Reference documentation for deal.II version 9.2.0
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Public Types | |
using | Derivative = Tensor< 2, dim > |
using | ProjectedDerivative = Tensor< 1, dim > |
Public Member Functions | |
double | derivative_norm (const Derivative &d) |
double | derivative_norm (const Derivative &d) |
double | derivative_norm (const Derivative &d) |
Static Public Member Functions | |
template<class InputVector , int spacedim> | |
static ProjectedDerivative | get_projected_derivative (const FEValues< dim, spacedim > &fe_values, const InputVector &solution, const unsigned int component) |
static double | derivative_norm (const Derivative &d) |
static void | symmetrize (Derivative &derivative_tensor) |
Static Public Attributes | |
static const UpdateFlags | update_flags = update_gradients |
The following class is used to describe the data needed to compute the finite difference approximation to the second derivatives on a cell. See the general documentation of this class for more information on implementational details.
Definition at line 193 of file derivative_approximation.cc.
using DerivativeApproximation::internal::SecondDerivative< dim >::Derivative = Tensor<2, dim> |
Declare the data type which holds the derivative described by this class.
Definition at line 206 of file derivative_approximation.cc.
using DerivativeApproximation::internal::SecondDerivative< dim >::ProjectedDerivative = Tensor<1, dim> |
Likewise declare the data type that holds the derivative projected to a certain directions.
Definition at line 212 of file derivative_approximation.cc.
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inlinestatic |
Given an FEValues object initialized to a cell, and a solution vector, extract the desired derivative at the first quadrature point (which is the only one, as we only evaluate the finite element field at the center of each cell).
Definition at line 256 of file derivative_approximation.cc.
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inlinestatic |
Return the norm of the derivative object. Here, for the (symmetric) tensor of second derivatives, we choose the absolute value of the largest eigenvalue, which is the matrix norm associated to the \(l_2\) norm of vectors. It is also the largest value of the curvature of the solution.
Definition at line 492 of file derivative_approximation.cc.
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inlinestatic |
If for the present derivative order, symmetrization of the derivative tensor is necessary, then do so on the argument.
For the second derivatives, each entry of the tensor is set to the mean of its value and the value of the transpose element.
Note that this function actually modifies its argument.
Definition at line 515 of file derivative_approximation.cc.
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inline |
Definition at line 285 of file derivative_approximation.cc.
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inline |
Definition at line 294 of file derivative_approximation.cc.
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inline |
Definition at line 317 of file derivative_approximation.cc.
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static |
Declare which data fields have to be updated for the function get_projected_derivative
to work.
Definition at line 200 of file derivative_approximation.cc.