dolfin team mailing list archive

[Matthew Knepley <knepley@xxxxxxxxx>]

On Wed, Apr 29, 2009 at 4:37 AM, Jed Brown <jed@xxxxxxxx> wrote:

> Matthew Knepley wrote:
>
> > Really? This is ugly. It is not an algorithm, it is just sticking a
> > whole bunch of known shapes into a database.
>
> Yes, but it is what most mesh-generators provide, it is low-memory, and
> is conducive to efficient query and modification, especially those
> involving a geometric model.
>
> Since I care about higher than second order elements, I disagree with
> the solution presented in Section 2.3 to the extent that many degrees of
> freedom (nodes or modes) need to be associated with each entity.  When
> setting up a function space, I assign an anisotropic order to every mesh
> entity, reduce with a minimum rule (for continuity), label everything
> with a global offset, broadcast, and then build the element assembly
> matrix (a Scatter/IS is not enough because an element dof may correspond
> to a linear combination of global dofs).
>
> When building the element assembly matrix, I do something similar to
> you, where each region only looks directly at it's faces, faces at
> edges, etc, but I orient them based on vertex connectivity rather than
> storing an orientation for each relation.  In the end, I don't see how
> to avoid writing something specific to each topology you want to handle,
> but you do not have to write anything special for each order.
>
> > We have a real algorithm that can compute all this on the fly with
> > simple rules.
>
> I assume you are talking about storing one-level downward adjacencies
> (region->faces, faces->edges, edges->vertices) and orientations, and
> inferring the rest.  This is perfectly valid but you still have to make
> the same sort of arbitrary choices.  It changes the complexity of
> certain operations and changes what sort of operations need to be
> special-cased on topology.  The Sieve source has plenty of special
> casing and doesn't support the zoo, so I'm not convinced that it is the
> One True Way


I cannot be more emphatic here. <voice_of_god>THERE IS NO SPECIAL
CASING</voice_of_god>.
At all. In the whole thing. You can argue that in some cases it might be
slower, but it works for any
arrangement in any dimension. I will never put that special case crap in my
code. Ever.

  Matt


>
> Jed
>
>
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-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener