Simulating MOSFET equations with ModelingToolkit

[ChrisRackauckas]

@pepijndevos

# Turn into a first order differential equation system
# sys = ModelingToolkit.ode_order_lowering(sys)

# Perform index reduction to get an index 1 DAE
# sys = StructuralTransformations.dae_index_lowering(sys)
prob = ODEProblem(sys, u0, tspan, params, jac=true)

Is there a reason why you commented out the index lowering? @shashi @YingboMa you might want to take a look at making this into the tutorial we were discussing. The key might be missing the simple alias elimination?

@pepijndevos

I’m realizing I’m kind of rusty on all the algebra definitions. Like… with the nonlinear transistor model and the algebraic Kirchhoff laws, I was sorta expecting to have a nonlinear Differential Algebraic Equation, but in the end it’s handled just fine as an Ordinary Differential Equations.

A differential algebraic equation (DAE) is a differential equation which mixes in algebraic equations. A purely algebraic system is a NonlinearSystem, and a purely differential equation is an index-0 DAE. So indeed you can think of a DAE as an ODE with algebraic loops.

@pepijndevos

One solver even complained it could only be used on a DAE and not on an ODE.

Right now MTK always targets ODEProblem and thus needs to use the methods for mass matrices:

https://diffeq.sciml.ai/stable/solvers/dae_solve/#OrdinaryDiffEq.jl-(Mass-Matrix)

But that should change soon.