Dear Wolfgang Bangerth I found "FE_DGQLegendre" in dealii, and I think it is the spectral methods but use discontinous Galerkin. I also found "FESeries::Legendre", this class provide the transformation <https://www.dealii.org/current/doxygen/deal.II/classFESeries_1_1Legendre.html#ae2dae601bf1167c237969be15c66d7fd:~:text=%E2%97%86-,precalculate_all_transformation_matrices,-()> between the polynomial space and physical space. But it lack tutorial of the two classes.
Best Chen 陈敏 <[email protected]> 于2024年6月23日周日 18:53写道： > Dear Wolfgang Bangerth > > I learn spectral methods from the book "Hesthaven, Nodal Discontinuous > Galerkin Methods, 2008". This book focuses on the Nodal Discontinuous > Galerkin Methods, and use Legendre polynomials to expanse the solution of a > nodal element on a polynomial space like the followed equations[Page 53 of > the book]: > [image: image.png] > ψn is the Legendre polynomial basis on polynomial space, and *lik is the > *lagrangian > polynomial basis on physical space. There will be a transform between the > two spaces by projection. > > Anyway, if I want to implement a spectral method in dealii, I just need to > use Legendre polynomial basis and do quadrature on Legendre-Gauss-Lobatto > (LGL) quadrature points? > > Thanks! > > Best > Chen > > Wolfgang Bangerth <[email protected]> 于2024年6月19日周三 07:08写道： > >> On 6/15/24 09:51, 陈敏 wrote: >> > >> > I have a question of Spectral Methods using dealii. As far as I know, >> we can >> > you the Legendre function and some other Orthogonal polynomials as >> basis >> > function in dealii. But we need the projection from polynomial space to >> > physical space, how to do the projection in dealii? >> >> I am not familiar with the term "projection from polynomial space to >> physical >> space". Do you mean the transformation from reference cell to a >> particular >> cell of the mesh? If not, can you elaborate? >> >> Best >> Wolfgang >> >> – >> ------------------------------ >> Wolfgang Bangerth email: [email protected] >> www: http://www.math.colostate.edu/~bangerth/ >> >> >> – >> The deal.II project is located at http://www.dealii.org/ >> For mailing list/forum options, see >> https://groups.google.com/d/forum/dealii?hl=en >> — >> You received this message because you are subscribed to the Google Groups >> "deal.II User Group" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/dealii/9cc4ed3b-3c65-4071-b1e8-918de2373470%40colostate.edu >> . >> > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CADr3OdLgD9drskoOOYU3ZROcEoQGn2k8j_4oo__M_jVeL7TGAg%40mail.gmail.com.
