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.
Eighty Years of the Finite Element Method (2022)
61–70 of 106 posts
Re: Eighty Years of the Finite Element Method (2022)
#62Re: Eighty Years of the Finite Element Method (2022)
#63Earlier quoted context omitted.
Also, might work for a mechanical arm the size of an arm, but not for the size of the Eiffel tower.
Eiffel Tower was built before FEM existed. In fact I doubt they even did FEM like calculations
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.
Re: Eighty Years of the Finite Element Method (2022)
#64Interesting 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.
Re: Eighty Years of the Finite Element Method (2022)
#65Earlier quoted context omitted.
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....
It reminds me of the old joke that half of the students are below average…
Expect in Lake Woebegone, all of the children are above average
Re: Eighty Years of the Finite Element Method (2022)
#66I'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…
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?
Start with FDM. Solve Bernoulli deflection of a beam
Re: Eighty Years of the Finite Element Method (2022)
#67Interesting 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 method…
> 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.
Re: Eighty Years of the Finite Element Method (2022)
#68During 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 scie…
> 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.
Re: Eighty Years of the Finite Element Method (2022)
#69Earlier quoted context omitted.
I ment a mechanical arm the size of the eifel tower. You don't want to iterate physical products at that size.
Going by Boeing vs. SpaceX, iteration seems to be the most effective approach to building robotic physical products the size of the Eiffel Tower.
I'm sure they are doing plenty of calculations beforehand, too.
Re: Eighty Years of the Finite Element Method (2022)
#70Earlier quoted context omitted.
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.
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.
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.