Dune::PDELab::JacobianToCurl< Jacobian, 1, 2 > Class Template Reference

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

template<typename Jacobian>
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