OrdinaryDiffEqOperatorSplitting.jl

OrdinaryDiffEqOperatorSplitting.jl is a component package in the DifferentialEquations ecosystem. It holds operator splitting solvers and utilities.

Installation

Assuming that you already have Julia correctly installed, it suffices to import OrdinaryDiffEqOperatorSplitting.jl in the standard way:

import Pkg;
Pkg.add("OrdinaryDiffEqOperatorSplitting");

API

OrdinaryDiffEqOperatorSplitting.jl is part of the SciML common interface. The only requirement is that the user passes an algorithm compatible to the corresponding function to solve. For example, we can solve a simple split problem using the Euler() algorithm for each subproblem with the LieTrotterGodunov algorithm, by defining a problem tree and an analogue solver tree via tuples:

using OrdinaryDiffEqLowOrderRK, OrdinaryDiffEqOperatorSplitting
# This is the true, full ODE.
function ode_true(du, u, p, t)
    du   .-= 0.1u
    du[1] -= 0.01u[3]
    du[3] -= 0.01u[1]
end

# This is the first operator of the ODE.
function ode1(du, u, p, t)
    @. du = -0.1u
end
f1 = ODEFunction(ode1)
f1dofs = [1,2,3]

# This is the second operator of the ODE.
function ode2(du, u, p, t)
    du[1] = -0.01u[2]
    du[2] = -0.01u[1]
end
f2 = ODEFunction(ode2)
f2dofs = [1,3]

# This defines the split of the ODE.
f = GenericSplitFunction((f1, f2), (f1dofs, f2dofs))

# Next we can define the split problem.
u0 = [-1.0, 1.0, 0.0]
tspan = (0.0, 1.0)
prob = OperatorSplittingProblem(f, u0, tspan)

# And the time integration algorithm.
alg = LieTrotterGodunov(
    (Euler(), Euler())
)

# Right now OrdinaryDiffEqOperatorSplitting.jl does not implement the SciML solution interface,
# but we can only intermediate solutions via the iterator interface.
integrator = init(prob, alg, dt=0.1)
for (u, t) in TimeChoiceIterator(integrator, 0.0:0.5:1.0)
    @show t, u
end

Available Solvers

For the list of available solvers, please refer to the OrdinaryDiffEqOperatorSplitting.jl Solvers pages.