<div dir="ltr"><div dir="ltr">On Fri, Jun 23, 2023 at 10:28 AM neil liu <<a href="mailto:liufield@gmail.com">liufield@gmail.com</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Dear Petsc developers,<div><br></div><div>I am learning  <span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol""><b>PetscDTSimplexQuadrature </b>and plan to use it.</span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">I found that, in the biunit simplex (tetra), </span><span style="color:rgb(0,0,0)">(-1,-1,-1),(1,-1,-1),(-1,1,-1),(-1,-1,1)</span><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">, </span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">degree 1: npoints 4, the sum of weights = 4/3(the volume of this simplex)</span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">degree 2 : npoints 8;</span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">For my previous experience, I used Gauss quadrature rules, (npoints =4 , 5, 11, 15).</span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">Then  I am curious what rule is Petsc using ?</span></div></div></blockquote><div><br></div><div>There are two supported types:</div><div><br></div><div>  - Stroud Conical Quadrature</div><div><br></div><div>  - Minimal Symmetric Quadrature</div><div><br></div><div>I think we prefer symmetric when it is available.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>And is <b style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">PetscDTSimplexQuadrature </b><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">used by PetscFE? </span></div></div></blockquote><div><br></div><div>Yes.</div><div><br></div><div>  Thanks,</div><div><br></div><div>    Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol""><br></span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">Thanks a lot,</span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol""><br></span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol"">Xiaodong </span></div><div><span style="font-family:-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol""><br></span></div></div>
</blockquote></div><br clear="all"><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>