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<p><font size="4"><font face="monospace">Hey all,</font></font></p>
<p><font size="4"><font face="monospace">so I have a nonlinear problem that can be abstractly written as</font></font></p>
<p><font size="4"><font face="monospace">| F(u,P) | | 0 |<br>
</font></font></p>
<p><font size="4"><font face="monospace">| | = | |<br>
</font></font></p>
<p><font size="4"><font face="monospace">| G(u,P) | | 0 | </font></font><br>
</p>
<pre class="moz-signature" cols="72">
Here u is a variable that comes from a discretization of a PDE and P are four scalars that come from some coupled attached ODEs (P = (P1,P2,P3,P4) )
I know abstract how to apply Newton-Raphson in this context as the Jacobian is simply
d_u F d_P F
d_u G d_P G
where d_P F and d_u G are formed from 4 Vecs resp, and d_P G is a 4x4 matrix.
So what I have troubles with is how I could squeeze something like this into an SNES context, at the moment I'm doing a Schur-Complement for Solving this problem for each Newton solve. This however entails, that I'm, solving (d_u F)^-1 to a very low tolerance inside the SC.
In the End I want to have something that can work with an inexact Newton method, but I don't know which would be the correct tool (MATSHELL for the jacobian maybe?) to squeeze this into an SNES.
Any ideas?
Best regards
Elias
--
Dr. Elias Karabelas
Research Associate
University of Graz
Institute of Mathematics and Scientific Computing
Heinrichstraße 36
A-8010 Graz
Austria
Phone: +43 316 380 8546
Email: <a class="moz-txt-link-abbreviated" href="mailto:elias.karabelas@uni-graz.at">elias.karabelas@uni-graz.at</a>
Web: <a class="moz-txt-link-freetext" href="https://ccl.medunigraz.at/">https://ccl.medunigraz.at/</a></pre>
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