Optimize field propagation performance

[sethrj]

• [ ] Refactor FieldPropagator to have internal state and function calls rather than being one huge function with tons of if statements
• [x] Rename classes (https://github.com/celeritas-project/celeritas/issues/721)
• [ ] Rethink field intersection algorithm as a root finder (maybe using Regula Falsi iteration)
• [ ] Add a derived field propagator that uses safety: https://github.com/celeritas-project/celeritas/issues/762
• [ ] Perform propagation in local coordinate system for improved accuracy https://github.com/celeritas-project/celeritas/issues/994#issuecomment-1836508438
  • Perform integration in local coordinate system?
  • Then we could use single precision
• [ ] Make substep length in field driver (due to change in discretization error) persistent across calls in propagator (or even across steps)

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• Input: step length
• Super small: accept immediately
• Goal: longest step allowed by chord length and acceptable discretization error
• If discretization limited, accumulate until step length is reached
• Use distance between endpoints versus dchord to tell if we're within the asymptotic region

Start with last successful step if available

• Converged if chord length is within tolerance, discretization is in limits
• Calculate target next step length for chord length ( * sqrt(eps / distance_chord)
• Calculate target next step length for discretization error
• Increase next guess if error is too large??

---

• MicroFieldAdvancer
  • No iteration
  • Success if step < minimum_step (evaluated first of course)
• ChordAdvancer: reduce step until chord is within a tolerance
  • Iteration: reduce step (exponential, no more than halving each iter)
  • Convergence: max_nsteps
  • Convergence: chord distance
  • Success if discretization error is small enough
• Reduce step size based on scale factor
• AccurateAdvancer:
  • sub-sub steps to accumulate to maximum step, but sub-step length changes
  • Success when accumulated length is greater than or equal to requested step length * (1 - epsilon_step)
  • StepIntegrator
    • MicroFieldAdvancer if step < minimum_step and update new step
    • GoodAdvancer otherwise:
      • Iteration: reduce step

[sethrj]

Not quite the ideas that we discussed with @LSchwiebert today, but at least the same part of the code with the same goal.