DUNE PDELab (2.7)
extract the curl of a 1D-valued function in 2D from the jacobian of that function More...
#include <dune/pdelab/common/jacobiantocurl.hh>
Detailed Description
class Dune::PDELab::JacobianToCurl< Jacobian, 1, 2 >
extract the curl of a 1D-valued function in 2D from the jacobian of that function
The two coordinates are the \(x\)- and \(y\) coordinates and the one value component is the \(z\)-component of the quantity. It is assumed that the quantity shows no variation in the \(z\)-direction (thus \(\partial_z=0\)) and that its \(x\)- and \(y\)-components vanish. 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 first two survive:
\begin{align*} a_x &= \partial_yb_z \\ a_y &= -\partial_xb_z \end{align*}
Replacing \(x\), \(y\) and \(z\) by the apropriate indices yields
\begin{align*} a_0 &= \partial_1b_0 \\ a_1 &= -\partial_0b_0 \end{align*}
The documentation for this class was generated from the following file:
- dune/pdelab/common/jacobiantocurl.hh
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