kineticEQ Documentation

kineticEQ is a numerical library for BGK-type kinetic equations. It combines a high-level Python interface built around Config and Engine with optimized C++/CUDA extensions for the BGK1D production path. This documentation is written against the current src/kineticEQ implementation rather than the legacy notebook workflow.

Current implementation status

Model Scheme torch cuda_kernel cpu_kernel Status
BGK1D1V explicit supported supported not registered runnable
BGK1D1V implicit not registered supported supported runnable
BGK1D1V holo not registered supported not registered runnable
BGK2D2V explicit registered in the registry not registered not registered incomplete Engine path

Notes:

  • The BGK1D cuda_kernel path requires float64 in the fused explicit and implicit bindings.
  • The BGK1D cpu_kernel path is currently implicit-only and also requires float64.
  • BGK2D2V can allocate state, but the Engine path is not operational because the model config lacks scheme_params and the stepper itself is unfinished.

Numerical highlights

  • BGK1D explicit: direct velocity-space quadrature, Maxwellian reconstruction, first-order upwind transport, and local collision relaxation.
  • BGK1D implicit: Picard iteration with batched tridiagonal solves, optionally accelerated by Anderson acceleration and CNN warm-starts.
  • BGK1D holo: coupled HO/LO iterations, with a block-tridiagonal LO solve and a tridiagonal HO distribution update.
  • CNN warm-start: a 1D CNN predicts moment increments and provides a better initialization for implicit Picard iterations.

Documentation map

Table of contents