hop: All-Dielectric 3D FDTD Solver w/GPU Acceleration

hop solves Maxwell's equations, for arbitrary dielectric mediums in a Yee-discretized 3D domain.

Warning

This project is currently in a prototype state. Proceed at your own risk!

Development

Development Tools

• (optional) prek is suggested to make it easy to conform to all project rules, via pre-commits.
• (optional) cocogitto is suggested to ease creating conformant commit messages, conformant changelog entries, and standardized release processing.
• (optional) licensesnip is suggested to make adding correct license headers easy.

Release Process

Releases shall proceed in the following fashion:

1. Execute cog bump --auto (nothing may be staged). This performs a few checks ex. prek on all files and a passing test-suite.
2. Validate that the generated tags, changelog, and bump-commit are appropriate and as expected. If anything is wrong, this is the last chance to revert.
3. Do git push origin main and git push origin --tags.
4. Publish docs, packages, create a Forgejo release TODO. Perhaps a Justfile that validates the GPG signature, builds and publishes the docs to locally defined destination, builds and publishes any packages, and creates a Forgejo release using the changelog and a custom string entry - maybe even publishes a blog post somewhere too, with the custom string entry?

TODO

In-Scope

• Bounds

  • Naive

• Sources

  • EPointDipole

• Structures

  • Cuboid
  • Sphere

• Mediums

  • Vacuum
  • SimpleDielec
  • CPML

• Dispersive Mediums: These are "trivial" in the sense that it's "just" a function that takes aux fields / data that we've already moved into place for it. NOTE: We may want to reconsider how aux fields are updated with subpixel averaging. Also, could PMLs be made better with subpixel averaging?

• Inhomogeneous Mediums: Requires some kind of sampling within the single-medium structure.

  • Frankly, this is just another aux-field thing. No solver logic needed.

• Nonlinear Mediums: Weirdly enough, nothing special in the solver. The medium will be doing all kinds of special stuff; namely, solving an auxiliary differential equation with substeps.

Fanciness

• Bounds

  • PEC
  • PMC
  • Bloch(k=0)
  • Bloch(k!=0)

• Sources

  • GaussBeam
  • PlaneWave
  • TFSF: Not really a source, but likely best expressed as one. Think on this.

• Structures

  • Cylinder
  • TriMesh
  • VoxCloud
  • Really just everything from https://iquilezles.org/articles/distfunctions/ .
  • Also some choice common structures ex. a ring resonator.

• Mediums

  • SimpleChiral
  • Lorentz
  • Drude
  • DrudeLorentz
  • Debye

• Medium Enhancements:

  • General: Medium built from a models of P, J_f, M.
    • We then split up "how do I model mediums" into "how do I model P, J_f, M".
    • We keep existing mediums as-is, since they are sensible "special cases".
  • Animated: Requires recomputing kernel layout on every time step with altered parameters.
  • Nonlinear: This is just a P model, for use in the General medium.
  • Chiral: This is just a P model, for use in the General medium. Only kink is that we need an approximation of the local value of the dual field, since chirality is fundamentally a crossover effect.
  • Spatial Variation: This is just a P model, for use in the General medium.

• Bloch periodic bounds: Much like NaivePeriodic, except a phase shift is applied, forcing fields to be complex. This is the only correct method of doing periodic boundary conditions - in fact, periodic sim results require a photonic band gap computation.

  • There is a split-field formulation that allows keeping all the same real sim logic. F_real and F_imag are both kept, real and imag parts of a bloch mode - and are both updated independently (I don't know how sources fit in). Boundaries then enforce crossover, aka. phase shifting.
  • That does require running the sim twice per time step, effectively. Anyway, the problem is well studied.
  • See: https://arxiv.org/pdf/2007.05091

• Subpixel Averaging: Integrate by sampling medium at various points (if it's varying). For two-medium regions, integrate by multiplying sample-point-wise SDF with sample-point-wise medium.

  • Can we use Lines cretively to do this very efficiently? An interesting thought.

• Subgrids: Needed for TFSF, but also generally useful.

• Structure Kernel Layout Optimization: Directly use SDFs to find label cells without binning, and use the standard binned algo first. Then, refine the solution by annealing, using a cost function that rewards finding larger z-stripes.

  • Experiment with loading data into Lines more aggressively, esp. in structure vectors. Each kernel thus has more data to load - and much will be strided and inefficient, yes - but can also do its actual calculations very quickly. In particular, using Z lines