NSDETimeParallel.jl

Parareal with explicit stopping targets, chunk schedules, and work diagnostics.

Start here

using NSDERungeKutta, NSDETimeParallel
problem = Logistic(0.3, (0.0, 2.0))
par = Parareal(RK4(h=0.005), RK4(h=0.05); N=4)
result = solve(problem, par; backend=ThreadsBackend())
@assert result.diagnostics.status in (:converged, :exact)
result.diagnostics.fine_batches

Start Julia with --threads=4 for this example; SerialBackend() is the default. Parareal constructs the fine/coarse chunk schedules itself. The default RelativeUpdate() requires every stored start to pass a mixed absolute/relative update test. WeightedDefect deliberately changes the acceptance target.

For deterministic finite bulk solves, NoStop() with K=N reaches the matching chunked fine reference in N fine batches and N-1 corrections. This is discrete exactness, not exactness relative to the ODE. Use reference(problem, par) to check it. Read status before interpreting residuals or speed-up estimates.

• Criteria and weights: per-unit-time weights and tail limits.
• Conventions: histories, counts, reuse, failures, and cost models.
• Backends: serial, threads, Distributed, and MPI.
• Extensions: a complete criterion and solver wrapper.
• Quick reference: glossary and common calls.

MPI remains a required dependency. Pipelined MPI has a distinct frontier protocol: it has no global batch count and supports only a subset of criteria.

Learn by running

The guided tour explains each step. Its companion examples/guided_tour.jl runs the numerical examples with assertions. Run it in a project containing this package and its example dependencies; use Julia 1.10 or later.

The ecosystem is NSDEBase → NSDERungeKutta → NSDETimeParallel → NSDEMovingWindow. ArrowMacros provides supporting macros; they are not required in user examples.

Installation and versions

For a registered release, use Pkg.add("NSDETimeParallel"). These docs describe the current development API; a registered version may differ. To use a local checkout, activate your working environment and Pkg.develop(path="/path/to/NSDETimeParallel"). Develop matching local dependency checkouts in that environment too, then check Pkg.status(). The serial and parallel guides also require NSDERungeKutta; plotting requires Plots.

See the documentation and API reference for details.

Build the manual locally

From the package root, with matching dependency checkouts already available:

julia --project=docs -e 'using Pkg; Pkg.develop(path="."); Pkg.instantiate()'
julia --project=docs --threads=4 docs/make.jl

Documenter executes the guided-tour examples during the build. For local unreleased dependencies, develop their paths into docs before instantiating. The deployment step only publishes in an appropriately configured CI environment.