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PETScDiffEq.jl

PETScDiffEq.jl contains bindings for the PETSc TS time integrators to allow them to be used with the SciML common interface. PETSc's linear and nonlinear solvers are already reachable from SciML through LinearSolve.jl and NonlinearSolve.jl; this package covers the third layer, TS.

Installation

using Pkg
Pkg.add("PETScDiffEq")

Precompiling the package runs a few small solves through PETSc, so that the first solve of a session compiles much less. To precompile without them:

using PETScDiffEq, Preferences
set_preferences!(PETScDiffEq, "precompile_workload" => false; force = true)

Precompiling under mpiexec or srun skips these solves, and later sessions reuse that build until the package or one of its dependencies changes, so load the package once without the launcher before the first parallel run.

Common API Usage

This library adds the common interface to PETSc's TS solvers, documented in the DifferentialEquations.jl documentation. Following the Lorenz example from the ODE tutorial:

using PETScDiffEq, SciMLBase

function lorenz(du, u, p, t)
    du[1] = 10.0(u[2] - u[1])
    du[2] = u[1] * (28.0 - u[3]) - u[2]
    du[3] = u[1] * u[2] - (8 / 3) * u[3]
end
u0 = [1.0; 0.0; 0.0]
tspan = (0.0, 100.0)
prob = SciMLBase.ODEProblem(lorenz, u0, tspan)
sol = SciMLBase.solve(prob, TSRK("5dp"); dt = 0.01, abstol = 1e-8, reltol = 1e-8)

dt sets the first step. An adaptive solve can leave it out, and the first step is then Hairer and Wanner's estimate as OrdinaryDiffEq uses it, taken with the abstol and reltol keywords (SciML's defaults, abstol = 1e-6 and reltol = 1e-3, when not given). DAE and mass-matrix problems start from a small step instead. A solve PETSc steps at a fixed size needs dt: adaptive = false, -ts_adapt_type none, the fixed-step families (TSImplicit and TSDAE other than bdf, TSIRK, TSMPRK), and subtypes registered without an embedded error estimate. What counts is the type PETSc runs after petsc_options: TSImplicit("beuler", ["-ts_type", "bdf"]) runs without dt and TSImplicit("bdf", ["-ts_type", "beuler"]) needs it. A TSGeneric naming a type no other constructor covers needs it too, since whether that type adapts is not known here.

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `~/work/PETScDiffEq.jl/PETScDiffEq.jl/docs/Project.toml`
  [e30172f5] Documenter v1.19.0
  [0a65194f] PETScDiffEq v0.9.9 `~/work/PETScDiffEq.jl/PETScDiffEq.jl`
and using this machine and Julia version.
Julia Version 1.13.1
Commit 96ca370cf0e (2026-09-25 19:34 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-20.1.8 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
A more complete overview of all dependencies and their versions is also provided.
Status `~/work/PETScDiffEq.jl/PETScDiffEq.jl/docs/Manifest.toml`
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`