Dear CADET team,
First, thank you for the engaging discussions over the last couple of days in Lund at SoCSS 2024 – great to meet up with you 
Here is a summary of my notes regarding our discussions:
- CADET-DG uses a full Newton’s solver in IDAs. I think this is 99% of the reason why CADET-julia is faster than CADET-DG in recent benchmarking results? The point here is it does not make sense to update the Jacobian so often when using DG, instead, it is better to use IDAs internal error controller for updating the Jacobian when necessary instead. This can be MUCH more cost efficient, as is the case in Julia. I realize that this is not the case for the FV code, due to the large size of the linear system, but with high-order methods, it is just not necessary. This makes it hard to mix things? can you go: if FV do full newton solver end, if DG use SUNDIALS internal error controller end ?
- SUNDIALS 6.?? Supports Ginkgo: “Ginkgo (ginkgo-project.github.io)”. This is a pretty interesting linear solver that can be compiled easily on Windows due to cmake support, Indeed, this means that we never again have to waste our time with SuperLU and/or KLU make-type installations. By swapping to Ginkgo, you do not have to override the linear solver module in IDAS, just simply use their abstract linear solver implementation of Ginkgo. If you insist on using SuperLU from Eigen (strong linear solver of course), then I think you need to implement it through the Abstract linear solver module of SUNDIALs, so that you can swap to using the internal error controller.
- CADET-DG uses IDAS to solve ODEs – not really a big issue, I wouldn’t even change this. Simpler to keep everything DAE if this is the structure necessary in your code.
This was basically just some constructive criticism that may be important to you, otherwise I’m just happy to see the impressive and many use-cases and all the nice on-going development and projects 