dune-pdelab  2.4-dev
Public Types | Public Member Functions | Static Public Attributes | List of all members
Dune::PDELab::JacobianToCurl< Jacobian, 2, 2 > Class Template Reference

extract the curl of a 2D-valued function in 2D from the jacobian of that function More...

#include <dune/pdelab/common/jacobiantocurl.hh>

Public Types

typedef Jacobian::block_type CurlField
 
typedef FieldVector< CurlField, dimCurlCurl
 

Public Member Functions

void operator() (const Jacobian &jacobian, Curl &curl) const
 

Static Public Attributes

static const std::size_t dimCurl = 1
 

Detailed Description

template<typename Jacobian>
class Dune::PDELab::JacobianToCurl< Jacobian, 2, 2 >

extract the curl of a 2D-valued function in 2D from the jacobian of that function

The two coordinates are the $x$- and $y$ coordinates and the two value components the $x$- and $y$-components of the quantity. It is assumed that the quantity shows no variation in the $z$-direction (thus $\partial_z=0$) and that its $z$-component vanishes. From the general 3D formula for the curl

\begin{align*} A &=\nabla\times B \\ & \Downarrow \\ a_x &= \partial_yb_z-\partial_zb_y \\ a_y &= \partial_zb_x-\partial_xb_z \\ a_z &= \partial_xb_y-\partial_yb_x \end{align*}

only the last survives:

\begin{align*} a_z &= \partial_xb_y-\partial_yb_x \end{align*}

Replacing $x$, $y$ and $z$ by the apropriate indices yields

\begin{align*} a_0 &= \partial_0b_1-\partial_1b_0 \end{align*}

Member Typedef Documentation

template<typename Jacobian >
typedef FieldVector<CurlField, dimCurl> Dune::PDELab::JacobianToCurl< Jacobian, 2, 2 >::Curl
template<typename Jacobian >
typedef Jacobian::block_type Dune::PDELab::JacobianToCurl< Jacobian, 2, 2 >::CurlField

Member Function Documentation

template<typename Jacobian >
void Dune::PDELab::JacobianToCurl< Jacobian, 2, 2 >::operator() ( const Jacobian &  jacobian,
Curl curl 
) const
inline

Member Data Documentation

template<typename Jacobian >
const std::size_t Dune::PDELab::JacobianToCurl< Jacobian, 2, 2 >::dimCurl = 1
static

The documentation for this class was generated from the following file: