Hello SimPEG community,
I’m Luca Peruzzo, postdoc at the Berkeley Lab.
First of all, thank you for this project, very educational, and yet powerful and with real-world applicability. I have worked a little bit with the SimPEG ERT module, understanding the Finite Volume approach from some of your papers and Shashkov’s book and papers.
I appreciate some of the benefits of the FVMs, for example their higher stability and more direct physical derivation, compared to FEMs (at least for me).
I agree with you that the trade off between complex (e.g., body-fitted meshes) and simplicity- transparency in mesh generation and modeling algorithms depends on the goal, the geophysical inversion being more toward the latter (Why Discretize? page). However, I am curious and interested in having your feedback on more irregular grids (quadrilateral or triangular in 2D). In particular, on the possibility of applying your FV technique to these types of mesh. I have read some papers discussing and proposing this, including Shashkov’s book itself if I am not wrong. Do you see it as a possibility, although not a priority? I have worked a lot with GMSH and have most of my models built with it, this is also part of the motivation and I think it may be common also to other geophysicists.
I would also be happy to chat about this if any of you may be interested.
Thank you in advance, and again for the great work you have done so far.