-only access operator.
DerivativeForm & DerivativeForm< order, dim, spacedim, Number >::operator= | ( | const Tensor< order+1, dim, Number > & | ) |
Assignment operator.
DerivativeForm & DerivativeForm< order, dim, spacedim, Number >::operator= | ( | const Tensor< order, spacedim, Tensor< 1, dim, Number > > & | ) |
Assignment operator.
DerivativeForm & DerivativeForm< order, dim, spacedim, Number >::operator= | ( | const Tensor< 1, dim, Number > & | ) |
Assignment operator.
DerivativeForm & DerivativeForm< order, dim, spacedim, Number >::operator= | ( | const DerivativeForm< order, dim, spacedim, OtherNumber > & | df | ) |
Number conversion operator.
DerivativeForm< order, dim, spacedim, Number >::operator Tensor< order+1, dim, Number > | ( | ) | const |
Converts a DerivativeForm <order, dim, dim, Number> to Tensor<order+1, dim, Number>. In particular, if order == 1 and the derivative is the Jacobian of
DerivativeForm< order, dim, spacedim, Number >::operator Tensor< 1, dim, Number > | ( | ) | const |
Converts a DerivativeForm<1, dim, 1, Number> to Tensor<1, dim, Number>.
DerivativeForm< 1, spacedim, dim, Number > DerivativeForm< order, dim, spacedim, Number >::transpose | ( | ) | const |
Return the transpose of a rectangular DerivativeForm, viewed as a two dimensional matrix.
numbers::NumberTraits< Number >::real_type DerivativeForm< order, dim, spacedim, Number >::norm | ( | ) | const |
Compute the Frobenius norm of this form, i.e., the expression
Number DerivativeForm< order, dim, spacedim, Number >::determinant | ( | ) | const |
Compute the volume element associated with the jacobian of the transformation
DerivativeForm< 1, dim, spacedim, Number > DerivativeForm< order, dim, spacedim, Number >::covariant_form | ( | ) | const |
Assuming that the current object stores the Jacobian of a mapping
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static |
Determine an estimate for the memory consumption (in bytes) of this object.
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private |
Auxiliary function that computes
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related |
One of the uses of DerivativeForm is to apply it as a linear transformation. This function returns
The transformation corresponds to
in index notation and corresponds to
Definition at line 454 of file derivative_form.h.
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related |
Similar to the previous apply_transformation(). Each row of the result corresponds to one of the rows of D_X
transformed by grad_F
, equivalent to
Definition at line 479 of file derivative_form.h.
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related |
Similar to the previous apply_transformation(), specialized for the case dim == spacedim
where we can return a rank-2 tensor instead of the more general DerivativeForm
. Each row of the result corresponds to one of the rows of D_X
transformed by grad_F
, equivalent to
Definition at line 505 of file derivative_form.h.
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related |
Similar to the previous apply_transformation(). Each row of the result corresponds to one of the rows of D_X
transformed by grad_F
.
Definition at line 532 of file derivative_form.h.
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related |
Similar to the previous apply_transformation(). In matrix notation, it computes
Definition at line 565 of file derivative_form.h.
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related |
Transpose of a rectangular DerivativeForm DF, mostly for compatibility reasons.
Definition at line 586 of file derivative_form.h.
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private |
Array of tensors holding the subelements.
Definition at line 189 of file derivative_form.h.