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Eighty Years of the Finite Element Method

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Re: Eighty Years of the Finite Element Method

#41

Post by adrian_b »

perilunar wrote: post #39
hydrogen7800 wrote: post #32

Earlier quoted context omitted.

I once read or heard a similar anecdote about Ludwig Prandtl who set up computation method using a room full of people each doing one step of a calculation. I recall it describing a finite element method, but that would predate the origin of FEM in this article by a few decades. Maybe it was just some numerical method.

Huh? Theres's a long history of doing this — 'computers' were people long before they are machines.

Yes, indeed. My father's first job was as a "computer" at an astronomical observatory (in the fifties of the 20th century, when vacuum tube computers had just started to appear, but they had astronomical prices, so they were out of reach for an astronomical observatory).

Re: Eighty Years of the Finite Element Method

#42

Post by geysersam »

halffaday wrote: post #29
geysersam wrote: post #28

Earlier quoted context omitted.

It's probably impossible to accurately simulate the climate of the planet decades into the future. That does not meaningfully detract from the evidence for human caused global warming however.

I have to applaud the subtle elegance of the sarcasm here

No sarcasm intended. The science of climate change rests on many legs. It was already established long before massive models on the scale we have today were possible. Computer simulations attempts to understand how it will affect us, but does not contribute much evidence.

Re: Eighty Years of the Finite Element Method

#43

Post by bluenose69 »

badpun wrote: post #19
kqr wrote: post #12

Earlier quoted context omitted.

For physical processes, you can sometimes lean on conservation laws. Financial, no-arbitrage "laws". Sometimes it can help to run two different models, or different numerical methods, and compare their results. More generally, it's very, very hard. I am fairly sure there are multiple published results in computational fluid dynamics that are subtly wrong.

> I am fairly sure there are multiple published results in computational fluid dynamics that are subtly wrong. I wonder what that means for the accuraccy of the climate models...

All manner of tests are done in fluid-dynamical modelling. Test suites are developed along with models. Simulations are done with a range of alternative models, or individual models with different conditions are applied, and the differences between the simulations are studied in detail. Models must rely on a fairly large set of parameterizations of processes that cannot be resolved directly, and tests are done to see which parameterizations make the most sense.

Models stem from the academic environment, not the business environment. This means that the models are open-source, so everyone can see what everyone else is doing. And 'everyone' is a pretty large set.

Note that there is no commercial element to any of this, which means there is no incentive to hide problems. It's the reverse: reputation is earned by finding problems, not by hiding them.

A large part of the challenge of climate modelling is the leveraging of increasing computer power to resolve progressively smaller scales of motion, and this uncovers the need to understand those scales in isolation. Modelling is often used at this level also.

None of this is to say that climate models are perfect. They obviously are not. But the system of academic science is very good at improving models and, importantly, exposing their limits. An indication of the latter is the pairing of uncertainties with predictions: a hallmark of this scientific community.

Re: Eighty Years of the Finite Element Method

#44

Post by hydrogen7800 »

perilunar wrote: post #39
hydrogen7800 wrote: post #32

Earlier quoted context omitted.

I once read or heard a similar anecdote about Ludwig Prandtl who set up computation method using a room full of people each doing one step of a calculation. I recall it describing a finite element method, but that would predate the origin of FEM in this article by a few decades. Maybe it was just some numerical method.

Huh? Theres's a long history of doing this — 'computers' were people long before they are machines.

I'm aware of human "computers" but my recollection was that in the case of Prandtl, it was an application FEM. I did not know FEM wasn't developed at that time, as this article shows, so it must have been something else.

Re: Eighty Years of the Finite Element Method

#45

Post by adrian_b »

hydrogen7800 wrote: post #44
perilunar wrote: post #39

Earlier quoted context omitted.

Huh? Theres's a long history of doing this — 'computers' were people long before they are machines.

I'm aware of human "computers" but my recollection was that in the case of Prandtl, it was an application FEM. I did not know FEM wasn't developed at that time, as this article shows, so it must have been something else.

As a poster above has already said, it might have been a finite difference method, because they solve the same problems.

Unlike FEM, finite difference methods have been used right since the origins of differential and integral calculus, with Newton and Leibniz.

There are also precursors of the modern FEM, like the Ritz or Galerkin methods, which could have been used by Prandtl.

Re: Eighty Years of the Finite Element Method

#46

Post by marmetio »

pclmulqdq wrote: post #34
hydrogen7800 wrote: post #32

Earlier quoted context omitted.

I once read or heard a similar anecdote about Ludwig Prandtl who set up computation method using a room full of people each doing one step of a calculation. I recall it describing a finite element method, but that would predate the origin of FEM in this article by a few decades. Maybe it was just some numerical method.

I assume it would be a finite differences calculation, which is also very easy to parallelize/vectorize. They solve the same class of problems, but calculations with finite differences don't always converge the way that finite elements do.

That's correct, it was finite difference methods. There are many variations with different properties such as whether they'll definitely converge or not.

Re: Eighty Years of the Finite Element Method

#47

Post by simplotek »

wheelinsupial wrote: post #9
icks wrote: post #8

My first programming role was on the back of work by an engineer in this article. The core of the solver was a FORTRAN implementation of a paper on p-convergence. It was really amazing seeing our software predict how a small crack in a part of an aircraft would propagate. The 3D model produced matched the photograph shared later. The lead developer (at the time) once said that the biggest software failure we can have…

I know it's not a simple answer, but how would you embed checks to flag or highlight potentially incorrect results to the user?

> I know it's not a simple answer, but how would you embed checks to flag or highlight potentially incorrect results to the user?

For starters, some problems do have analytical solutions. Yo can compare a FEM model of these problems with the known analytical solution and see if it's close enough or not. One of them is the elasto-plastic plate with a hole.

You can also run unit tests at the element level.

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