Maxwell Equations
Finite Difference Time Domain Maxwell Equations
The simple example solves the Maxwell equations in two dimensions.
Equations of motion
The Maxwell equations are
\[\nabla \times E = -\frac{\partial B}{\partial t}.\]
\[\begin{aligned} \nabla\cdot\mathbf{E} &= 4 \pi \rho \\ \nabla\cdot\mathbf{B} &= 0 \\ \nabla\times\mathbf{E} &= - \frac{1}{c} \frac{\partial\mathbf{B}}{\partial t} \\ \nabla\times\mathbf{B} &= - \frac{1}{c} \left(4 \pi \mathbf{J} + \frac{\partial\mathbf{E}}{\partial t} \right) \end{aligned}\]