5 ms·

I've been a full-time FEM Analyst for 15 years now. It's generally a nice article, though in my opinion paints a far rosier picture of the last couple decades t

I've been a full-time FEM Analyst for 15 years now. It's generally a nice article, though in my opinion paints a far rosier picture of the last couple decades than is warranted. Actual, practical use of FEM has been stagnate for quite some time. There have been some nice stability improvements to the numerical algorithms that make highly nonlinear problems a little easier; solvers are more optimized; and hardware is of course dramatically more capable (flash storage has been a godsend). Basically every advanced/"next generation" thing the article touts has fallen flat on its face when applied to real problems. They have some nice results on the world's simplest "laboratory" problem, but accuracy is abysmal on most real-world problems - e.g. it might give good results on a cylinder in simple tension, but fails horribly when adding bending. There's still nothing better, but looking back I'm pretty surprised I'm still basically doing things the same way I was as an Engineer 1; and not for lack of trying. I've been on countless development projects that seem promising but just won't validate in the real world. Industry focus has been far more on Verification and Validation (ASME V&V 10/20/40) which has done a lot to point out the various pitfalls and limitations. Academic research and the software vendors haven't been particularly keen to revisit the supposedly "solved" problems we're finding.

catgary 2y ago
I kind of thought Neural Operators were slotting into the some problem domains where FEM is used (based on recent work in weather modelling, cloth modelling, etc) and thought there was some sort of FEM -> NO lineage. Did I completely misunderstand that whole thing?
- angry_moose 2y ago
  Those are definitely up next in the flashy-new-thing pipeline and I'm not that up to speed on them yet. Another group within my company is evaluating them right now and the early results seems to be "not very accurate, but directionally correct and very fast" so there may be some value in non-FEM experts using them to quickly tell if A or B is a better design; but will still need a more proper analysis in more accurate tools. It's still early though and we're just starting to see the first non-research solvers hitting the market.
  - kk58 2y ago
    Very curious, we are getting good results with PiNN and operators, what's your domain?
- amelius 2y ago
  I was under the impression that the linear systems that come out of FEM methods are in some cases being solved by neural networks (or partially, e.g. as a preconditioner in an iterative scheme), but I don't know the details.
akomtu 2y ago
Could you write a blogpost-style article on how to model the shallow water wave equation on a sphere? The article would start with the simplest possible method, something that could be implemented in short C program, and would continue with a progressively more accurate and complex methods.
- neumann 2y ago
  If you are interested in this, I'd recommend following an openfoam tutorial, c++ though. You could do SWE with finite elements, but generally finite volumes would be your choice to handle any potential discontinuities and is more stable and accurate for practical problems. Here is a tutorial. https://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2010/johanPilqvist/johanPilqvistReport.pdf https://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2010/johanPi...
  - akomtu 2y ago
    I'm looking for something like this, but more advanced. The common problem with such tutorials is that they stop with the simplest geometry (square) and the simplest finite difference method. What's unclear to me is how do I model the spherical geometry without exploding the complexity of the solution. I know that a fully custom mesh with a pile of formulas for something like beltrami-laplace operator would work, but I want something more elegant than this. For a example, can I use the Fibbonacci spiral to generate a uniform spherical mesh, and then somehow compute gradients and the laplacian? I suspect that the stability of FE or FV methods is rooted in the fact that the FE functions slightly overlap, so computing the next step is a lot like using an implicit FD scheme, or better, a variation of the compact FD scheme. However I'm interested in how an adept in the field would solve this problem in practice. Again, I'm aware that there are methods of solving such systems (Jacobi, etc.), but those make the solution 10x more complex, buggier and slower.
- fastasucan 2y ago
  Interesting that this reads almost like an chatgpt prompt.
  - 2y ago
ccosm 2y ago
>Basically every advanced/"next generation" thing the article touts has fallen flat on its face when applied to real problems Even Arnold's work? FEEC seemed quite promising last time I was reading about it, but never seemed to get much traction in the wider FEM world.
digdugdirk 2y ago
I'm a mechanical engineer, and I've been wanting to better understand the computational side of the tools I use every day. Do you have any recommendations for learning resources if one wanted to "relearn" FEA from a computer science perspective?
- piuantiderp 2y ago
  Start with FDM. Solve Bernoulli deflection of a beam
- physicsguy 2y ago
  Have a look at FEniCs to start with.
- albrewer 2y ago
  I learned it for the first time from this[0] course; part of the course covers deal.ii[1] where you program the stuff you're learning in C++. [0]: https://open.umich.edu/find/open-educational-resources/engineering/introduction-finite-element-methods https://open.umich.edu/find/open-educational-resources/engin... [1]: https://www.dealii.org/ https://www.dealii.org/
the5avage 2y ago
Have you heard of physics informed neural nets? It seems like a hot candidate to potentially yield better results in the future
MakerSam 2y ago
stagnate last 15 years??? Contact elements, bolt preload, modeling individual composite fibers, delamination progressive ply failure, modeling layers of material to a few thousandths of an inch. Design optimization. ANSYS Workbench = FEA For Dummies. The list goes on.

catgary 2y ago

I kind of thought Neural Operators were slotting into the some problem domains where FEM is used (based on recent work in weather modelling, cloth modelling, etc) and thought there was some sort of FEM -> NO lineage. Did I completely misunderstand that whole thing?

angry_moose 2y ago
Those are definitely up next in the flashy-new-thing pipeline and I'm not that up to speed on them yet. Another group within my company is evaluating them right now and the early results seems to be "not very accurate, but directionally correct and very fast" so there may be some value in non-FEM experts using them to quickly tell if A or B is a better design; but will still need a more proper analysis in more accurate tools. It's still early though and we're just starting to see the first non-research solvers hitting the market.
- kk58 2y ago
  Very curious, we are getting good results with PiNN and operators, what's your domain?
amelius 2y ago
I was under the impression that the linear systems that come out of FEM methods are in some cases being solved by neural networks (or partially, e.g. as a preconditioner in an iterative scheme), but I don't know the details.

akomtu 2y ago

Could you write a blogpost-style article on how to model the shallow water wave equation on a sphere? The article would start with the simplest possible method, something that could be implemented in short C program, and would continue with a progressively more accurate and complex methods.

neumann 2y ago
If you are interested in this, I'd recommend following an openfoam tutorial, c++ though. You could do SWE with finite elements, but generally finite volumes would be your choice to handle any potential discontinuities and is more stable and accurate for practical problems. Here is a tutorial. https://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2010/johanPilqvist/johanPilqvistReport.pdf https://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2010/johanPi...
- akomtu 2y ago
  I'm looking for something like this, but more advanced. The common problem with such tutorials is that they stop with the simplest geometry (square) and the simplest finite difference method. What's unclear to me is how do I model the spherical geometry without exploding the complexity of the solution. I know that a fully custom mesh with a pile of formulas for something like beltrami-laplace operator would work, but I want something more elegant than this. For a example, can I use the Fibbonacci spiral to generate a uniform spherical mesh, and then somehow compute gradients and the laplacian? I suspect that the stability of FE or FV methods is rooted in the fact that the FE functions slightly overlap, so computing the next step is a lot like using an implicit FD scheme, or better, a variation of the compact FD scheme. However I'm interested in how an adept in the field would solve this problem in practice. Again, I'm aware that there are methods of solving such systems (Jacobi, etc.), but those make the solution 10x more complex, buggier and slower.
fastasucan 2y ago
Interesting that this reads almost like an chatgpt prompt.
- 2y ago

ccosm 2y ago

>Basically every advanced/"next generation" thing the article touts has fallen flat on its face when applied to real problems Even Arnold's work? FEEC seemed quite promising last time I was reading about it, but never seemed to get much traction in the wider FEM world.

digdugdirk 2y ago

I'm a mechanical engineer, and I've been wanting to better understand the computational side of the tools I use every day. Do you have any recommendations for learning resources if one wanted to "relearn" FEA from a computer science perspective?

piuantiderp 2y ago
Start with FDM. Solve Bernoulli deflection of a beam
physicsguy 2y ago
Have a look at FEniCs to start with.
albrewer 2y ago
I learned it for the first time from this[0] course; part of the course covers deal.ii[1] where you program the stuff you're learning in C++. [0]: https://open.umich.edu/find/open-educational-resources/engineering/introduction-finite-element-methods https://open.umich.edu/find/open-educational-resources/engin... [1]: https://www.dealii.org/ https://www.dealii.org/

the5avage 2y ago

Have you heard of physics informed neural nets? It seems like a hot candidate to potentially yield better results in the future

MakerSam 2y ago

stagnate last 15 years??? Contact elements, bolt preload, modeling individual composite fibers, delamination progressive ply failure, modeling layers of material to a few thousandths of an inch. Design optimization. ANSYS Workbench = FEA For Dummies. The list goes on.