Dune::PDELab::JacobianToCurl< Jacobian, 3, 3 > Class Template Reference

extract the curl of a 3D-valued function in 3D from the jacobian of that function More...

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

Detailed Description

template<typename Jacobian>
class Dune::PDELab::JacobianToCurl< Jacobian, 3, 3 >

extract the curl of a 3D-valued function in 3D from the jacobian of that function

In 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*}

we just need to replace \(x\), \(y\) and \(z\) by the apropriate indices

\begin{align*} a_0 &= \partial_1b_2-\partial_2b_1 \\ a_1 &= \partial_2b_0-\partial_0b_2 \\ a_2 &= \partial_0b_1-\partial_1b_0 \end{align*}

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

• dune/pdelab/common/jacobiantocurl.hh