Numerical accuracy#

The validation scripts construct fields with known harmonic content and save machine-readable JSON before plotting. This keeps calculations separate from presentation and makes paper figures reproducible.

What is tested#

  • Cartesian interpolation leakage for known \(m=0,\pm3\) fields

  • mode-power errors versus Cartesian resolution

  • radial quadrature convergence

  • default radial-resolution strategies

  • angular Nyquist behavior and exact FFT aliasing

  • adaptive truncation against analytically known spectral powers

  • Parseval-predicted versus directly measured reconstruction errors.

Main conclusions from the current validation campaign#

The current benchmark set shows approximately second-order radial quadrature convergence, exact recovery of the discrete FFT alias in the tested analytic angular cases, and near-machine-precision agreement between Parseval-predicted and directly measured truncation errors. Cubic Cartesian-to-polar interpolation strongly suppresses spurious harmonic leakage relative to linear interpolation on smooth fields.

The automatic choice Nr=min(len(x), len(y)) was selected because it provides a substantially better radial-accuracy/cost compromise than the previous half-resolution rule.

Accuracy comparison of radial resolution strategies

Accuracy/cost motivation for the default radial resolution.#

Radial convergence

Independent radial-convergence study.#

Predicted versus measured adaptive truncation error

Parseval error certification for adaptive truncation.#

Reproduce#

python validation/run_accuracy_validation.py
python validation/plot_accuracy_validation.py
python validation/run_angular_resolution_validation.py
python validation/plot_angular_resolution_validation.py
python validation/run_truncation_validation.py
python validation/plot_truncation_validation.py

The exact quantitative values in a publication should always be taken from the archived JSON corresponding to the cited software version and benchmark environment.