Execution backends

Select with backend=.... The string-valued mode keyword has been removed.

Start Julia with --threads=N for threads. Adaptive NSDERungeKutta solves keep the current step size and history local to each solution, so they do not mutate a shared chunk solver. User right-hand sides must likewise avoid shared mutable state.

For Distributed, start workers with the same project and load the packages on each:

using Distributed
addprocs(2; exeflags="--project=.")
@everywhere using NSDERungeKutta, NSDETimeParallel
solution = solve(problem, parareal; backend=DistributedBackend())

MPI requires MPI.Init() and an SPMD launch. MPI remains a required dependency in this release. See test/mpi/runtests_mpi.jl for an executable example.

Pipeline contract

The pipeline overlaps coarse propagation and fine work, passing a convergence frontier from left to right. It does not have a shared current iterate at every instant. Consequently RelativeUpdate, MeanRelativeUpdate, averaged defects, and changing secant weights are rejected rather than silently replaced.

Use WeightedDefect(ϵ=..., p=Inf, weight=FixedWeight(...)) for maximum-defect acceptance. A rank waits for the incoming start to freeze before accepting its outgoing defect. FrontierRelativeUpdate(ϵ=...) explicitly selects the legacy relative outgoing-update heuristic. NoStop() runs to the budget or diagonal. At least N ranks are required; surplus ranks take part only in collectives.

diagnostics.local_sweeps records each chunk's local iteration count. Global fine/coarse call totals include final fine solves needed after a late start update. fine_batches and sweeps are nothing. Residuals aggregate ranks active at each local iteration index and must not be interpreted as bulk residuals.

Full or interface histories would require additional synchronization and are rejected. With NoStop() and K≥N, the final collected result matches the chunked fine reference. For performance comparisons use the matching scheduling model.

Under MPIBackend, all ranks receive a residual history trimmed to the completed fine-batch count, and solution.errors === solution.diagnostics.residuals holds on every rank, including zero-batch failures and reused solutions.

The pipelined backend initializes interior starts through its coarse communication chain. It does not use makeGs overlap guesses from a window driver; only the window's initial value is preserved. Use a bulk backend for interior warm starts.

Complete launch examples

examples/distributed.jl starts two workers in the active project, loads NSDE on each, checks the chunked fine reference, and removes the workers. Load named right-hand-side functions on every worker too. Each worker needs access to the same package environment and any data used by its right-hand side.

examples/mpi.jl runs the bulk backend with one rank per chunk, checks the returned histories on every rank, and checks the collected result against the chunked fine reference on the root rank, where the chunks are gathered. With MPI.jl's compatible launcher installed:

mpiexecjl -n 2 julia --project examples/mpi.jl

Launch all ranks into the same project. Both MPI backends require at least N ranks. Do not run a multi-rank program by starting a single Julia process and expecting MPIBackend() to create workers. The pipeline is a separate protocol, not an interchangeable performance switch; see its supported criteria above.

For threaded matrix-heavy workloads, consider BLAS.set_num_threads(1) after using LinearAlgebra, then measure: nested BLAS and chunk parallelism can oversubscribe cores. Each chunk must own any mutable scratch storage used by its right-hand side. Thread safety is a property of user functions as well as the solver.