Re: [Libmesh-users] boundary condition treatment

[li p. <li...@ya...>]

hi,
there are too many elements need to set. It's too
expensive. So what's the advantage to do it in
comparison with penalty method in libmesh?

regards

pan


--- Hae-Won Choi <ha...@uc...> wrote:

> Hi, actually John clarify what I exactly want. Thank
> you John,
> For PetSc, MatZeroRows set 1 for all diagonal
> entities
> of all Dirichlet boundary rows (other entities will
> be zero) as I  
> mentioned last time.
> In fact you can find examples using this approach
> from PetSc since I  
> have learned
> this from PetSc.
> What you have to do is modify RHS as John's example
> shows.
> I have used this method for my other codes using
> PetSc (but not for  
> libMesh yet).
> This approach gives same results as reduced matrix
> method.
> 
> Hae-Won
> 
> On Sep 29, 2006, at 5:45 AM, John Peterson wrote:
> 
> > Just as an addendum to Tim's note, you can
> maintain any
> > symmetry originally present in the problem by
> "subtracting"
> > the column entries multiplied by the Dirichlet
> value from
> > the right hand side vector.
> >
> > If Au=b, where
> >
> > [a_11 a_12 a_13]  [u1] = [b1]
> > [a_21 a_22 a_23]  [u2] = [b2]
> > [a_31 a_32 a_33]  [u3] = [b3]
> >
> > and u1 = g1, a non-homogeneous BC val, we can
> modify Au=b as:
> >
> > [ 1   0    0   ]  [u1] = [g1]
> > [ 0   a_22 a_23]  [u2] = [b2 - g1*a21]
> > [ 0   a_32 a_33]  [u3] = [b3 - g1*a31]
> >
> >
> > This imposes u1=g1, and maintains any original
> symmetry of A.
> >
> >
> > -John
> >
> >
> >
> > Tim Kröger writes:
> >> Dear all,
> >>
> >> On Fri, 29 Sep 2006, li pan wrote:
> >>
> >>> I'm also thinking about this. Are you sure that
> you
> >>> only need to zero all the enties of rows? I read
> >>> somewhere that columes should also be zeroed.
> Could
> >>> somebody confirm this?
> >>
> >> If you zero only the row entries, the matrix will
> no longer be
> >> symmetric.  This is often considered as a
> drawback (provided that the
> >> matrix was symmetric before) because certain
> solvers (e.g. CG) cannot
> >> be used then any more.
> >>
> >> On the other hand, if the column entries are also
> zeroed, the  
> >> solution
> >> of the system will be wrong -- except for the
> case of *homogeneous*
> >> Dirichlet conditions.  For this reason, some
> people transform their
> >> problems to homogeneous boundary conditions, i.e.
> they do in practice
> >> the same thing that is usually done theoretically
> anyway, i.e. they
> >> subtract a function that fulfills all Dirichlet
> boundary conditions
> >> but not the PDE.  Note that in the discrete case,
> such a function is
> >> trivial to find.
> >>
> >> Because I find this all quite unsatisfactory, I
> was glad to see that
> >> libMesh uses the penalty method (which I did not
> know before) because
> >> it is easy to implement, works in all cases, and
> does not destroy
> >> symmetry or positivity of the matrix.
> >>
> >> Best Regards,
> >>
> >> Tim
> >
> >
>
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