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<p>Hi,</p>
<p>to add some more specific details to Olivers answer:</p>
<p>Boundary conditions like Neumann/Robin are implemented with
surface integrals as you have written. The "surface" thereby is
represented by a set of boundary intersections in Dune, i.e.,
intersections of grid elements with the boundary. Each element can
iterate over all its intersections (with neighboring elements and
also with the boundary) and the intersection has the information
whether it is on the boundary or not. Thus, during your assembling
over the grid elements, you could iterate over the element
intersections and for each boundary intersection construct a
quadrature rule from the intersection geometry. All necessary
geometric mappings are provided by the intersection object.</p>
<p>See the following documentation pages for more details:</p>
<p>
<a class="moz-txt-link-freetext" href="https://dune-project.org/doxygen/2.8.0/classDune_1_1Intersection.html">https://dune-project.org/doxygen/2.8.0/classDune_1_1Intersection.html</a>
// the Intersection class<br>
<a class="moz-txt-link-freetext" href="https://dune-project.org/doxygen/2.8.0/group__GIIteration.html#ga0927181ebf10ed59531e262a63f92daf">https://dune-project.org/doxygen/2.8.0/group__GIIteration.html#ga0927181ebf10ed59531e262a63f92daf</a>
// the intersections "range generator" to iterator of
intersections of an entity</p>
<p>In the book "DUNE - The Distributed and Unified Numerics
Environment", O. Sander, 2020
(<a class="moz-txt-link-freetext" href="https://www.springer.com/gp/book/9783030597016">https://www.springer.com/gp/book/9783030597016</a>) in chapter 5.4.
there it is also described in more detail.</p>
<p>Best regards,<br>
Simon<br>
</p>
<div class="moz-cite-prefix">Am 13.09.21 um 08:48 schrieb Oliver
Sander:<br>
</div>
<blockquote type="cite"
cite="mid:cfee2a42-dd12-26c1-71cd-f19d2ed37122@tu-dresden.de">Hi
Genki,
<br>
<br>
are you using one of the standard discretization modules?
<br>
If so, you should ask the respective maintainers of those.
<br>
<br>
If you want to compute those integrals using only the Dune core
<br>
the Dual Mortar Basis example from the book may help you
<br>
(a little).
<br>
<br>
Best,
<br>
Oliver
<br>
<br>
On 12.09.21 13:38, Unagami, Genki wrote:
<br>
<blockquote type="cite">Hello,
<br>
<br>
<br>
I am trying to solve a heat transfer problem (Poisson's
equation) with the Robin boundary condition; and in its weak
formulation, the surface integral term appears. Is there a way
to compute this integral on Dune?
<br>
<br>
<br>
Thanks in advance,
<br>
<br>
Best regards,
<br>
<br>
Genki Unagami
<br>
<br>
<br>
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</blockquote>
<br>
<br>
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<pre class="moz-quote-pre" wrap="">_______________________________________________
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<pre class="moz-signature" cols="72">--
Dr. Simon Praetorius
Technische Universität Dresden
Institute of Scientific Computing
phone: +49 351 463-34432
mail: <a class="moz-txt-link-abbreviated" href="mailto:simon.praetorius@tu-dresden.de">simon.praetorius@tu-dresden.de</a>
web: <a class="moz-txt-link-freetext" href="https://tu-dresden.de/mn/math/wir/das-institut/beschaeftigte/simon-praetorius">https://tu-dresden.de/mn/math/wir/das-institut/beschaeftigte/simon-praetorius</a></pre>
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