Thanks for your reply. I thought about this problem in the past month. The fundamental cause of the difference lie in different spaces built by Nedelec and CG basis functions. Nedelec elements create singularity at stage corner while CG not. Visualization expressed what the solution is. There's defect for certain geometry to simulate EM waves with CG elements. 在2023年1月18日星期三 UTC+8 11:10:57<Wolfgang Bangerth> 写道：
> > > I'm solving a 3-d vector Maxwell's wave equation problem with nodal > basis > > functions. To overcome spurious solution and singularity, the > "regularized > > Maxwell equation > > < > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F233149933_Regularized_Maxwell_Equations_and_Nodal_Finite_Elements_for_Electromagnetic_Field_Computations%3FenrichId%3Drgreq-f9f1ce993e048a2fa4a19555b0bfd719-XXX%26enrichSource%3DY292ZXJQYWdlOzIzMzE0OTkzMztBUzoxMDIzMTM5NzY5MjYyMDhAMTQwMTQwNDk2MTE0MQ%253D%253D%26el%3D1_x_3%26_esc%3DpublicationCoverPdf&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7C2ec5fd5b09f04d1949f508dae1cf4792%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C638070577855923173%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=S%2BCRm%2FERX40V4gn0M63l7oLsnBV7BSg%2F2gsWD1zTsno%3D&reserved=0>" > > is applied. The question is, I cannot judge if my solution is same as the > one solved with Nedelec elements (shown in the figure, FE_Q(3) on the left > with "Nonlinear subdivision Level" and Nedelec(0) on the right) from > visualization. Even if the results are identical, FE_Q has dof on nodes and > FE_Nedelec has dof on edge, so FE_Q's visualization results always have > a asymptotic effect around singularity on the central edge. Is there a away > to display nodal-based result as edge-based? FETools::interpolate does not > support this because Nedelec is non-primitive. > > I think it took all of us a month to get back to your question because > it's > not quite clear what it is you want to do. If I understand correctly, you > want > to *compare* the two solutions somehow, and for that you tried (i) to > interpolate the Nedelec solution to the FE_Q space and (ii) to interpolate > the > FE_Q solution onto the Nedelec space. > > The first of these does not immediately work because the Nedelec solution > is, > in general, discontinuous at nodes and so the interpolation operator is > not > easily defined. The second of these does not immediately work because > FETools::interpolate() does not work for Nedelec target elements. > > But in the end, what that points out is that it isn't quite clear to me > what > you are trying to do. The two solutions live in different function spaces > that > are not nested, and so interpolation in either direction can not preserve > the > solution: Even if FETools::interpolate() would work, the FE_Q solution > would > not be equal to the interpolated function. > > As a consequence, I don't quite know what you would learn from comparing > the > interpolated FE_Q solution and the Nedelec solution. My suggestion would > be to > treat both the FE_Q solution and the Nedelec solution as L2 functions > (namely, > piecewise polynomials, possibly discontinuous). Then compare them as such. > In > fact, that would be easy enough if you just output both in a graphical > format > via DataOut and show both solutions at the same time; typical > visualization > programs also allow you to define derived variables that can, for example, > be > the difference between the two solutions which will help you understand > how > the two differ. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > 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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/265461e4-96ce-48d9-8cc7-9519939e8f85n%40googlegroups.com.
