The DGTD acronym stands for Discontinuous Galerkin Time-Domain and describes a method
that can rigorously solve Maxwell’s equations in time domain.
As the name already suggests, the method can handle discontinuous fields at material interfaces
This means that the method is particularly well suited for applications, where there
is a large contrast in the dielectric function across material interfaces.
A typical example for this are plasmonic structures.
It’s important to note that our DGTD implementation can handle general dispersive materials, by
automatically fitting a model to permittivity data given in the frequency domain.
Despite being a time-domain method, DGTD is a variation of the well-known finite-element
method and also operates on an unstructured mesh.
So, for a 2D simulation, the mesh is formed of triangles and in 3D it is made of tetrahedra.
This unstructured form of mesh can accurately model curved geometries and offers the ability
to locally refine the simulation mesh for areas of interest.
In addition, it enables the simulation objects such as sources, monitors, boundary conditions
or even simulation region to have arbitrary shapes as opposed to the traditional box shaped
A mesh with smaller elements generally leads to a more accurate representation of the geometry
and the fields and therefore gives more accurate results.
However, more elements also increase the simulation time.
By default, the mesh generator will use approximately two elements per shortest wavelength in each
In some cases, it is necessary to add a mesh constraint to refine the mesh locally.
In a DGTD simulation, on each mesh element, the solver expands the electric field and
the magnetic field into polynomials up to a user-specified order.
A higher polynomial order leads to a more accurate solution, but it also increases the
In the next video, we will go over the differences and similarities between DGTD and FDTD as
a more common time domain optical solver.