Algorithms

`cubie.integrators.algorithms`

Factories in cubie.integrators.algorithms assemble explicit and implicit step implementations that plug into the CUDA-based integrator loop. Explicit steps wrap direct right-hand-side evaluations, while implicit steps couple user-supplied device callbacks with matrix-free Newton–Krylov helpers to satisfy nonlinear solves. Precision handling is central: every factory propagates the configured precision through compiled device helpers and the shared linear and nonlinear solver stack.

Base infrastructure

BaseStepConfig – attrs configuration shared by explicit and implicit steps.
BaseAlgorithmStep – base class that wires precision and CUDA compilation helpers.
StepCache – container storing compiled kernels and loop scratch buffers.

Explicit steps

ExplicitStepConfig – configuration for explicit step factories.
ExplicitEulerStep – Euler step that invokes the RHS device function.
ERKStep – multistage explicit Runge–Kutta step with adaptive control defaults.
ERK tableau registry – named explicit Runge–Kutta tableaus and references.

Implicit steps

ImplicitStepConfig – configuration for implicit step factories.
BackwardsEulerStep – backward Euler implicit algorithm.
BackwardsEulerPCStep – predictor-corrector backward Euler variant.
CrankNicolsonStep – Crank–Nicolson implicit algorithm.
DIRKStep – diagonally implicit Runge–Kutta family with embedded error estimates.
DIRK tableau registry – named diagonally implicit Runge–Kutta tableaus and references.

Factory helpers

get_algorithm_step – resolves step factories by enum or name.

Dependencies

Implicit steps depend on cubie.integrators.matrix_free_solvers for the linear and Newton–Krylov factories and reuse cubie.CUDAFactory utilities for JIT compilation and caching. All algorithms expect caller supplied device callbacks for time derivatives, operator assembly, and observable evaluation, operating on preallocated device buffers whose precision matches the configured integration precision.