fenics team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

Gideon Simpson wrote:
> Ok, I see the error.  However, would you expect Poisson + zero Dirichlet 
> data to no longer have a symmetric matrix?

The method DOLFIN uses to apply Dirichlet boundary conditions destroys 
symmetry. Other approaches which would preserve might eventually make it 
onto the TODO list . . .

Garth


> -gideon
>
>
> On Jan 8, 2008, at 3:17 AM, Garth N. Wells wrote:
>
> > Gideon Simpson wrote:
> > > Something I discovered that I'm hoping someone will clarify is the 
> > > following.  Let A be the matrix associated with a Finite Element 
> > > formulation of Poisson's equation, as in the example in the demo 
> > > directory.  If one exams the eigenvalues of A before the application 
> > > of the BC's, there is a zero eigenvalue, while afterwards, there is 
> > > no such troublemaker. 
> >
> > This is correct. What it's telling you is that you need to supply a 
> > Dirichlet boundary condition to ensure that the solution is unique.
> >
> > > Thinking of A in terms of its associated weak form, I fully expected 
> > > A to be a positive definite, symmetric matrix.  This is not the case.
> > Inspecting of the form, I would expect a positive semi-definite matrix 
> > if you don't say anything about the value of functions at the boundary.
> >
> > Garth
> >
> > > -gideon
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