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ClimaTimeSteppers.jl

ClimaTimeSteppers.jl is a suite of ordinary differential equation (ODE) solvers for use as time-stepping methods in a partial differential equation (PDE) solver, such as ClimateMachine.jl. They are specifically written to support distributed and GPU computation, while minimising the memory footprint.

ClimaTimeSteppers.jl is built on top of DiffEqBase.jl, and aims to be compatible with the DifferentialEquations.jl ecosystem.

ClimaTimeSteppers — Module
ClimaTimeSteppers

Ordinary differential equation solvers

JuliaDiffEq terminology:

  • Function: the right-hand side function df/dt.

    • by default, a function gets wrapped in an ODEFunction
    • define new IncrementingODEFunction to support incrementing function calls.

  • Problem: Function, initial u, time span, parameters and options

    du/dt = f(u,p,t) = fL(u,p,t) + fR(u,p,t)

    fR(u,p,t) == f(u.p,t) - fL(u,p,t) fL(u,_,_) == A*u for someA(matrix free)

    SplitODEProlem(fL, fR)

  • ODEProblem from SciMLBase.jl

    • use jac option to ODEFunction for linear + full IMEX (https://docs.sciml.ai/latest/features/performanceoverloads/#odeexplicit_jac-1)

  • SplitODEProblem for linear + remainder IMEX

  • MultirateODEProblem for true multirate

  • Algorithm: small objects (often singleton) which indicate what algorithm + options (e.g. linear solver type)

  • define new abstract DistributedODEAlgorithm, algorithms in this pacakge will be subtypes of this

  • define new Multirate for multirate solvers

  • Integrator: contains everything necessary to solve. Used as:

  • define new DistributedODEIntegrator for solvers in this package

    init(prob, alg, options...) => integrator step!(int) => runs single step solve!(int) => runs it to end solve(prob, alg, options...) => init + solve!

  • Solution (not implemented): contains the "solution" to the ODE.

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