In this unit we explore the similarities and differences between DGTD and FDTD as time-domain
The DGTD solver and the FDTD solver share several similarities:
They both solve the same physics, namely Maxwell’s equation in the time-domain.
They can deal with arbitrary dispersive materials thanks to Lumerical’s multi-coefficient
Both solvers support the same type of boundary conditions, such as PML, periodic, Perfect
Electric Conductor and Perfect Magnetic Conductor.
FDTD and DGTD support plane wave and gaussian beam sources.
Data can be recorded using either frequency-domain and time-domain monitors
And finally: both solvers include far-field and grating projection tools.
On the other hand, DGTD differs from FDTD in several aspects:
While FDTD uses a rectilinear mesh, DGTD uses an unstructured mesh to model the geometry.
The mesh is made of triangles (in 2D) or tetrahedra in 3D.
The simulation region can have an arbitrary shape instead of just a rectangular box.
Simulation objects such as sources or monitors can be assigned to existing geometric objects.
The accuracy of the calculation can be increased by controlling the polynomial order.
And finally, the DGTD solver is integrated into the DEVICE Multiphysics simulation environment.
As we just mentioned, the accuracy of a DGTD calculation can be controlled via both the
mesh and the polynomial order.
To demonstrate this in more detail, we have run a basic test case: we calculate the transmission
through a 400nm thick glass slab for different mesh sizes and polynomial orders.
We then plot the RMS error of the transmission calculation as a function of the number of
edges per wavelength for different polynomial orders: 1, 2 and 3.
As we can see, increasing the polynomial order increases the accuracy of the calculations
for a specific mesh size, but it also increases how quickly the accuracy gets better as we
reduce the mesh.
This is indicated by the slope of the different plots.
In the next unit, we will learn about the application areas where DGTD is a good candidate
as an optical solver.