Hi Barry,<br>Thank you very much for the suggestion. I totally agree with you on using the same scaling for all the points include the Boundary points. <br><br>Yan<br><br><br><br><br><br><br><div class="gmail_quote">On Fri, Dec 11, 2009 at 8:28 PM, Barry Smith <span dir="ltr"><<a href="mailto:bsmith@mcs.anl.gov">bsmith@mcs.anl.gov</a>></span> wrote:<br>
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On Dec 11, 2009, at 7:18 PM, Ryan Yan wrote:<br>
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Hi Matt,<br>
Thank you very much for the reply. Now, I got the Neumann part. But I am still a bit confused about the Dirichlet part. Please see the following quote.<br>
<br>
Yan<br>
<br>
<br>
For the Dirichlet B.C.s, I did not understand the coefficients given below. Isn't correct to set the v[0]=Hx*Hy here?<br>
if (i==0 || j==0 || i==mx-1 || j==my-1) {<br>
if (user->bcType == DIRICHLET) {<br>
v[0] = 2.0*rho*(HxdHy + HydHx);<br>
}<br>
}<br>
<br>
This is the proper scaling.<br>
<br>
the Dirichlet B.C.s:<br>
Which scaling do you think is proper, "v[0]=Hx*Hy" or 2.0*rho*(HxdHy + HydHx)?<br>
If it is 2.0*rho*(HxdHy + HydHx), can you say a little bit more about why is this one? I only see a factor of Hx*Hy when we set up the RHS. Did I miss something?<br>
<br>
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Ryan,<br>
<br>
You can scale the equations for Dirichlet boundary conditions anyway you want; you could multiply them by 1,000,000 if you want. The answer in exact precision with direct solvers will be the same. The reason we use the given scaling is to make the scaling work well with multigrid. If you use a different scaling the Dirichlet boundary conditions on the coarser grid matrices would have a different scaling then the interior equations and this would slow down MG's convergence rate. For toy problems people usually eliminate the Dirichlet boundary conditions, then there is no scaling issue for multigrid.<br>
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<br>
Barry</font><div><div></div><div class="h5"><br>
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<br>
Matt<br>
<br>
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-- <br>
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<br>
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