Talk:Finite element method: Difference between revisions

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As you can see from my user name, I teach PDE's online, in many flavors. The comments on this talk page range from complimentary to outright hostile regarding the complexity level and quality of this article, lots of emotion about math, wow. Since I teach both undergrads and graduate engineers, let me suggest a solution for folks finding this too much or too tough: 1. Schaum's Outline of Finite Element Analysis is a great starting point for those who get lost at a beginning stage. Although FEA is a simple reductionist framework, implementation can involve hundreds of thousands of PDEs, some of which we run on supercomputers, and proofs and derivations are tough. 2. Once you get beyond the basics of proofs and the math, you'll be into algorithms immediately. Dover's 700 page book (The Finite Element Method) for $30 US is a great "next step" -- it is by Thomas J.R. Hughes, and goes from basics to advanced algorithm design (my field). It, however, is grad level and requires facility in PDEs and LP as a background. This is all to help frustrated Wiki editors and visitors, but to stay true to the talk page intent, I'd also like to humbly suggest that a section on algorithms might be warranted. I'd write it, but given the comments here, want to be sure there is at least some consensus that it is worth it. My reasoning is that although the proofs and derivations can get very difficult, the algorithmic designs are simple and elegant in many cases, and just crunch away at those PDEs! Frankly, this is more the reality today in practical solutions with Autocad, matlab, julia and even haskell, and users often don't have to know the full polygon story running beneath. In fact, many current interfaces allow you to drag and drop splines and beziers, OR write your own code in a little drop down command prompt box, OR do both! I would also like to thank the many contributors to this article, because, regardless of your opinion or feelings, it IS a lot of work! [[User:Pdecalculus|Pdecalculus]] ([[User talk:Pdecalculus|talk]]) 14:57, 30 March 2016 (UTC)
 
== FEM and FEA -- not exactly synonyms ==
 
I'm noticing that Finite Element Method and Finite Element Analysis are treated a synonyms in the introduction chapter. Though, "method" and "analysis" don't sound like the same thing to me at all. The way I have learned to understand it, FEM means the way calculations are done to perform FEA.
 
FEA is the larger context that includes first setting up a model of a practical case, then computing the numbers and finally interpretting the results of into events in the real world (often with recommendations of action).
 
FEM only means the technical part, essentially chopping the original problem into simpler parts whose behavior is "known" and constructing the bigger picture based on the interaction of all the simple elements. That alone is not yet an analysis.
 
The reason I wish to point this out is, that even very skilled and experienced people, who use these terms, some times seem unsure of, which to use and why, especially if they are not exactly in the business themselves -- say managing larger development projects, but with their background on a different field of technology. (Saw that happen just today ... again.)
 
A typical FEA, for example in the case of structural analysis may contain several runs in FEM, with different load cases and alternative structural or material build-ups. The results may contain information on mechanical durability, stability, response to vibration ... and for example a recommendation of a materials set to use.
 
So, if everybody agrees, that FEM and FEA are not synonyms, I'd be happy if somebody could take the effort of fitting a short explanation in the beginning of the introduction without breaking, what already is in there. :)
 
[[User:Peteihis|Peteihis]] ([[User talk:Peteihis|talk]]) 20:02, 21 May 2018 (UTC)