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, dimCurl >	Curl

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

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