[HN Gopher] Eighty Years of the Finite Element Method (2022)
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Eighty Years of the Finite Element Method (2022)
Author : sandwichsphinx
Score : 188 points
Date : 2024-11-02 19:23 UTC (1 days ago)
(HTM) web link (link.springer.com)
(TXT) w3m dump (link.springer.com)
| pvg wrote:
| A 45 comment thread at the time
| https://news.ycombinator.com/item?id=33480799
| weinzierl wrote:
| I started my career doing FE modeling and analysis with ANSYS and
| NASTRAN. Sometimes I miss these days. Thinking about how to
| simplify a real world problem so far that it is solvable with the
| computational means available was always fun. Then pushing quads
| around for hours until the mesh was good had an almost meditative
| effect. But I don't feel overwhelmingly eager to learn a new
| software or language.
|
| Much to my surprise, it seems there hasn't been much movement
| there. ANSYS still seems to be the leader for general simulation
| and multi-physics. NASTRAN still popular. Still no viable open-
| source solution.
|
| The only new player seems to be COMSOL. Has anyone experience
| with it? Would it be worth a try for someone who knows ANSYS and
| NASTRAN well?
| kayo_20211030 wrote:
| As a recovering fe modeler, I understand completely.
| magicalhippo wrote:
| > Still no viable open-source solution.
|
| For the more low-level stuff there's the FEniCS project[1], for
| solving PDEs using fairly straight forward Python code like
| this[2]. When I say fairly straight forward, I mean it follows
| the math pretty closely, it's not exactly high-school level
| stuff.
|
| [1]: https://fenicsproject.org/
|
| [2]: https://jsdokken.com/dolfinx-
| tutorial/chapter2/linearelastic...
| lll-o-lll wrote:
| Interesting. Please bear with me as this is going off 25 year
| old memories, but my memory is that the workflow for using
| FEA tools was: Model in some 3D modelling engineering tool
| (e.g. SolidWorks), ansys to run FEA, iterate if needed,
| prototype, iterate.
|
| So to have anything useful, you need that entire pipeline?
| For hobbyists, I assume we need this stack. What are the
| popular modelling tools?
| magicalhippo wrote:
| Yeah not my domain so wouldn't really know. For FEniCS I
| know Gmsh[1] was used. There's some work[2][3] been done to
| integrate FEniCS with FreeCAD. It seems FreeCAD also
| supports[4] other FEM solvers.
|
| But, I guess you get what you pay for in this space still.
|
| [1]: https://gmsh.info/
|
| [2]: https://github.com/qingfengxia/Cfd
|
| [3]: https://github.com/qingfengxia/FenicsSolver
|
| [3]: https://wiki.freecad.org/FEM_Solver
| physicsguy wrote:
| You can export other CAD meshes for use in it
| fn-mote wrote:
| > For hobbyists, I assume we need this stack.
|
| Just curious what kind of hobby leads to a finite element
| analysis?
| kragen wrote:
| Electronics (when you start to care about EMI or antenna
| design), model airplanes (for aerodynamics), rocketry,
| machining (especially if you want to get into SPIF),
| robotics, 3-D printing (especially for topology
| optimization), basically anything that deals with
| designing solid structures in the physical world. Also,
| computer graphics, including video games.
|
| Unfortunately the barrier to entry is too high for most
| hobbyists in these fields to use FEM right now.
| nativeit wrote:
| There are some obvious downsides and exceptions to this
| sentiment, but on balance, I really appreciate how the
| expansive access to information via the internet has
| fostered this phenomenon: where an unremarkable fella
| with a dusty media studies degree, a well-equipped
| garage, and probably too much free time can engineer and
| construct robotic machines, implement/tweak machine
| vision mechanisms, microwave radio transceivers,
| nanometer-scale measurements using laser diodes and
| optical interferometry, deep-sky astrophotography, etc.,
| etc.. Of course, with burgeoning curiosity and expanding
| access to surplus university science lab equipment, comes
| armchair experts and the potential for
| insufferability[0]. It's crucial to maintain perspective
| and be mindful of just how little any one person
| (especially a person with a media studies degree) can
| possibly know.
|
| [0] I'm pretty sure "insufferability" isn't a real word.
| [ _Edit: don't use an asterisk for footnotes._ ]
| kragen wrote:
| > _comes armchair experts and the potential for
| insufferability_
|
| Hey, I resemble that remark! I'd be maybe a little less
| armchair with more surplus equipment access, but maybe no
| less insufferable.
|
| By all accounts, though, a degree of insufferability is
| no bar to doing worthwhile work; Socrates, Galileo,
| Newton, Babbage, and Heaviside were all apparently quite
| insufferable, perhaps as much so as that homeless guy who
| yells at you about adrenochrome when you walk by his park
| encampment. (Don't fall into the trap of thinking it's an
| advantage, though.) Getting sidetracked by trivialities
| and delusions is a greater risk. Most people spend their
| whole lives on it.
|
| As for how little any person can know, you can certainly
| know more than anyone who lived a century ago: more than
| Einstein, more than Edison, more than Noether, more than
| Tesla, more than Gauss. Any one of the hobbies you named
| will put you in contact with information they never had,
| and you can draw on a century or more of academic
| literature they didn't have, thanks to Libgen and Sci-Hub
| (and thus Bitcoin).
|
| And it's easy to know more than an average doctorate
| holder; all you have to do is study, but not forget
| everything you study the way university students do, and
| not fall into traps like ancient aliens and the like. I
| mean, you can still do good work if you believe in
| ancient aliens (Newton and Tesla certainly believed
| dumber things) but probably not good archeological work.
|
| Don't be discouraged by prejudice against autodidacts.
| Lagrange, Heaviside, and du Chatelet were autodidacts,
| and Ptolemy seems to have been as well. And they didn't
| even have Wikipedia or Debian! Nobody gets a Nobel for
| passing a lot of exams.
| jasomill wrote:
| IMO, the mathematics underlying finite element methods
| and related subjects -- finite element exterior calculus
| comes immediately to mind -- are interesting enough to
| constitute a hobby in their own right.
| bauta-steen wrote:
| To get started with Fenics you can maybe use the FEATool
| GUI, which makes it easier to set up FEA models, and also
| export Python simulation scripts to learn or modify the
| Fenics syntax [1].
|
| [1]: https://www.featool.com/tutorial/2017/06/16/Python-
| Multiphys...
| physicsguy wrote:
| FEniCs is mostly used by academic researchers, I used it
| for FEM modelling in magnetic for e.g. where the sorts of
| problems we wanted to solve you can't do in a commercial
| package.
| hhoorzad wrote:
| Abaqus is pretty big too. I've worked with both Ansys and
| Abaqus and I generally prefer the latter.
| navane wrote:
| I've used ansys daily for over a decade, and the only movement
| is in how they name their license tiers. It's a slow muddy
| death march. Every year I'm fighting the software more and
| more, the sales men are clearly at the wheel.
|
| They buy "vertical aligned" software, integrate it, then slowly
| let it die. They just announced they're killing off one of
| these next year, that they bought ten years ago, because they
| want to push a competitive product with 20% of the features.
|
| I've been using nastran for half as long but it isn't much
| better. It's all sales.
|
| I dabbed a bit in abaqus, that seems nice. Probably cause I
| just dabbed in it.
|
| But here I'm just trying to do my work, and all these companies
| do is move capabilities around their license tiers and boil the
| frog as fast as they get away with.
| angry_moose wrote:
| I've gone Abaqus > Ansys > Abaqus/LS-DYNA over my career and
| hate Ansys with a fiery passion. It's the easiest one to run
| your first model in, but when you start applying it to real
| problems its a fully adversarial relationship. The fact you
| have to make a complete copy of the geometry/mesh to a new
| Workbench "block" to run a slightly different load case (and
| you can't read in an orphaned results files) is just
| horrible.
|
| Abaqus is more difficult to get up to speed in, but its
| really nice from an advanced usability standpoint. They
| struggle due to cost though, it is hugely expensive and we've
| had to fight hard to keep it time and time again.
|
| LS-Dyna is similar to Abaqus (though I'm not fully up in it
| yet), but we're all just waiting to see how Ansys ruins it,
| especially now that they got bought out by Synopsys.
| navane wrote:
| I don't know how long ago you used ansys, and i definitely
| don't want to sell it, but you can share geometry/mesh
| between those "blocks" (by dragging blocks on top of each
| other), and you can read in result orphaned result files.
| angry_moose wrote:
| COMSOL's big advantage is it ties together _a lot_ of different
| physics regimes together and makes it very easy to couple
| different physics together. Want to do coupled structures
| /fluid? Or coupled electromagnetism/mechanical? Its probably
| the easiest one to use.
|
| Each individual physics regime is not particularly good on its
| own - there are far better mechanical, CFD, electromagnetism,
| etc solvers out there - but they're all made by different
| vendors and don't play nicely with each other.
| littlestymaar wrote:
| > The only new player seems to be COMSOL
|
| Ouch. I kind of know Comsol because it was already taught in my
| engineering school 15 years ago, so that it still counts as a
| "new entrant" really gives an idea of how slow the field
| evolves.
| petters wrote:
| The COMSOL company was started in 1986....
| arnejenssen wrote:
| It used to be called FEMLAB :)
|
| But they changed to COMSOL because they didn't have the
| trademark in Japan and FEM also gave associations to the
| feminine gender.
| master_crab wrote:
| _Still no viable open-source solution._
|
| Wait? What? NASTRAN was originally developed by NASA and open
| sourced over two decades ago. Is this commercial software built
| on top that is closed source?
|
| I'm astonished ANSYS and NASTRAN are still the only players in
| town. I remember using NASTRAN 20 years ago for FE of
| structures while doing aero engineering. And even then NASTRAN
| was almost 40 years old and ancient.
| formerly_proven wrote:
| There's a bunch of open source fem solvers e.g. Calculix,
| Code_Aster, OpenRadioss and probably a few unmaintained forks
| of (NASA) NASTRAN, but there's no multiphysics package I
| don't think.
| bobim wrote:
| These are at least capable of thermomechanical with fluid-
| structure coupling. Not all-physics but still multi. True
| that things with multi species diffusion or
| electromagnetics are missing, but maybe Elmer can fill the
| gap.
| MengerSponge wrote:
| Once you have a mesh that's "good enough", you can use any
| number of numeric solvers. COMSOL has a very good mesher, and a
| competent geometry editor. It's scriptable, and their solvers
| are also very good.
|
| There might be better programs for some problems, but COMSOL is
| quite nice.
| foxglacier wrote:
| I work in this field and it really is stagnant and dominated by
| high-priced Ansys/etc. For some reason silicon valley's open
| sourceness hasn't touched it. For open source, there's CalculiX
| which is full of bugs and Code Aster which everybody I've heard
| about it from say it's too confusing to use. CalculiX has
| Prepomax as a fairly new and popular pre/post.
| drpossum wrote:
| I've worked with COMSOL (I have a smaller amount of ANSYS
| experience to compare to). For the most part I preferred
| COMSOL's UI and workflow and leveraged a lot of COMSOL's
| scripting capabilities which was handy for a big but procedural
| geometry I had (I don't know ANSYS's capabilities for that).
| They of course largely do the same stuff. If you have easy
| access to COMSOL to try it out I'd recommend it just for the
| experience. I've found sometimes working with other tools make
| me recognize some capabilities or technique that hadn't clicked
| for me yet.
| karencarits wrote:
| OpenFOAM seems like an opensource option but I have found it
| rather impenetrable - there are some youtube videos and pdf
| tutorials, but they are quite dense and specific and doens't
| seem to cover the entire pipeline
|
| Happy to hear if people have good resources!
| goodtruck wrote:
| I am hoping this open source FEM library will catch on :
| https://www.dealii.org/. The deal in deal.II stands for
| Differential Equation Analysis Library.
|
| It's written in C++, makes heavy use of templates and been in
| development since 2000. It's not meant for solid mechanics or
| fluid mechanics specifically, but for FEM solutions of general
| PDEs.
|
| The documentation is vast, the examples are numerous and the
| library interfaces with other libraries like Petsc, Trilinos
| etc. You can output results to a variety of formats.
|
| I believe support for triangle and tetrahedral elements has
| been added only recently. In spite of this, one quirk of the
| library is that meshes are called "triangulations".
| class3shock wrote:
| Abaqus is up there with Ansys aswell as others have mentioned.
| greesil wrote:
| I took a course in undergrad, and was exposed to it in grad
| school again, and for the life of me I still don't understand the
| derivations either Galerkin or variational.
| faustlast wrote:
| I learned from the structural engineering perspective. What are
| you struggling with? In my mind I have this logic flow: 1.
| strong form pde; 2. weak form; 3. discretized weak form; 4.
| compute integrals (numerically) over each element; 5. assemble
| the linear system; 6. solve the linear system.
| foxglacier wrote:
| Luckily the integrals of step 4 are already worked out in
| text books and research papers for all the problems people
| commonly use FEA for so you can almost always skip 1. 2. and
| 3.
| sashank_1509 wrote:
| My hot take is that, FEM is best used as unit testing of Machine
| Design, not a guide towards design that it's often used as. The
| greatest mechanical engineer I know, once designed an entire
| mechanical wrist arm with five fingers, actuations, lots of parts
| and flexible finger tendon. He never used FEM at any part of his
| design. He instead did it in the old fashioned, design and fab a
| simple prototype, get a feel for it, use the tolerances you
| discovered in the next prototype and just keep iterating quickly.
| If I went to him and told him to model the flexor of his fingers
| in FEM, and then gave him a book to tell him how to correctly use
| the FEM software so that you got non "non-sensical" results I
| would have slowed him down if anything. Just build and you learn
| the tolerances, and the skill is in building many cheap
| prototypes to get the best idea of what the final expensive build
| will look like.
| eru wrote:
| > The greatest mechanical engineer I know, [...]
|
| And with that you wrote the best reply to your own comment.
| Great programmers of the past wrote amazing systems just in
| assembly. But you needed to be a great programmer just to get
| anything done at all.
|
| Nowadays dunces like me can write reasonable software in high
| level languages with plenty of libraries. That's progress.
|
| Similar for mechanical engineering.
|
| (Doing prototypes etc might still be a good idea, of course. My
| argument is mainly that what works for the best engineers
| doesn't necessarily work for the masses.)
| navane wrote:
| Also, might work for a mechanical arm the size of an arm, but
| not for the size of the Eiffel tower.
| sashank_1509 wrote:
| Eiffel Tower was built before FEM existed. In fact I doubt
| they even did FEM like calculations
| navane wrote:
| I ment a mechanical arm the size of the eifel tower. You
| don't want to iterate physical products at that size.
| kragen wrote:
| Going by Boeing vs. SpaceX, iteration seems to be the
| most effective approach to building robotic physical
| products the size of the Eiffel Tower.
| eru wrote:
| I'm sure they are doing plenty of calculations
| beforehand, too.
| kragen wrote:
| Unquestionably! Using FEM.
| mitthrowaway2 wrote:
| This is true, although it was notable as an early
| application of Euler-Bernoulli beam theory in structural
| engineering, which helped to prove the usefulness of that
| method.
| fluorinerocket wrote:
| Would FEM be useful for that kind problem? It's more for
| figuring out if your structure will take the load, where stress
| concentrations are, what happens with thermal expansion. FEM
| won't do much for figuring out what the tolerance need to be on
| intricate mechanisms
| NathanaelRea wrote:
| Garbage in garbage out. If you don't fully understand the
| model, then small parameter changes can create wildly different
| results. It's always good to go back to fundamentals and hand
| check a simplification to get a feel for how it should behave.
| antegamisou wrote:
| Good luck designing crash resilient structures without
| simulating it on FEM based software though.
| tightbookkeeper wrote:
| They did this just fine until without such tools for the
| majority of innovation in the last century.
| antegamisou wrote:
| Except that everything's gotten abysmally complex. Vehicle
| crash test experiments are a good example of validating the
| FEM simulation (yes that's the correct order, not vice
| versa)
| tightbookkeeper wrote:
| How can you assert so confidently you know the cause and
| effect?
|
| Certainly computers allow more complexity, so there is
| interplay between what it enables and what's driven by
| good engineering.
| drpossum wrote:
| Having worked on the design of safety structures with
| mechanical engineers for a few projects, it is far, far
| cheaper to do a simulation and iterate over designs and
| situations than do that in a lab or work it out by hand.
| The type of stuff you can do on paper without FEM tends to
| be significantly oversimplified.
|
| It doesn't replace things like actual tests, but it makes
| designing and understanding testing more efficient and more
| effective. It is also much easier to convince reviewers
| you've done your job correctly with them.
|
| I'd argue computer simulation has been an important
| component a majority of mechanical engineering innovation
| in the last century. If you asked a mechanical engineer to
| ignore those tools in their job they'd (rightly) throw a
| fit. We did "just fine" without cars for the majority of
| humanity, but motorized vehicles significantly changed how
| we do things and changed the reach of what we can do.
| tightbookkeeper wrote:
| > It is also much easier to convince reviewers you've
| done your job correctly with them.
|
| In other words, the work that doesn't change the
| underlying reality of the product?
|
| > We did "just fine" without cars for the majority of
| humanity
|
| We went to the moon, invented aircraft, bridges,
| skyscrapers, etc, all without FEM. So that's why this is
| a bad comparison.
|
| > If you asked a mechanical engineer to ignore those
| tools in their job they'd (rightly) throw a fit.
|
| Of course. That's what they are accustomed to. 80/20
| paper techniques that were replaced by SW were forgotten.
|
| When tests are cheap, you make a lot of them. When they
| are expensive, you do a few and maximize the information
| you learn from them.
|
| I'm not arguing FEM doesn't provide net benefit to the
| industry.
| V_Terranova_Jr wrote:
| What is your actual assertion? That tools like FEA are
| needless frippery or that they just dumb down
| practitioners who could have otherwise accomplished the
| same things with hand methods? Something else? You're
| replying to a practicing mechanical engineer whose
| experience rings true to this aerospace engineer.
|
| Things like modern automotive structural safety or
| passenger aircraft safety are leagues better because
| engineers can perform many high-fidelity simulations long
| before they get to integrated system test.
|
| The argument that computational tools are eroding deep
| engineering understanding is long-standing,and has
| aspects of both truth and falsity. Yep, they designed the
| SR-71 without FEA, but you would never do that today
| because for the same budget, we'd expect a lot more out
| of the design. Tools like FEA are what help engineers
| fulfill those expectations.
| sashank_1509 wrote:
| I'd guess most of the bridges in US were built before FEM
| existed
| double0jimb0 wrote:
| FEM runs on the same math and theories those bridges were
| designed on on paper.
| meindnoch wrote:
| Anyone can design a bridge that holds up. Romans did it
| millenia ago.
|
| Engineering is designing a bridge that holds up to a
| certain load, with the least amount of material and/or
| cost. FEM gives you tighter bounds on that.
| drpossum wrote:
| The average age of a bridge in the US is about 40-50 years
| old and the title of the article has "80 years of FEM".
|
| https://www.infrastructurereportcard.org/wp-
| content/uploads/...
|
| I'd posit a large fraction were _designed_ with FEM.
| somat wrote:
| The FEM is just a model of the crash resistant structure.
| Hopefully it will behave like the actual structure, but that
| is not guaranteed. We use the FEM because it is faster and
| cheaper than doing the tests on the actual thing. However if
| you have the time and money to do your crash resiliency tests
| on the actual product during the development phase. I expect
| the results would be much better.
| formerly_proven wrote:
| Yes, with infinite time and budget you'd get much better
| results. That does not sound like an interesting
| proposition, though.
| angry_moose wrote:
| To be fair, FEM is not the right tool for mechanical linkage
| design (if anything, you'd use rigid body dynamics).
|
| FEM is the tool you'd use to tell when and where the mechanical
| linkage assembly will break.
| amelius wrote:
| If he were designing a bridge, however ...
| fastasucan wrote:
| Its wrong to assume that everyone and every projects can use an
| iterative method with endless prototypes. Id you do I have a
| prototype bridge to sell you.
| kaonwarb wrote:
| I also studied FEM in undergrad and grad school. There's
| something very satisfying about breaking an intractably difficult
| real-world problem up into finite chunks of simplified, simulated
| reality and getting a useful, albeit explicitly imperfect, answer
| out of the other end. I find myself thinking about this approach
| often.
| angry_moose wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Very curious, we are getting good results with PiNN and
| operators, what's your domain?
| amelius wrote:
| 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 wrote:
| 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 wrote:
| 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/johanPi...
| akomtu wrote:
| 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 wrote:
| Interesting that this reads almost like an chatgpt prompt.
| gwern wrote:
| Lazy people have been lazy forever. I stumbled across an
| example of this the other day from the 1990s, I think, and
| was shocked how much the student emails sounded like LLM
| prompts: https://www.chiark.greenend.org.uk/~martinh/poems/
| questions....
| MichaelZuo wrote:
| It reminds me of the old joke that half of the students
| are below average...
| wombatpm wrote:
| Expect in Lake Woebegone, all of the children are above
| average
| meindnoch wrote:
| But that's not true, unless by "average" you mean the
| median.
| KeplerBoy wrote:
| Normally, it's all the same.
| meindnoch wrote:
| Only if the distribution has zero skewness.
|
| Unless "normally" you mean the normal distribution, which
| indeed has zero skewness.
| KeplerBoy wrote:
| Yes, it was a admittedly bad pun.
| pixelpoet wrote:
| At least those had some basic politeness. So often I'm
| blown away not only how people blithely write "I NEED
| HELP, GIMME XYZ NOW NERDS" but especially how everyone is
| just falling over themselves to actually help! WTF?
|
| Basic politeness is absolutely dead, nobody has any
| concept of acknowledging they are asking for a favour; we
| just blast Instagram/TikTok reels at top volume and smoke
| next to children and elderly in packed public spaces etc.
| I'm 100% sure it's not rose-tinted memories of the 90s
| making me think, it wasn't always like this...
| CamperBob2 wrote:
| "As an AI language model, I am happy to comply with your
| request ( https://chatgpt.com/share/6727b644-b2e0-800b-b613-3
| 22072d9d3... ), but good luck finding a data set to verify
| it, LOL."
| sampo wrote:
| > Could you write a blogpost-style article on how to model
| the shallow water wave equation on a sphere?
|
| Typically, Finite Volume Method is used for fluid flow
| problems. It is possible to use Finite Element Methods, but
| it is rare.
| ccosm wrote:
| >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 wrote:
| 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 wrote:
| Start with FDM. Solve Bernoulli deflection of a beam
| physicsguy wrote:
| Have a look at FEniCs to start with.
| the5avage wrote:
| Have you heard of physics informed neural nets?
|
| It seems like a hot candidate to potentially yield better
| results in the future
| mlhpdx wrote:
| I have such a fondness for FEA. ANSYS and COSMOS were the ones I
| used, and I've written toy modelers and solvers (one for my HP
| 48g) and even tinkered with using GPUs for getting answers faster
| (back in the early 2000s).
|
| Unfortunately my experience is that FEA is a blunt instrument
| with narrow practical applications. Where it's needed, it is
| absolutely fantastic. Where it's used when it isn't needed, it's
| quite the albatross.
| cyberax wrote:
| FEM - because we can't solve PDEs!
| niraj-agarwal wrote:
| Predicting how things evolve in space-time is a fundamental need.
| Finite element methods deserve the glory of a place at the top of
| the HN list. I opted for "orthogonal collocation" as the method
| of choice for my model back in the day because it was faster and
| more fitting to the problem at hand. A couple of my fellow
| researchers did use FEM. It was all the rage in the 90s for sure.
| westurner wrote:
| From "Chaos researchers can now predict perilous points of no
| return" (2022) https://news.ycombinator.com/item?id=32862414 :
|
| > _FEM: Finite Element
| Method:https://en.wikipedia.org/wiki/Finite_element_method _
|
| >> _FEM: Finite Element Method (for ~solving coupled PDEs
| (Partial Differential Equations))_
|
| >> _FEA: Finite Element Analysis (applied FEM)_
|
| > _awesome-mecheng > Finite Element Analysis:
| https://github.com/m2n037/awesome-mecheng#fea _
|
| And also, "Learning quantum Hamiltonians at any temperature in
| polynomial time" (2024) https://arxiv.org/abs/2310.02243 re: the
| "relaxation technique" ..
| https://news.ycombinator.com/item?id=40396171
| antononcube wrote:
| During my industrial PhD, I created an Object-Oriented
| Programming (OOP) framework for Large Scale Air-Pollution (LSAP)
| simulations.
|
| The OOP framework I created was based on Petrov-Galerkin FEM.
| (Both proper 2D and "layered" 3D.)
|
| Before my PhD work, the people I worked with (worked for) used
| spectral methods and Alternate-direction FEM (i.e. using 1D to
| approximate 2D.)
|
| In some conferences and interviews certain scientists would tell
| me that programming FEM is easy (for LSAP.) I always kind of
| agree and ask how many times they have done it. (For LSAP or
| anything else.) I was not getting an answer from those
| scientists...
|
| Applying FEM to real-life problems can involve the resolving of
| quite a lot of "little" practical and theoretical gotchas, bugs,
| etc.
| chipdart wrote:
| > Applying FEM to real-life problems can involve the resolving
| of quite a lot of "little" practical and theoretical gotchas,
| bugs, etc.
|
| FEM at it's core ends up being just a technique to find
| approximate solutions to problems expressed with partial
| differential equations.
|
| Finding solutions to practical problems that meet both boundary
| conditions and domain is practically impossible to have with
| analytical methods. FEM trades off correctness with an
| approximation that can be exact in prescribed boundary
| conditions but is an approximation in both how domains are
| expressed and the solution,and has nice properties such as the
| approximation errors converging to the exact solution by
| refining the approximation. This means exponentially larger
| computational budgets.
| fngarrett wrote:
| For anyone interested in a contemporary implementation, SELF is a
| spectral element library in object-oriented fortran [1]. The devs
| here at Fluid Numerics have upcoming benchmarks on our MI300A
| system and other cool hardware.
|
| [1] https://github.com/FluidNumerics/SELF
| bgoated01 wrote:
| Interesting perspective. I just attended an academic conference
| on isogeometric analysis (IGA), which is briefly mentioned in
| this article. Tom Hughes, who is mentioned several times, is now
| the de facto leader of the IGA research community. IGA has a lot
| of potential to solve many of the pain points of FEM. It has
| better convergence rates in general, allows for better timesteps
| in explicit solvers, has better methods to ensure stability in,
| e.g., incompressible solids, and perhaps most exciting, enables
| an immersed approach, where the problem of meshing is all but
| gone as the geometry is just immersed in a background grid that
| is easy to mesh. There is still a lot to be done to drive
| adoption in industry, but this is likely the future of FEM.
| chipdart wrote:
| > IGA has a lot of potential to solve many of the pain points
| of FEM.
|
| Isn't IGA's shtick just replacing classical shape functions
| with the splines used to specify the geometry?
|
| If I recall correctly convergence rates are exactly the same,
| but the whole approach fails to realize that, other than
| boundaries, geometry and the fields of quantities of interest
| do not have the same spatial distributions.
|
| IGA has been around for ages, and never materialized beyond the
| "let's reuse the CAD functions" trick, which ends up making the
| problem more complex without any tangible return when compared
| with plain old P-refinent. What is left in terms of potential?
|
| > Tom Hughes, who is mentioned several times, is now the de
| facto leader of the IGA research community.
|
| I recall the name Tom Hughes. I have his FEM book and he's been
| for years (decades) the only one pushing the concept. The
| reason being that the whole computational mechanics community
| looked at it,found it interesting, but ultimately wasn't worth
| the trouble. There are far more interesting and promising ideas
| in FEM than using splines to build elements.
| bgoated01 wrote:
| > Isn't IGA's shtick just replacing classical shape functions
| with the splines used to specify the geometry?
|
| That's how it started, yes. The splines used to specify the
| geometry are trimmed surfaces, and IGA has expanded from
| there to the use of splines generally as the shape functions,
| as well as trimming of volumes, etc. This use of smooth
| splines as shape functions improves the accuracy per degree
| of freedom.
|
| > If I recall correctly convergence rates are exactly the
| same
|
| Okay, looks like I remembered wrong here. What we do
| definitely see is that in IGA you get the convergence rates
| of higher degrees without drastically increasing your degree
| of freedom, meaning that there is better accuracy per degree
| of freedom for any degree above 1. See for example Figures 16
| and 18 in this paper:
| https://www.researchgate.net/profile/Laurens-
| Coox/publicatio...
|
| > geometry and the fields of quantities of interest do not
| have the same spatial distributions.
|
| Using the same shape functions doesn't automatically mean
| that they will have the same spatial distributions. In fact,
| with hierarchical refinement in splines you can refine the
| geometry and any single field of interest separately.
|
| > What is left in terms of potential?
|
| The biggest potential other than higher accuracy per degree
| of freedom is perhaps trimming. In FEM, trimming your shape
| functions makes the solution unusable. In IGA, you can
| immerse your model in a "brick" of smooth spline shape
| functions, trim off the region outside, and run the
| simulation while still getting optimal convergence
| properties. This effectively means little to no meshing
| required. For a company that is readying this for use in
| industry, take a look at https://coreform.com/ (disclosure, I
| used to be a software developer there).
| Iwan-Zotow wrote:
| Is it related to Galerkin?
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