# [Getdp] How one can solve the problem with coupled FEM + BEM in GetDP?

Dmitry Matison matison.d at mephi.org
Fri Apr 25 16:00:19 CEST 2008

Thanks for your answer!
It would be good to see what others think about your proposal.

There is one document explaining BEM for beginners, but i have no idea of
it's quality, although it's good in opinion.
http://www.ntu.edu.sg/home/mwtang/bemsite.htm
There is "FEM/BEM NOTES"  by someone from Bioengineering Institute The
University of Auckland, New Zealand, where FEM/BEM coupling is described,
also containing  BEM  formulation. 2005
http://www.bioeng.auckland.ac.nz/cmiss/fembemnotes/fembemnotes.pdf
Brebbia C.A. Domingues J. Boundary elements. An introductuory course 1998
http://djvu.504.com1.ru:8019/WWW/47b408cf1d20943646258d1ec0d4ef07.djvu

-------------
Dmitry

2008/4/24, Olivier Castany

> > Did anyone try it? My problem deals with two regions: nonlinear region,
> > where I want to use FEM, with infinite region around, where BEM is
> better.
> > How could one use this coupling in GetDP?
>
>
> I've wanted to do it for a long time... but I don't have the time...
>
> I am also rather a dilettante concerning thoses things : just a user
> of the program, no deep understanding. I don't know if this coupling is
> possible, because I don't really know what BEM is... (if you have a
> clear and short description of the BEM or of your pb, I would be very
> interested)
>
> However, I think it is possible and my idea is the following :
>
> In the "Formulation", you can define "integral quantities" involving
> Dofs ("Type Integral"). Example :
>
> Quantity {  ...
>       { Name ResultingQuantity ; Type Integral ;
>         [ G[] * Dof{SomeField} ];
>         In support_of_SomeField ; Jacobian JSur ; Integration I ; }
>
> There, G[] can be whatever function, for example :
> G[] = Exp[- SquNorm[XYZ[]-XYZS[]] / (d1^2) ] / (Sqrt[Pi]*d1) ;
> (the integration is made over the "source point" XYZS[] \in
> support_of_SomeField) (some predefined functions exist, like : Laplace
> or Helmholtz, see the manual)
>
> Then this integral quantity can be used later in an "Equation".
> Example :
>
> Galerkin { [ Dof{ResultingQuantity} , {what you want} ] ;
>         In support_of_ResultingQuantity ; Jacobian JSur ; Integration I ; }
>
>
> I don't answer on the list because I am interested to see if other