Interface to DifferentialEquations.jl

Since version 0.9 VoronoiFVM provides an experimental interface to the ODE solvers in DifferentialEquations.jl. The general pattern is as follows:

using VoronoiFVM
using DifferentialEquations

sys=VoronoiFVM.System(...)

tspan = (t0,tend)
    
ode_func = ODEFunction(eval_rhs!,
                       jac=eval_jacobian!,
                       jac_prototype=jac_prototype(sys),
                       mass_matrix=mass_matrix(sys))
    
problem = ODEProblem(ode_func,vec(inival),tspan,sys)
    sol = DifferentialEquations.solve(problem,Rodas5())

Some caveats with this evolving implementation:

Ensure that you handle problems wit "trivial" storage function:

    storage!(f,u,node)= f.=u

Eventually it is possible to generalize this to multiplication of u by species and/or region dependent constants, but this has to be implemented with the mass matrix

The choice of ODE methods is limited to those able to handle mass matrices

VoronoiFVM.eval_jacobian! — Method

eval_jacobian!(J, u, sys, t)

Assume the discrete problem is an ODE problem. Provide the jacobi matrix calculation function for DifferentialEquations.jl.

source

VoronoiFVM.eval_rhs! — Method

eval_rhs!(du, u, sys, t)

Assume the discrete problem is an ODE problem. Provide the rhs function for DifferentialEquations.jl.

source

VoronoiFVM.jac_prototype — Method

jac_prototype(sys)

Complete the system and provide the jacobi matrix as prototype for the Jacobian.

source

VoronoiFVM.mass_matrix — Method

mass_matrix(this)

Calculate the mass matrix for use with DifferentialEquations.jl.

source