On Sun, Feb 13, 2011 at 8:12 PM, Kontsantinos Kontzialis <span dir="ltr"><<a href="mailto:ckontzialis@lycos.com">ckontzialis@lycos.com</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Message: 1<br>
Date: Sat, 12 Feb 2011 16:12:36 -0600<br>
From: Matthew Knepley<<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
Subject: Re: [petsc-users] Guidelines for solving the euler equations<br>
with an implicit matrix free approach<br>
To: PETSc users list<<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
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<<a href="mailto:AANLkTimus8N2jUu7Bvu0TZe59dr4FTpoJFh%2Bm0QQUN-V@mail.gmail.com" target="_blank">AANLkTimus8N2jUu7Bvu0TZe59dr4FTpoJFh+m0QQUN-V@mail.gmail.com</a>><br>
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On Fri, Feb 11, 2011 at 10:37 AM, Kontsantinos Kontzialis<<br>
<a href="mailto:ckontzialis@lycos.com" target="_blank">ckontzialis@lycos.com</a>> wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Dear Petsc team,<br>
<br>
I'm new in Petsc and I'm trying to solve the euler equations of fluid<br>
dynamics<br>
using an implicit matrix free approach with a spatial discontinues galerkin<br>
discretization.<br>
I need some directions about how can I solve the following system:<br>
<br>
(M/dt+dR/du)*DU=R<br>
<br>
where R denotes the residual of the system and dR/du the residual jacobian.<br>
Please help.<br>
<br>
</blockquote>
Petsc provides linear algebra and nonlinear solvers. This is fine once you<br>
have discretized.<br>
It sounds like you will use DG:<br>
<br>
a) on a structured or unstructured grid?<br>
<br>
The PETSc DA supports structured grids in any dimension. After this, you<br>
want to use the<br>
TS object to present your system. There are many examples in the TS, e.g.<br>
ex10 for<br>
radiation-diffusion or ex14 for hydrostatic ice flow.<br>
<br>
Once you have your problem producing the correct residual and Jacobian, we<br>
can talk<br>
about solvers.<br>
<br>
Matt<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Kostas<br>
<br>
</blockquote></blockquote>
Mat,<br>
<br>
Thank you for your reply. I have done the discretization and the residual and jacobian are computes correctly. Furthermore, I managed to do some calculation using TS but with an explicit scheme. I need to work with an implicit time discretization and I have read in a quite few papers that they follow the matrix free approach.<br>
</blockquote><div><br></div><div>Once you plug your Residual and Jacobian into the TS, you can start to try out different solvers. Is this working?</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Thank you,<br>
<br>
Kostas<br>
</blockquote></div><br><br clear="all"><br>-- <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>