matrix-free vector FEM with Nedelec space
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Vinta Yinda Wang
Dec 18, 2022, 6:43:48 AM12/18/22
to deal.II User Group
Hello everyone!
I want to implement the matrix-free method in computational electromagnetic problems. However, the popular Nedelec basis functions are not supported.
Anyway, I am overjoyed to find that some contributors and users have contributed to the same problems as I concern. The support for RT elements had been implemented several months before.
I wonder if there are any progress in Nedelec space in this problem? Or maybe I can develop on my own. How much work will it takes?
Thank you all!
Peter Munch
Dec 19, 2022, 5:20:40 PM12/19/22
to deal.II User Group
Hi Abbas, Vinta, and Wayne,
it's nice to see that there is increasing interest regarding doing matrix-free computations with Nedelec elements! It's a very interesting and cool topic.
Unfortunately, there has been no progress regarding our Nedlec elements on our (matrix-free) side in the last few months. We have started to integrate RT support in MatrixFree. See the Niklas Wik's Master thesis: https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1676116&dswid=8895. The reason for starting with RT instead of Nedelec is that the groups, which are involved, are primarily interested in the solution of the incompressible Navier Stokes equations.
However, the generalization done for RT (anisotropic tensor product evaluation, lexicographic definition of shape functions done by Niklas Wik and Julius Witter) is also useful for the future generalization needed for Nedelec. Martin Kronbichler and Katharina Kormann have been working on the lexicographic definition of shape functions in the Nedelec element class. We will create for a PR for that soon.
Starting with that, we will continue to work on Nedelec elements in the MatrixFree infrastructure. At that stage maybe one of you would be also interested to take over some implementation tasks?
In one the threads, there was the discussion "DG vs. Nedelec". In Niklas Wik's Master thesis, there is a comparison of the performance of DG and of RT. Maybe that is interesting for you as well, since the performance characteristics of Nedelec will be similar.
Regards,
Peter
it's nice to see that there is increasing interest regarding doing matrix-free computations with Nedelec elements! It's a very interesting and cool topic.
Unfortunately, there has been no progress regarding our Nedlec elements on our (matrix-free) side in the last few months. We have started to integrate RT support in MatrixFree. See the Niklas Wik's Master thesis: https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1676116&dswid=8895. The reason for starting with RT instead of Nedelec is that the groups, which are involved, are primarily interested in the solution of the incompressible Navier Stokes equations.
However, the generalization done for RT (anisotropic tensor product evaluation, lexicographic definition of shape functions done by Niklas Wik and Julius Witter) is also useful for the future generalization needed for Nedelec. Martin Kronbichler and Katharina Kormann have been working on the lexicographic definition of shape functions in the Nedelec element class. We will create for a PR for that soon.
Starting with that, we will continue to work on Nedelec elements in the MatrixFree infrastructure. At that stage maybe one of you would be also interested to take over some implementation tasks?
In one the threads, there was the discussion "DG vs. Nedelec". In Niklas Wik's Master thesis, there is a comparison of the performance of DG and of RT. Maybe that is interesting for you as well, since the performance characteristics of Nedelec will be similar.
Regards,
Peter
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