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_mlir.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_mlir.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.