[!IMPORTANT] This package will be no longer maintained. Its functionality is available in VoronoiFVM.jl starting with version 1.18. The repository will archived.

VoronoiFVMDiffEq.jl

Glue package between VoronoiFVM.jl and DifferentialEquations.jl

The package extends the constructors for ODEFunction and ODEProblem by methods taking in a VoronoiFVM.System:

using VoronoiFVMDiffEq, DifferentialEquations
system = VoronoiFVM.System(...)
inival = unknowns(system)
problem = ODEProblem(system,inival,tspan)
odesolution = DifferentialEquations.solve(problem, QNDF2())
voronoifvmsolution = reshape(odesolution, system)

Instead of QNDF2 you can try all mass matrix form capable stiff ode solvers form the DifferentialEquations.jl suite.

The package re-exports all of VoronoiFVM, so that it is sufficient to use this package instead of VoronoiFVM.jl.

The package requires a recent Julia version (currently 1.8) due to significant advances in package precompilation.

Choice of ODE/DAE solver

As this package interfaces to the PDE solver package VoronoiFVM.jl, a general advise is to choose methods able to handle stiff problems. Moreover, often, discretized PDE systems (e.g. containing elliptic equations) are differential agebraic equation (DAE) systems which should be solved by DAE solvers.

Methods

SciMLBase.ODEProblem — Type

ODEProblem(system,inival,tspan,callback=DifferentialEquations.CallbackSet())

Create an ODEProblem in mass matrix form which can be handeled by ODE solvers from DifferentialEquations.jl.

Parameters:

system: A VoronoiFVM.System
inival: Initial value. Consider to pass a stationary solution at tspan[1].
tspan: Time interval
callback : (optional) callback for ODE solver

The method returns an ODEProblem which can be solved by DifferentialEquations.solve().

source

SciMLBase.ODEFunction — Type

 ODEFunction(system,inival=unknowns(system,inival=0),t0=0)

Create an ODEPFunction in mass matrix form to be handeled by ODE solvers from DifferentialEquations.jl.

Parameters:

system: A VoronoiFVM.System
jacval (optional): Initial value. Default is a zero vector. Consider to pass a stationary solution at time tjac.
tjac (optional): tjac, Default: 0

The jacval and tjac are passed for a first evaluation of the Jacobian, allowing to detect the sparsity pattern which is passed to the DifferentialEquations.jl solver.

source

Base.reshape — Function

reshape(ode_solution, system)

Create a TransientSolution from the output of the ode solver. The main difference between them is that the TransientSolution reflects the species structure of the probem which is not seen by the ODE solver.

source