Matrix-free solvers

`cubie.integrators.matrix_free_solvers`

The matrix_free_solvers package gathers factories that build CUDA device functions for matrix-free linear and nonlinear solves. These factories are used by the integrator loops to update implicit states without forming Jacobian matrices. The solvers rely on numba.cuda for device kernels and perform warp-synchronisation via lightweight vote helpers.

Public API

linear_solver_factory – emits steepest-descent/minimal-residual CUDA solvers that operate on matrix-free operators.
newton_krylov_solver_factory – wraps the linear solver to construct damped Newton–Krylov iterations for implicit steps.
SolverRetCodes – enumerates solver completion status codes.

Modules

`linear_solver`

Constructs preconditioned steepest-descent and minimal-residual solvers that operate on matrix-free operators. The factory emits CUDA device functions that maintain only vector workspaces, which keeps GPU memory usage predictable.

`newton_krylov`

Wraps the linear solver factory to assemble damped Newton–Krylov iterations for implicit integration steps. The solver encodes completion status using the SolverRetCodes enumeration.

Dependencies

Warp synchronisation helpers implement collective convergence tests.
numba.cuda compiles device functions and manages kernel launches.
cubie.integrators.matrix_free_solvers.linear_solver provides the inner linear solver used by Newton–Krylov iterations.