Higher-order FDTD for electrically-large domains

[philippwindischhofer]

Hi all,

We are using MEEP to study broadband wave propagation in large, inhomogeneous media (over several hundred wavelengths). We control numerical dispersion by choosing an appropriately-dense computational grid.

The computing resource usage has been manageable so far, but is soon going to be the bottleneck if we scale up our geometry any further.

I am currently exploring higher-order FDTD schemes to see if they could provide a feasible way forward in applications like ours. Presumably there is a turn-over point at which the higher complexity of these schemes becomes worthwhile given the improved phase accuracy.

Would you consider e.g. a (2,4) scheme a useful extension of MEEP? I understand that extended stencils bring additional complexity, especially concerning dispersive media and discontinuous changes in material properties. As such, this might go against MEEP's generality, but could be useful for at least some part of the community (our class of problems certainly being one of them).

Please let me know if you have any thoughts. If this is something you consider worth including, I'm happy to see if I can contribute a useful implementation. Also happy to provide more details about our use case if it would be of interest.

Thank!

Best,
Philipp

Related discussion: #2121

[stevengj]

I am currently exploring higher-order FDTD schemes to see if they could provide a feasible way forward in applications like ours. Presumably there is a turn-over point at which the higher complexity of these schemes becomes worthwhile given the improved phase accuracy.

Are your inhomogeneous media smoothly varying in space? If they have discontinuous interfaces, then most of the high-order schemes will fail. (One exception is this recent method, which allows high-order handling of certain kinds of discontinuities, but not corners.)

If you have a problem where everything is smooth (analytic), you should consider spectral methods, ala dedalus, which have exponential convergence.

[philippwindischhofer]

Are your inhomogeneous media smoothly varying in space? If they have discontinuous interfaces, then most of the high-order schemes will fail. (One exception is this recent method, which allows high-order handling of certain kinds of discontinuities, but not corners.)

We're mostly interested in cylindrically-symmetric, plane-stratified media for now. They have at least one discontinuity (typically between n = 1 and n ~ 1.3). Apart from that discontinuity, the rest of the medium is analytic with superimposed band-limited "noise" (to a good approximation).

If you have a problem where everything is smooth (analytic), you should consider spectral methods, ala dedalus, which have exponential convergence.

Thanks for pointing this out! I suppose one could always construct an analytic approximation of a "perturbed" medium such as the above by replacing discontinuities with smeared-out smooth transitions. I could imagine that this would come at the expense of slowing down convergence?