dolfin team mailing list archive

[Catherine Micek <mice0012@xxxxxxx>]

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?

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)

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?

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>
> > >
> > >
> > >
> > >
> > >
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