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Higher order element visualization

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Higher order element visualization

Slaughter, Andrew E
I am working on a finite element visualization of simulations that uses arbitrary order monomial shape functions. Currently, we are visualizing the results with a single value on a cell, but we would like to write out the monomial coefficients and do a proper projection of the solution. Is this something that is possible with VTK? If it is, we are happy to write some custom code, but would like a nudge in the correct direction.

Thanks,
Andrew

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Re: Higher order element visualization

David Thompson-2
Hi Andrew,

> I am working on a finite element visualization of simulations that uses arbitrary order monomial shape functions. Currently, we are visualizing the results with a single value on a cell, but we would like to write out the monomial coefficients and do a proper projection of the solution. Is this something that is possible with VTK? If it is, we are happy to write some custom code, but would like a nudge in the correct direction.

Monomial shape functions are not numerically stable. There is some work[1,2] to extend VTK to handle arbitrary order Lagrange shape functions (also not numerically stable). Ideally, Legendre or spline-basis interpolation would be used and other bases would be projected to it.

        David

[1]: https://gitlab.kitware.com/dcthomp/vtk/commits/lagrange-progess
[2]: https://gitlab.kitware.com/tjcorona/vtk/commits/lagrange-elements
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Re: Higher order element visualization

Slaughter, Andrew E


On Thu, Apr 13, 2017 at 3:29 PM, David Thompson <[hidden email]> wrote:
Hi Andrew,

> I am working on a finite element visualization of simulations that uses arbitrary order monomial shape functions. Currently, we are visualizing the results with a single value on a cell, but we would like to write out the monomial coefficients and do a proper projection of the solution. Is this something that is possible with VTK? If it is, we are happy to write some custom code, but would like a nudge in the correct direction.

Monomial shape functions are not numerically stable.
We are not actually use them to solve, but using them to compute auxiliary fields explicitly. 
There is some work[1,2] to extend VTK to handle arbitrary order Lagrange shape functions (also not numerically stable). Ideally, Legendre or spline-basis interpolation would be used and other bases would be projected to it.

        David
Thanks for the help. 
[1]: https://urldefense.proofpoint.com/v2/url?u=https-3A__gitlab.kitware.com_dcthomp_vtk_commits_lagrange-2Dprogess&d=DwIFAg&c=54IZrppPQZKX9mLzcGdPfFD1hxrcB__aEkJFOKJFd00&r=h7heP8xwI1i_HikChvhFbEBurKirgfOCdwgBxB9lM8c&m=ki0L7eRrMB5mjs7yj2NZg3lkFJB8jBHLaKYSWg7ih7Y&s=5ll6uecAmULVdNeqEQ16GmThoMD2bc6lEUW5RNpS4iI&e=
[2]: https://urldefense.proofpoint.com/v2/url?u=https-3A__gitlab.kitware.com_tjcorona_vtk_commits_lagrange-2Delements&d=DwIFAg&c=54IZrppPQZKX9mLzcGdPfFD1hxrcB__aEkJFOKJFd00&r=h7heP8xwI1i_HikChvhFbEBurKirgfOCdwgBxB9lM8c&m=ki0L7eRrMB5mjs7yj2NZg3lkFJB8jBHLaKYSWg7ih7Y&s=YHaO6S_WmgR7ieLcfMNlxGXgmKaZ2U1XRAiZWL2d9mg&e=


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