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Clarify limitations of periodic meshes

As part of a recent discussion with @pazner on the mfem slack channel, it sounds like there may be a handful of limitations of periodic meshes in mfem that do not seem to be currently communicated in https://mfem.org/howto/periodic-boundaries/ . Concretely, if the mechanism of enforcing periodicity in mfem is just a 1-to-1 correspondence between nodes on periodic faces then it may not work correctly in general for:

  • vector-valued H1 spaces (e.g. rotational symmetry like in the torus example on the web page)
  • Hcurl (due to sign / orientation discrepancies, especially with triangular faces of cubic or higher order in 3D)
  • Hdiv (due to sign)

I'm hoping to find out more information on the potential limitations above (the signedness problem for Hcurl/Hdiv could likely be resolved easily if not already, but the orientation mismatch might be more involved). Has anyone successfully simulated elasticity or E&M problems with periodic meshes, especially with more interesting symmetries than just translation?

Also, the webpage does not indicate if the discretization is expected to be conforming along the periodic boundaries (I'm guessing this is a requirement, given the discussion above). If so, does this impose restrictions on mesh refinement (adaptive, uniform)?

Doxygen frame cuts off bottom of page

Showing the Doxygen documentation inside a frame is great, but currently the bottom of the page is cut off, see e.g. the bottom of the main page

Screen Shot 2021-09-03 at 12 32 50 PM

which should look like this:

Screen Shot 2021-09-03 at 12 33 55 PM

Can we adjust dox.md to show the full page?

Update publications

There have been several recent preprints (with arxiv versions) that will be good to mention on the publication page:

  • "Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinemenet"
  • "hr−adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm"
  • ...

Possible README changes

I recently set up a new laptop, then cloned my fork of this repo and started following the README instructions: https://github.com/mfem/web/blob/master/README.md. Specifically these commands:

  1. pip install --upgrade --user mkdocs==1.0.4
  2. pip install --upgrade --user Markdown==2.6.8
  3. pip install --upgrade --user PyYAML==3.13
  4. pip install --upgrade --user futures==3.3.0

Questions and/or suggested changes:

  • I didn't need to run the fourth command in order to get mkdocs serve or mkdocs build to work. I still haven't run it. Is futures necessary? If so, why?
  • Both the specified mkdocs and markdown versions are old. Other repos I work on use mkdocs 1.1 and markdown 3.3.4. When switching to this one and back, I had to up/downgrade until I got tired of it and installed mkdocs 1.1 and markdown 3.3.4 here to see if they would work. The site seems to build fine locally with these newer versions (including the dynamic /examples dropdowns), so perhaps the first two commands could be updated. Or must the respective versions 1.0.4 and 2.6.8 be enforced? If so, why?

(I don't know why these issues didn't come up on my old laptop, where I had been contributing to this repo since 2019. Maybe these are my problems and not the repo's problems! If you want the README updated according to anything in this issue, I'd be happy to do it.)

How to restart

At the workshop we received a request for a HowTo article on setting up and using restart capabilities with the DataCollection object.

Provide navigational context for tertiary+ pages

Pages that are not in the top-level menu (either primary or secondary dropdown) can lose a little context without navigational cues.

Example: Documentation > HowTo Articles > Parallel Element Numbering. To get back to the HowTo list (i.e., the parent of this page), I would have to know to go back to the top nav and select Documentation > HowTo Articles. I can't get back to the parent directly, and it's not active in the nav dropdown.

Breadcrumbs could be one solution. The bootstrap CSS files have a breadcrumbs style already defined. Another idea is to insert a "Back to HowTo Articles" link (or similar) on these pages, though contributors would have to remember to do that manually if it's not built in. Alternatively, I wonder if the right-side nav within a page (where the page's headings are listed) could be modified to include a link back to the parent page.

I don't have enough practice with mkdocs sites to know the correct logic. My initial attempts to modify content.html failed: capture breadcrumb from page title, link it to page URL, loop through a URL by its slashes to see if it has parents, add those to the breadcrumb string, etc.

(Side note: This site has many pages where the parent is Home and/or where they are only navigable from a link on another page. For instance, I got to https://mfem.org/mesh-format-v1.0/ via Documentation > Mesh Formats > MFEM's mesh formats page. For something like that, a breadcrumb to Home isn't helpful. Or I could ask, why isn't that page under Mesh Formats in the directory? Same with Documentation > Getting Started > Parallel Tutorial. But I like having things in directories and have zero insight into site analytics. Perhaps users aren't as confused as I think they might be. In any case, in the near term, I think the biggest user impact would be to focus on the non-Doxygen pages under Documentation. At minimum the HowTo pages.)

Add workshop artifacts to website

  • Update /workshop/ with
    • Presenters' slides
    • Links to presentation videos (YouTube) @hauten
    • Link to contest winners on /gallery/
  • Update /gallery/ with contest submissions, noting which are the winners
  • Update /news/ with link to forthcoming computing.llnl.gov article @hauten

Document the difference between LinearFormIntegrator::AssembleRHSElementVect methods L2 vs H1

From mfem/mfem#2550:

Mixing together several discretizations, i.e. H1 and L2, requires either implementation of the two versions of LinearFormIntegrator::AssembleRHSElementVect, or a single version with FaceElementTransformations. The documentation does not provide any guidance how the different versions are used in the code. The method with FaceElementTransformations is more general and can be used with H1 and L2 fields.

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