dolfin team mailing list archive

[Catherine Micek <mice0012@xxxxxxx>]

On Aug 10, 2009, at 2:49 AM, Kristian Oelgaard wrote:

> Quoting Ola Skavhaug <skavhaug@xxxxxxxxx>:
>
> > On Mon, Aug 10, 2009 at 5:46 AM, Catherine Micek<mice0012@xxxxxxx>  
> > wrote:
> > > On Aug 9, 2009, at 3:24 AM, Kristian Oelgaard wrote:
> > >
> > > > Quoting Peter Brune <prbrune@xxxxxxxxx>:
> > > >
> > > > > As a quick solution, you could, knowing the coordinates of a node,
> > > > > constrain
> > > > > everything within some epsilon smaller than the mesh feature size
> > > > > of the
> > > > > node (such as DOLFIN_EPS).
> > > >
> > > > Yes, and then make sure to use the "pointwise" method when creating
> > > > the
> > > > DirichletBC. See comment in dolfin/fem/DirichletBC.h.
> > > > You can also look at demo/pde/dg/advection-diffusion/main.cpp for
> > > > an example on
> > > > how to use the "geometric" approach. The majority of DOLFIN demos
> > > > uses the
> > > > "topological" approach which is the default.
> > >
> > > This seems simple enough, but I am having a little difficulty with
> > > it.  I am coding with the python interface, so I looked at the  
> > > python
> > > version of the demo in demo/pde/dg/advection-diffusion/.  In there,
> > > the Dirichlet boundary is specified as the line x=1 on the boundary,
> > > i.e.
> > >
> > > class DirichletBoundary(SubDomain):
> > >     def inside(self, x, on_boundary):
> > >        return (abs(x[0] - 1.0) < DOLFIN_EPS and on_boundary
> > >
> > > and I'm unclear as to why it's necessary to specify "pointwise" as
> > > opposed to "topological" boundary conditions.  So this condition
> > > would fix all the nodes on the line x=1; it doesn't appear to be
> > > picking out points.  Is it necessary here because we're using DG
> > > elements?
>
> Yes, you can use "geometric" for DG elements where you would  
> normally use
> "topological" for other elements. In this case it's not necessary  
> to use
> "pointwise" because we fix all nodes on the line x=1. Note that  
> "topological"
> is faster than "geometric" which is faster than "pointwise", how  
> big the
> difference is in practice I don't know.
>
> > > The other question is related to syntax.  Say I want to fix the  
> > > point
> > > (1,0).  When I set the boundary as
> > >
> > > class DirichletBoundary(SubDomain):
> > >     def inside(self, x, on_boundary):
> > >        return ( (abs(x[0] - 1.0) and abs(x[1] - 0.0) < DOLFIN_EPS  
> > > and
> > > on_boundary)
> >
> > This is not correct, since abs(x[0]-1.0]) almost always evaluates  
> > to True.
> > Try
> > return ( (abs(x[0] - 1.0) < DOLFIN_EPS and abs(x[1] - 0.0) <
> > DOLFIN_EPS and on_boundary)
> >
> > Ola
> >
> > > and set the Dirichlet boundary condition with the option set to
> > > "geometric," I am not getting the correct solution.  Is this not the
> > > correct way to set the boundary conditions?
>
> No, you want to set the dofs at a point, so you should use  
> "pointwise". Also
> note that the variable 'on_boundary' is ALWAYS False when using the  
> "pointwise"
> method, so you should modify Ola's suggestion to:
>
> class DirichletBoundary(SubDomain):
>   def inside(self, x, on_boundary):
>     return abs(x[0] - 1.0) < DOLFIN_EPS and abs(x[1] - 0.0) <  
> DOLFIN_EPS

Thanks for the clarification, it worked!

Katy


> Kristian
>
> > > Again, any suggestions would be appreciated -- thanks!
> > >
> > > Katy
> > >
> > >
> > > > Kristian
> > > >
> > > > > - Peter
> > > > >
> > > > > On Sat, Aug 8, 2009 at 11:27 PM, Catherine Micek
> > > > > <mice0012@xxxxxxx> wrote:
> > > > >
> > > > > > Hi,
> > > > > > I'm working with a group that's using Fenics to study the
> > > > > > equations of
> > > > > > linear elasticity (with a pure displacement formulation), and I
> > > > > > have a
> > > > > > question about boundary conditions.  Our goal is to study the
> > > > > > pure traction
> > > > > > problem, and this means we have to be careful in formulating the
> > > > > > boundary
> > > > > > conditions.  In order to prevent a singularity in our equations,
> > > > > > we need to
> > > > > > constrain certain nodes so as to prevent translations and rigid
> > > > > > rotations.
> > > > > >  There are many examples in the fenics demos about how to
> > > > > > prescribe mixed
> > > > > > conditions, but I have only seen examples where the Dirichlet
> > > > > > condition
> > > > > > occurs along an edge (as opposed to occurring at a few individual
> > > > > > nodes).
> > > > > >  So my question is, given a mesh, how does one prescribe  
> > > > > > Dirichlet
> > > > > > conditions for individual nodes?  Are there any demos that
> > > > > > address this?
> > > > > >
> > > > > > Any help would be greatly appreciated -- thanks!
> > > > > >
> > > > > > Katy
> > > > > >
> > > > > > ---
> > > > > > Catherine (Katy) A. Micek
> > > > > > Graduate Assistant, U of MN Mathematics Department
> > > > > > http://www.math.umn.edu/~mice0012 <http://www.math.umn.edu/%
> > > > > > 7Emice0012>
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > > _______________________________________________
> > > > > > DOLFIN-dev mailing list
> > > > > > DOLFIN-dev@xxxxxxxxxx
> > > > > > http://www.fenics.org/mailman/listinfo/dolfin-dev
> > >
> > > _______________________________________________
> > > DOLFIN-dev mailing list
> > > DOLFIN-dev@xxxxxxxxxx
> > > http://www.fenics.org/mailman/listinfo/dolfin-dev
> >
> >
> >
> > --
> > Ola Skavhaug
>
>
> _______________________________________________
> DOLFIN-dev mailing list
> DOLFIN-dev@xxxxxxxxxx
> http://www.fenics.org/mailman/listinfo/dolfin-dev

---
Catherine (Katy) A. Micek
Graduate Women Coordinator, U of MN Mathematics Department