Finite element method - Gilbert Strang
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- เผยแพร่เมื่อ 22 ธ.ค. 2013
- Mathematician Gilbert Strang from MIT on the history of the finite element method, collaborative work of engineers and mathematicians, and the challenges in applying this method to fluid and gas problems.
Read the text version here: serious-science.org/finite-el...
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Thank you Dr. Gilbert, I got so much from your books, your courses, and your mind. I see and get the beauty of the math almost the first time in my life. I don't mean that my previous teachers are not good, just maybe I met you at right time and right place. You bring me to touch the soul of math. You change me so much.
The best teacher ever,.... always want to hear from him.
lol no
In solid mechanics the finite element method (FEM) is widely used because the equations are dominated by elliptic equations. Fluid mechanics problems tend to be dominated by convection and diffusion and are thus hyperbolic or parabolic equations. FEM, Finite Volume Method (FVM) and Finite Differences Method (FDM) have all been used in fluid mechanics but FEM only shares a small portion of the solutions.
Both FEM and FVM are types of weighted residual methods and can be numerically identical but the simplified versions of FEM, typically used in common solid mechanics, impose a symmetry on the fluid problem that produces lots of problems. That is the resason why, in my humble opinion, we use FEM widely in solid mechanics while we almost never use it in fluid mechanics and gas dynamics.
It has been a pleasure to listen and learn from Professor Strang.
That was informative , thank you :)
thanks
Nicely summarized.
That is not true. Dynamic problems are dominated by hyperbolic equations, i.e. wave equation
There are lots of ways to use FEM in stuff that is dynamic. It is used on heat (laws of thermodynamic), on air (aerodynamic), on fuilds (fluid mechanics) and on electric flow. FEM is based on differential equations wich can be applied on anything.
Pleasure to listen and learn from Prof. Strang.
Grazie.
Thanks for feedback. Much more interesting to come! We are on hold for a while, but we will continue very soon.
SeriousScience Awesome videos
He is a real teacher in all sense. I hope I could be a student in his classes. I have attended so many classes through youtube and I feel I was really his student. I hope I had met him once..
Thanks for sharing. I love listening to Prof. Strang: it is a pleasure to see that he genuinely tries to allow his audience to follow along. This is a rare quality in a mathematician.
First came across this about 25 years ago, modelling plastic flow where we had to consider pressure, temperature, viscosity, etc. I was working on the graphics engine and UI, but the FE part was really interesting. The part was cut into a triangular net, quite course for simple planes and then fine where there were variations (for example holes or changes in thickness) - this was to reduce the size of the data set to a manageable level. Even so, while the finite element equations were written in Fortran, we had to use a special C compiler to handle the array sizes. The Apricot 486 had just come out and was a big jump forward.
If anyone is majoring in maths or computing and thinking what they could do with it, this field is worth taking the time to look into - very interesting and diverse applications. And the theory is still developing.
Out if curiosity, what's the real life application of plastic flow? Something to do with manufacturing?
@@thetedmang injection molding maybe.
Very interesting to learn from such a knowledgeable person.
I like the mathematician within him...Just greatly amazing, this man!
what a knowledge and what a way to explain things, simply awesome
Couldn't expect a better understanding of FEM, thank you!
A very interesting video. I teach Theory of Structures and, at the end of the course, I always show this video to provide my students a critical and enthusiastic vision of the finite element method, which is an extremely powerful tool that every engineer working with structures must use in their everyday life. Thank you very much for sharing.
Love to hear his voice again. Learned 18.06 from mit ocw almost 10 years ago.
John Gabriel No, I'm not interested in listening to you.
Ahahaha!
Great. Thanks for sharing and thanks to professor Gilbert Strang for the great lecture. Thanks
My Idol! My online teacher! So respectful!
Many thanks
Iam absolutely impressed
Deepest understanding
Great! what a nice explanaition of FEM. As fantastic as his linear algebra lectures! Thank for the video Serious Science
Respect for this man!
one of the best lecture about how finite element have evolved over the years
Absolutely wonderful. Thank you for sharing.
I could listen to him all day honestly
Same here
@@malebitsatimbuktu3352
🖕🏻🖕🏻
The man is simply amazing
Love physic and math one again! Thank you professor!
Gilbert Strang is Awesome!
Great Video... It's a pleasure to listen Prof. Gilbert Strang ... I love all his books and lectures. What would you ask Gilbert Strang next time?
Numberphile top candidate, topic history of mathematics!!10/10 would watch that.
Prof. Strang may be one of my all time favorite professors, and yet I have never sat within a classroom with him.
So clear the speech is that I can totally understand what he said !
the best explanation to this topic. loads of love from india
Every single word coming out of the mouth of this wise man is like a book well written
+John Gabriel screw you
+John Gabriel What you think of him doesn't really matter. You are insignificant.
All your work is irrelevant.They do not and will not ever contribute anything worthwhile to humanity.
It's rubbish. How sad
Aumft You must be a sci.math cockroach. How did you crawl out of that shit hole? You sound like YBM/Python. Chuckle. Mooooroooon that you are.
I don't know this professor, but I'm thoroughly enjoying his talk right now. I have no doubt that he teaches well and would love to take a class from him.
There are already lectures of him online on mit opencourseware
my fvt teacher
Dr Gilbert is a legend!
I love the Strang!
Is there Dr Gilbert has complete lectures on this topic? If yes where I can get these as his incredible work on Linear Algebra
I love Gilbert Strang
i like this professor very much ..... he is awesome
thanks, dr. strang!
The knowledge of this man.. 😱
Beautiful Video.
best teacher ever
Engineers invented Finite Element method- Prof Gilbert Strang. I was into Engineering from my age of 5 years old inspired by my late father to whom I dedicated a website since 2002.
Prof. Strang mentioned Feng Kang in this video, who is a mathematician in Beijing. One of the founder of FEM idea.
Like prof Balakrishnan, he is a great teacher. i studied linear algebra on his very good text
Very useful!
computer engineers are also somehow involved in Finite Element Method. There have been many improved versions of FEM in term of accuracy but the computational cost is too expensive.
Amazing.
Mr. Strang, prof. dr.,
What do you think if IGA-G uses weak fprmulation and spline basis functions as the test function?
If we formate a strong treatment of boundary conditions to formally have the same approach for all with Grevill points on the Dirichlet boundary in such a way taht spline ~APPROXIMATION~.exactly satisfied the Dirichlet boundary conditions in this points. What it means on Dirac delta function. For me it is used for the test function on Dirichlet boundary?
In case of weak satisfied homogegeneous Dirichlet and not chage the Neumann boundary conditions. Substition formulations and weak boundary condition yields the finala IGA-G fprmulation. Substition will be
1.following spline representation
2.basiv function for the flow problem
3.WEAK Green-Gausse-Ostrogradski intergration
theorem
4. all derivates and elementa areas
As hydroengeer THANK YOU!
I ask because of groundwater flow problem for the future research for the development of FULLY space and time adaptor IGA methods for efficient modeli g of flow with continuous velocity field and its derivatives.
WISH YOU ALL WELL
Real teacher
thank u ...
Respect from India.
It will be very interesting if examples beig followed
E.g examples structure stresses
Fluid dynamic and Gas dynamic
anyone, please help me in learning the finite element method ??
which software is used??
waiting for hearing by you please.
There are many softwares, what is your aim ? Linear or nonlinear problems ? Which industry are you aiming ? Aerospace, automotive etc. But before all of them you may start with learning about basics of the finite element method.
These are the people who makes America great all the time
Galerkin or Rayleigh-Ritz?
If my life turns out just like his, I would be happy
The method, and discussions in mathematics are add, subtraction, multiplication, and division. No matter how change the combinations, the results are always the same.
lenda viva
How can he explain everything no matter how complex so easily?.
It's not Galerkin method, it's Bubnov-Galerkin method. And main contribution was made by Bubnov. So really this method should have Bubnov's name, not Galerkin (if to choose one)
+Eugeny Kompaneytsev It matters little whose name it bears because it pales into nothing compared to the methods of my new calculus.
sir how to solve extreme value of the function for given equation
Why didn't Shelley live long enough to write the much-needed 'Ode to the Coefficient?' Who'd thought in first-year of algebra how often, subtle and amazingly-powerful the weights to the recipe are? Fun.
gut
MIT 18.06 by Prof Strang and Prof Grinfeld's (a former student of Prof Strang) series on Linear Algebra had the most profound impact on my mathematical career.
Thank you MIT OCW and Dr Strang for your timeless efforts!
You've read the textbook, now you can see the movie. #strang
dividir para reinar
hahaha ... i love this ... and i thinks of miles mathis ... hahaha
newton second law..............
I only understood 50 % of it :D I guess I am the worst engineer on the planet xD
Talk about FEM not about historic stories,
so boooring