<html>
  <head>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  </head>
  <body text="#000000" bgcolor="#FFFFFF">
    Philosophically it's certainly part of the job of the mesh
    generator, but realistically I don't think there are any really
    viable high-order mesh generators or even file formats right now
    (correct me if I'm wrong). And as Matthew put, the mesh generator
    has no business telling us what our function basis should be, and by
    extension has no basis telling us where we should place our face
    nodes.<br>
    <br>
    <br>
    <span style="font-size:12.8px">> I was simply stating that
      without access to the original geometric representation, I don't
      know if my simulation domain really has flat walls, > or even
      how curved are the walls if they are curved, so there's no general
      way for me to accurately determine the shape of the element.</span><br>
    <br>
    This comes up a lot in high order mesh discussions, but I always
    wonder when do you *not* have access to the original geometric
    representation? If you've generated the mesh yourself you must have
    the geometry.<br>
    <br>
    <br>
    <br>
    <div class="moz-cite-prefix">On 08/24/2016 11:48 AM, Andrew Ho
      wrote:<br>
    </div>
    <blockquote
cite="mid:CADhXwgt4t-aCiky4hkt-xBCO5-NQkJBY-47TQxFvCxiSS20v2g@mail.gmail.com"
      type="cite">
      <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
      <div dir="ltr"><span style="font-size:12.8px">That sounds like
          taking part of the job of the mesh generator and putting it
          into my code. I was simply stating that without access to the
          original geometric representation, I don't know if my
          simulation domain really has flat walls, or even how curved
          are the walls if they are curved, so there's no general way
          for me to accurately determine the shape of the element.</span><br>
      </div>
      <div class="gmail_extra"><br>
        <div class="gmail_quote">On Wed, Aug 24, 2016 at 10:40 AM, Mark
          Lohry <span dir="ltr"><<a moz-do-not-send="true"
              href="mailto:mlohry@princeton.edu" target="_blank">mlohry@princeton.edu</a>></span>
          wrote:<br>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <div text="#000000" bgcolor="#FFFFFF">
              <div lang="x-unicode"><span class=""> On 08/24/2016 11:27
                  AM, Andrew Ho wrote:<br>
                </span><span class="">
                  <blockquote type="cite">
                    <div dir="ltr">Good geometric accuracy is very
                      import for achieving appropriate convergence rates
                      in complex geometry, not just using higher order
                      polynomials on flat elements.<br>
                      <div><br>
                      </div>
                      <div>If you look at Hesthaven's book Nodal
                        Discontinuous Galerkin Methods, Table 9.1 shows
                        that without support for curved elements, higher
                        order DG element on flat elements converges at
                        sub optimal rates due to inaccuracies produced
                        by the boundary conditions.</div>
                      <div><br>
                      </div>
                      <div>There's no way to re-construct this curved
                        information correctly after the fact; it must be
                        generated by the meshing software.</div>
                    </div>
                    <div class="gmail_extra"><br>
                    </div>
                  </blockquote>
                  <br>
                </span><span class=""> I don't *entirely* agree with the
                  suggestion the mesh generator has to provide that
                  information. Some people reconstruct splines through
                  the nodes to create higher order meshes after the fact
                  (which also requires some detection or specification
                  of sharp corners to break the spline). I personally
                  take the given mesh from the generator in addition to
                  an IGES/NURBS type CAD file for complex geometries,
                  and then do a kind of projection for sub-cell curved
                  boundary faces.<br>
                  <br>
                  <br>
                </span><span class="">
                  <blockquote type="cite">
                    <div class="gmail_extra">
                      <div class="gmail_quote">On Wed, Aug 24, 2016 at
                        10:12 AM, Jed Brown <span dir="ltr"><<a
                            moz-do-not-send="true"
                            href="mailto:jed@jedbrown.org"
                            target="_blank"><a class="moz-txt-link-abbreviated" href="mailto:jed@jedbrown.org">jed@jedbrown.org</a></a>></span>
                        wrote:<br>
                        <blockquote class="gmail_quote" style="margin:0
                          0 0 .8ex;border-left:1px #ccc
                          solid;padding-left:1ex"><span>Matthew Knepley
                            <<a moz-do-not-send="true"
                              href="mailto:knepley@gmail.com"
                              target="_blank">knepley@gmail.com</a>>
                            writes:<br>
                            >> Yes, I do not support that since I
                            think its a crazy way to talk about<br>
                            >> things. All the topological
                            information is in the Tri3 mesh, and<br>
                            >> Cubit has no business telling me
                            about the function space.<br>
                            >><br>
                            >><br>
                            >> Do you support / plan to support
                            curved elements?<br>
                            >><br>
                            ><br>
                            > I had "support" in there, but there
                            were bugs. Toby and Mark discovered<br>
                            > these, and Toby has fixed them. I think<br>
                            > all of the fixes are in master now.<br>
                            <br>
                          </span>The context is clearly that the mesh
                          generator needs to express the<br>
                          curved elements.  DMPlex doesn't have a
                          geometric model available, so it<br>
                          doesn't know how to make the Tri3 elements
                          curve to conform more<br>
                          accurately to the boundary.  The mesh
                          generator has no business telling<br>
                          you what function space to use for your
                          solution, but it'd be a shame to<br>
                          prevent it from expressing element geometry.<br>
                        </blockquote>
                      </div>
                      <br>
                      <br clear="all">
                      <div><br>
                      </div>
                      -- <br>
                      <div data-smartmail="gmail_signature">
                        <div dir="ltr">Andrew Ho</div>
                      </div>
                    </div>
                  </blockquote>
                  <br>
                </span></div>
              <br>
            </div>
          </blockquote>
        </div>
        <br>
        <br clear="all">
        <div><br>
        </div>
        -- <br>
        <div class="gmail_signature" data-smartmail="gmail_signature">
          <div dir="ltr">Andrew Ho</div>
        </div>
      </div>
    </blockquote>
    <br>
  </body>
</html>