FDTD - Simulation time and memory dependence on mesh size


I’m wondering if anyone could help with this question: “why do the simulation time and memory requirements scale as λ/dx^4 & λ/dx^3 respectively for a 3D simulation?”



Hi @n.phillipson2
In the FDTD method, the simulation time scales as 1/dx4 for 3D simulations and 1/dx3 for 2D simulations. dx is the mesh size. You can find many information in the following page :

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Hi thanks for your help. The link was helpful, but I’m looking for some details for why there is a 1/dx^4 dependence on mesh size for the simulation time. Thanks, Nigel.

The 1/dx^4 dependences is because the time step, dt, depends on the mesh size as well.

Here is a link to a whitepaper about the conformal mesh technique:

We need to remember that the 1/dx^4 is only an approximation. It makes intuitive sense that there is at least 1/dx^3 dependence due to 3D structure. Then the differences could also be due to how the convergence works for the specific structure you are trying to simulate. Link to convergence process:
I hope that this helps!

Yes thanks! that’s really helpful,

kind regards,