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Reference documentation for deal.II version 9.3.3
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Go to the source code of this file.
Classes | |
class | DerivativeForm< order, dim, spacedim, Number > |
Functions | |
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 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) |
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One of the uses of DerivativeForm is to apply it as a linear transformation. This function returns , which approximates the change in
when
is changed by the amount
The transformation corresponds to
in index notation and corresponds to in matrix notation.
Definition at line 429 of file derivative_form.h.
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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 in matrix notation.
Definition at line 454 of file derivative_form.h.
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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 482 of file derivative_form.h.
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Similar to the previous apply_transformation(). In matrix notation, it computes . Moreover, the result of this operation
can be interpreted as a metric tensor in
which corresponds to the Euclidean metric tensor in
. For every pair of vectors
, we have:
Definition at line 515 of file derivative_form.h.
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Transpose of a rectangular DerivativeForm DF, mostly for compatibility reasons.
Definition at line 536 of file derivative_form.h.