On Mon 2009-04-06 07:42, Matthew Knepley wrote:
On Mon, Apr 6, 2009 at 1:09 AM, Anders Logg <logg@xxxxxxxxx> wrote:
On Sun, Apr 05, 2009 at 05:11:51PM -0500, Matthew Knepley wrote:
> On Sun, Apr 5, 2009 at 2:54 PM, Anders Logg <logg@xxxxxxxxx> wrote:
>
> Dirichlet BC would need to be added in/after each multiplication and
> it should be possible to build it into the mult() operator and make
it
> efficient.
>
>
> I still think the best way to handle this is to eliminate them, as I
talked
> about
> last time at Simula.
>
> Matt
I think we're in position to do that now with the new FunctionSpace
class. One could allow restrictions to be imposed, for example
V.restrict(bc);
But I haven't seen any good numbers to indicate it's worth the effort.
How much better is it to eliminate, condition numbers etc for letting
the constrained dofs just sit along?
Its not about performance, so much as
1) Programming ease, ESPECIALLY with nonlinear problems
2) Separation of storage organization from traversal organization
3) Cache performance
4) Interaction with external packages
I think I must have done a terrible job explaining this. I have always coded
both ways and always found that elimination is better.
I agree with all your points, but with caveats on 3.
There are much bigger gains in cache performance by interlacing the dofs
so as to enable the use of inodes and blocked matrix formats (BAIJ).
If we want to use blocked formats with slip boundary conditions, we need
to be able to leave the condition in. A slip boundary condition imposes
a Dirichlet condition on the normal component and stress conditions on
the tangent components. The global degrees of freedom can be written in
a rotated coordinate frame so that the Dirichlet condition can be
completely removed, but when using BAIJ we have to put something there.
This can be done, complete with "zeroing the column", but it requires
manipulations in function evaluation and when setting values in the
matrix. In some of my experiments, the performance benefits of BAIJ
over AIJ+inodes justify this strategy.
If you have Dirichlet conditions on all components, then removing these
dofs from the system really is better. Also, if you are not using
blocked matrix formats, you might as well remove all Dirichlet dofs for
all the reasons Matt states.
Jed
