
A Unified Finite Strain Theory for Membranes and Ropes - sel1
https://arxiv.org/abs/1909.12640
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ajross
OK, I'll ask the dumb question: was there a particular computational
disadvantage for the existing paradigms for solving for behavior of "membranes
and ropes"? This seems like extraordinarily well covered ground (and, let's be
honest, sort of a pedestrian problem area), and the abstract is talking about
what sound like aesthetic improvements and not breadth or performance
enhancements to the technique.

~~~
whatshisface
> _The numerical results show that the proposed finite strain theory yields
> higher-order convergence rates independent of the numerical methodology, the
> dimension of the manifold, and the geometric representation type._

From the abstract.

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ajross
That just says that the algorithmic behavior is unchanged under this list of
implementation choices, not that it converges faster. And I repeat the dumb
question: these haven't been typical complaints about the kind of boring
solvers we've been using for decades, so why do we care?

~~~
rumanator
> these haven't been typical complaints about the kind of boring solvers we've
> been using for decades

This statement is patently false. The "boring solvers" are computationally
expensive, to the point that some applications, such as structural
optimization, are practically impossible to employ. We're talking about models
which might take hours to run a single simulation.

Not to mention the fact that the computational cost of running high resolution
models typically grows exponentially with regards to refinement level.

Boring old solvers were adequate to provide approximate solutions without
having to resort to precalculated tables, but times moved on and so did the
tech applications.

~~~
ajross
So... can you rephrase that into an answer explaining why this is (was) on the
front page? It's not a significant advance as I see it, but I'm willing to be
educated.

Again, the abstract _does not appear to claim a performance benefit_ , so I'd
love it if you could explain where that's coming from.

