<div dir="ltr"><div dir="ltr">On Wed, Mar 24, 2021 at 7:17 PM Jorti, Zakariae via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</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">
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<p>Hi Patrick,</p>
<p><br>
</p>
<p>Thanks for your responses. </p>
<p>As for the code, I was not granted permission to share it yet. So, I cannot send it to you for the moment. I apologize for that.</p>
<p><br>
</p>
<p>I wanted to let you know that while I was testing my code, I discovered that when the periodic boundary conditions are activated, the coordinates accessed might be incorrect on one side of the boundary. </p>
<p>Let me give you an example in cylindrical coordinates with a 3x3x3 DMStag mesh: </p>
<p> </p>
<p><br>
</p>
<p><br>
</p>
<p>PetscInt<span style="white-space:pre-wrap"> </span> startr,startphi,startz,nr,nphi,nz,d;</p>
<p></p>
<p>PetscInt<span style="white-space:pre-wrap"> </span> er,ephi,ez,<span style="font-size:12pt">icErmphip[3];</span></p>
<p></p>
<p>DM dmCoorda, coordDA;</p>
<p>Vec coordaLocal;</p>
<p>PetscScalar ****arrCoord;</p>
<p>PetscScalar surf;</p>
<p><br>
</p>
<p>DMStagCreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,3,3,3,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,1,1,DMSTAG_STENCIL_BOX,1,NULL,NULL,NULL,&coordDA);<br>
</p>
<p><br>
</p>
<p>DMSetFromOptions(coordDA);</p>
<p>DMSetUp(coordDA);</p>
<p><br>
</p>
<p>DMStagGetCorners(coordDA,&startr,&startphi,&startz,&nr,&nphi,&nz,NULL,NULL,NULL);</p>
<p><br>
</p>
<p>DMGetCoordinateDM(coordDA,&dmCoorda);</p>
<p>DMGetCoordinatesLocal(coordDA,&coordaLocal);</p>
<p> DMStagVecGetArrayRead(dmCoorda,coordaLocal,&arrCoord);</p>
<p><br>
</p>
<p>for (d=0; d< 3; ++d){</p>
<p>DMStagGetLocationSlot(dmCoorda,UP_LEFT,d,&icErmphip[d]);<br>
</p>
<p>}</p>
<p><br>
</p>
<p>er = 1; ez = 0;</p>
<p>for (ephi=0; ephi< 3; ++ephi){</p>
<p><span style="font-size:12pt"> PetscPrintf(PETSC_COMM</span><span style="font-size:12pt">_</span><span style="font-size:12pt">WORLD,"Phi_p(%d,%d,%d) = %E</span><span style="font-size:12pt">\</span><span style="font-size:12pt">n</span><span style="font-size:12pt">",</span><span style="font-size:12pt">er</span><span style="font-size:12pt">,</span><span style="font-size:12pt">ephi</span><span style="font-size:12pt">,</span><span style="font-size:12pt">ez</span><span style="font-size:12pt">,(double)</span><span style="font-size:12pt">arrCoord[ez][ephi][er][icErmphip[1]</span><span style="font-size:12pt">);</span></p>
<p>}</p>
<p><br>
</p>
<p>When I execute this example, I get this output:</p>
<p><span style="font-size:12pt">Phi_p(1,0</span><span style="font-size:12pt">,0) =</span><span style="font-size:12pt"> </span><span style="font-size:12pt">2</span><span style="font-size:12pt">.094395</span><span style="font-size:12pt">E+00</span></p>
<p><span style="font-size:12pt"></span>Phi_p(1,1,0) = 4.188790E+00<br>
</p>
<p>Phi_p(1,2,0) = 0.000000E+00</p>
<p><br>
</p>
<p>Note here that the first two lines correspond to 2<span style="color:rgb(33,33,33);font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont;font-size:12pt">π / 3 and 4</span><span style="color:rgb(33,33,33);font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont;font-size:12pt">π
/ 3 respectively. Thus, nothing is wrong here. </span></p>
<p><span style="color:rgb(33,33,33);font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont;font-size:12pt">But the last line should rather give 2</span><span style="color:rgb(33,33,33);font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont;font-size:12pt">π
instead of 0.</span></p>
<p><span style="color:rgb(33,33,33);font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont;font-size:12pt"><br>
</span></p>
<p><span style="font-size:12pt">I understand that degrees of freedom should be the same on both sides of the boundary, but should the coordinates not be preserved? </span></p>
<p><span style="font-size:12pt"></span></p></div></div></blockquote><div>I don't think so. The circle has coordinates in [0, 2\pi), so the point at 2\pi is identified with the point at 0 and you must choose</div><div>one, so we choose 0.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div style="overflow-wrap: break-word;"><div id="gmail-m_-5207082944899504102divtagdefaultwrapper" style="font-size:12pt;color:rgb(0,0,0);font-family:Calibri,Helvetica,sans-serif" dir="ltr"><p><span style="font-size:12pt">Thank you.</span></p>
<p><span style="font-size:12pt">Best regards,</span></p>
<p><span style="font-size:12pt"><br>
</span></p>
<p><span style="font-size:12pt">Zakariae Jorti</span></p>
</div>
<hr style="display:inline-block;width:98%">
<div id="gmail-m_-5207082944899504102divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Patrick Sanan <<a href="mailto:patrick.sanan@gmail.com" target="_blank">patrick.sanan@gmail.com</a>><br>
<b>Sent:</b> Tuesday, March 23, 2021 11:37:04 AM<br>
<b>To:</b> Jorti, Zakariae<br>
<b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><br>
<b>Subject:</b> [EXTERNAL] Re: Question about periodic conditions</font>
<div> </div>
</div>
<div>Hi Zakariae - sorry about the delay - responses inline below.
<div><br>
</div>
<div>I'd be curious to see your code (which you can send directly to me if you don't want to post it publicly), so I can give you more comments, as DMStag is a new component. <br>
<div><br>
</div>
<div>
<div><br>
<blockquote type="cite">
<div>Am 23.03.2021 um 00:54 schrieb Jorti, Zakariae <<a href="mailto:zjorti@lanl.gov" target="_blank">zjorti@lanl.gov</a>>:</div>
<br>
<div>
<div id="gmail-m_-5207082944899504102divtagdefaultwrapper" dir="ltr" style="font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-size:12pt;font-family:Calibri,Helvetica,sans-serif">
<div style="margin-top:0px;margin-bottom:0px">Hi, </div>
<div style="margin-top:0px;margin-bottom:0px"><br>
</div>
<div style="margin-top:0px;margin-bottom:0px">I implemented a PETSc code to solve Maxwell's equations for the magnetic and electric fields (B and E) in a cylinder: </div>
<div style="margin-top:0px;margin-bottom:0px">0 < r_min <= r <= r_max; with <span style="font-size:12pt">r_max</span><span style="font-size:12pt"> > r_min</span></div>
<div style="margin-top:0px;margin-bottom:0px">phi_min = 0 <span style="font-size:12pt"><= r <= phi_max</span><span style="font-size:12pt"> = 2 </span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">π</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">z_min <= z =< z_max; </span><span style="font-size:12pt">with </span><span style="font-size:12pt">z_max</span><span style="font-size:12pt"> >
z_min.</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-size:12pt"><br>
</span></div>
<div style="margin-top:0px;margin-bottom:0px"><font size="3">I am using a PETSc staggered grid with the electric field E defined on edge centers and the magnetic field B </font>defined<font size="3"> on face centers. (</font><span style="font-size:12pt">dof0
= 0, dof1 = 1,dof2 = 1, dof3 = 0;</span><font size="3">). </font><font size="3"> </font></div>
</div>
</div>
</blockquote>
<blockquote type="cite">
<div>
<div id="gmail-m_-5207082944899504102divtagdefaultwrapper" dir="ltr" style="font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-size:12pt;font-family:Calibri,Helvetica,sans-serif">
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-size:12pt"></span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">I have two versions of my code: </span></div>
<div style="margin-top:0px;margin-bottom:0px"><font face="Calibri, Helvetica, sans-serif" size="3">1 - A first version<span> </span></font><font face="Calibri, Helvetica, sans-serif">in which I set
the boundary type to DM_BOUNDARY_NONE in the three directions r, phi and z</font></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">2- A second version in which I set </span><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">the boundary
type to DM_BOUNDARY_NONE in the r and z directions</span><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">, </span><font face="Calibri, Helvetica, sans-serif" size="3">and DM_BOUNDARY_PERIODIC in the phi di</font><font face="Calibri, Helvetica, sans-serif">rection.</font><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"> </span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">When I print the solution vector X, which contains both E and B components, I notice that the vector is shorter with
the second version compared to the first one. </span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">Is it normal? </span></div>
</div>
</div>
</blockquote>
Yes - with the periodic boundary conditions, there will be fewer points since there won't be the "extra" layer of faces and edges at phi = 2 * pi .</div>
<div><br>
</div>
<div>If you consider a 1-d example with 1 dof on vertices and cells, with three elements, the periodic case looks like this, globally,</div>
<div><br>
</div>
<div> x ---- x ---- x ----</div>
<div><br>
</div>
<div>as opposed to the non-periodic case,</div>
<div><br>
</div>
<div> x ---- x ---- x ---- x</div>
<div><br>
</div>
<div><br>
</div>
<div>
<blockquote type="cite">
<div>
<div id="gmail-m_-5207082944899504102divtagdefaultwrapper" dir="ltr" style="font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-size:12pt;font-family:Calibri,Helvetica,sans-serif">
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">Besides, I was wondering if I have to change the way I define the value of the solution on the boundary. What I am
doing so far in both versions is something like:</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">B_phi [phi = 0] = 1.0;</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif">B_phi </span><span style="font-family:Calibri,Helvetica,sans-serif">[phi = 2</span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">π</span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">]
= 1.0;</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">E_z [r, phi = 0</span><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">] = 1/r;</span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">E_z [r, phi = 2</span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">π</span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">]
= 1/r;</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</span></div>
<div style="margin-top:0px;margin-bottom:0px"><font face="Calibri, Helvetica, sans-serif">Assuming that values at phi = 0 should be the same as at phi=2</font><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">π
with the periodic boundary conditions, </span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">is it sufficient for example </span><font face="Calibri, Helvetica, sans-serif" size="3">to </font><font face="Calibri, Helvetica, sans-serif">have</font><font face="Calibri, Helvetica, sans-serif" size="3"> only
the following boundary conditions</font><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">:</span></div>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt">B_phi [phi = 0] = 1.0;</span></div>
<p style="margin-top:0px;margin-bottom:0px"><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"></span></p>
<div style="margin-top:0px;margin-bottom:0px"><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">E_z [r, phi = 0</span><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">] = 1/r
? </span><span style="font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><br>
</span></div>
</div>
</div>
</blockquote>
<div><br>
</div>
Yes - this is the intention, since the boundary at phi = 2 * pi is represented by the same entries in the global vector. </div>
<div><br>
</div>
<div>Of course, you need to make sure that your continuous problem is well-posed, which in general could change when using different boundary conditions. </div>
<div><br>
<blockquote type="cite">
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<div><span style="font-size:12pt;font-family:Calibri,Helvetica,sans-serif">Thank you.</span></div>
<div><font face="Calibri, Helvetica, sans-serif">Best regards,</font></div>
<div><font face="Calibri, Helvetica, sans-serif"><br>
</font></div>
<div><font face="Calibri, Helvetica, sans-serif">Zakariae Jorti</font></div>
</div>
</div>
</blockquote>
</div>
<br>
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</blockquote></div><br clear="all"><div><br></div>-- <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>