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A Unified Finite Strain Theory for Membranes and Ropes (arxiv.org)
41 points by sel1 22 days ago | hide | past | web | favorite | 5 comments

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.

>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.

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?

> 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.

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.

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