Add some documentation on basis functions #347
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nmnobre
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| length partitioning the $[0,1]$ interval, | ||
| $x_{i \in {0,...,n}} = (1/2+i)/(n+1)$. | ||
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| - `IntegratedGLL`: open basis; the basis of order $n$ histopolates all the |
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It might be wise to expand on the meaning of "histopolate" or provide a link to an explanation.
src/basis-functions.md
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| [ND](ND_FECollection) and [RT](RT_FECollection) spaces, of the one-dimensional | ||
| bases described above. In most cases the user can simply use the provided | ||
| defaults, Gauss-Lobatto for H1 spaces, Gauss-Lobatto plus Gauss-Legendre for | ||
| ND and RT spaces, and Gauss-Lobatto for L2 spaces. This should not be confused |
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I believe the default for L2 is Gauss-Legendre.
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🙈 Embarrassing. I can see from the way I wrote it that my brain was thinking of the right thing, but my hands didn't want to agree... but no excuses, just embarrassing. Thanks for reading this carefully and catching this.
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No need to be embarrassed. This is why we proof read for each other. Just a normal part of the process.
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| tag-fem: | |||
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| # Basis Functions | |||
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It would be good to have a section that describes a bit about the Basis object in MFEM. It's also worth noting that the object provides evaluations of basis functions and their spatial derivatives at a given set of quadrature points
| ND and RT spaces, and Gauss-Lobatto for L2 spaces. This should not be confused | ||
| with the integration rule default, which remains Gauss-Legendre for all cases. | ||
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| For tensor product elements, e.g. quadrilaterals or hexahedra, the basis |
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Perhaps mention that serendipity basis can be used with quads/hexes.
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We now mention serendipity elements, with notes for hexahedral elements, the one-dimensional and first order cases.
| one-dimensional basis of Chebyshev polynomials of the first kind. The user can | ||
| use the [`display-basis` miniapp](tools.md#display-basis) to visualize various | ||
| types of basis functions on a single mesh element of their choice. | ||
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Wedge elements are the tensor product of a triangle and segment, and Pyramids are based on Fuentes et al.'s work: https://doi.org/10.1016/j.camwa.2015.04.027
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I've basically reworded this slightly and added it in without expanding much (at all).
mlstowell
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This is a valuable addition to the web pages. Thank you for contributing.
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@nmnobre -- if you can address the remaining comments, we can make this part of the website updates for mfem-4.9 |
I shall write a bit tomorrow morning then. :) |
acfisher
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Looks great. Thanks for helping us with the documentation!
helloworld922
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Looks good to me, thank you for writing this.
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Thanks, @nmnobre ! |
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FYI, I had to replace the PDF figure with a PNG to render it properly with mkdocs, see 8cfdecb |
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Ah, shame, but not a huge deal, we just lose the ability to zoom indefinitely since it was a vector image. |
5 participants
Hi,
I thought it'd be nice to have some reference for the basis functions we use and build in MFEM.
I'd appreciate if someone could read over this. :) Please do feel free to modify or expand the text as you see fit.
Cheers,
-Nuno