Spatial bounds of integration of a PDE using DifferentialEquations

Specific Domains Modelling & Simulations
1

Hi there,
I am solving a PDE over a large domain discretizing with finite difference the RHS and using DifferentialEquations.jl to integrate the ODE system in time. Is there anyway in which I can limit the integration to only nodes in the grid comprised in a certain range. I would basically limit the integration in time to only part of my spatial domain, say comprised between indices l,m (1-d case) or (l,m,n,o) for the 2d case.
This indices might change with times and are successfully computed through callback functions. However, I don’t know how to tell the solver to limit integration only to this part of the spatial domain. Any ideas? Thanks!

2

Just make the ODE the interior

3

Thanks for the answer! To be sure I understand, you are suggesting to redefine the ODEproblem with only the interior points?

4

Yes, that’s generally the easiest way. ModelingToolkit.jl and MethodOfLines.jl do this automatically, but if you’re writing the code by hand then you should do this too.