Changes

where '''E''' and '''H''' are the electric and magnetic fields, respectively, ε is the permittivity and μ is the permeability. Both time- and space-derivatives are approximated with central finite differences. This results in six differential equations, one for each field component. For the field components in x-direction, the field equations result in:

where i, j, k are the grid position indices along the X, Y, Z axes and n is the current time step. Similar expressions are obtained for the Y and Z components of the electric and magnetic fields. When your physical structure involves lossy materials with nonzero electric conductivity σ and/or nonzero electric conductivity σ_m, the above update equations become more complicated. In the case of anisotropic materials with tensorial constitutive parameters, the electric displacement vector D and magnetic induction vector B need to be involved in the update of Maxwell's equations at every time step. This results in a total of twelve update equations at every time step. In the case of dispersive materials with time-varying constitutive parameters, additional auxiliary differential equations are invoked and updated at every time step. Applying the proper boundary conditions for all the materials inside the computational domain and at the boundaries of the domain itself, EM.Cube calculates and "updates" all the necessary field components at every mesh node, at every time step. The time marching loop continues in this way until it is terminated based on a certain criterion.