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philipcardiff / paper-newton-krylov

This repository contains the LaTeX files for a draft paper on Newton-Krylov methods for finite volume solid mechanics. The code is available in solids4foam.
MIT License
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Testing high-order procedure for gradient calculation #9

Open iBatistic opened 5 days ago

iBatistic commented 5 days ago

Here are some initial results; I’ll get back to you soon after I check in more detail how it works. I haven’t yet added treatment for boundary cells and faces on the edge. If you're interested in the code, you can check it on my solids4foam-ib fork on the branch solids4foam/feature-petsc-snes in linGeomTotalDispSolid.C from line 220 to 475 (everything is still in one place).

philipcardiff commented 3 days ago

This looks really impressive.

The code is nicely structured and easy to follow.

By the way, I was recently reading the Zienkiewicz book (volume 1) and interesting they suggest a similar least squares approach for "recovering" the stress from the displacement field (in Chapter 15 - Errors, Recovery Processes, and Error Estimates). Essentially, they can get more accurate (and higher order of accuracy) stresses by fitting a least squares plane about each vertex through the surrounding elements' Gauss points, and this is how they interpolate stresses from Gauss points to the mesh vertices.