[Dune] Implementation of Robin Boundary Condition

[Simon Praetorius]

Hi,

to add some more specific details to Olivers answer:

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.

See the following documentation pages for more details:

https://dune-project.org/doxygen/2.8.0/classDune_1_1Intersection.html // 
the Intersection class
https://dune-project.org/doxygen/2.8.0/group__GIIteration.html#ga0927181ebf10ed59531e262a63f92daf 
// the intersections "range generator" to iterator of intersections of 
an entity

In the book "DUNE - The Distributed and Unified Numerics Environment", 
O. Sander, 2020 (https://www.springer.com/gp/book/9783030597016) in 
chapter 5.4. there it is also described in more detail.

Best regards,
Simon

Am 13.09.21 um 08:48 schrieb Oliver Sander:
> Hi Genki,
>
> are you using one of the standard discretization modules?
> If so, you should ask the respective maintainers of those.
>
> If you want to compute those integrals using only the Dune core
> the Dual Mortar Basis example from the book may help you
> (a little).
>
> Best,
> Oliver
>
> On 12.09.21 13:38, Unagami, Genki wrote:
>> Hello,
>>
>>
>> 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?
>>
>>
>> Thanks in advance,
>>
>> Best regards,
>>
>> Genki Unagami
>>
>>
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>
>
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-- 
Dr. Simon Praetorius
Technische Universität Dresden
Institute of Scientific Computing
phone: +49 351 463-34432
mail: simon.praetorius at tu-dresden.de
web: https://tu-dresden.de/mn/math/wir/das-institut/beschaeftigte/simon-praetorius

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