Retour à The Finite Element Method for Problems in Physics

4.7

270 notes

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58 avis

This course is an introduction to the finite element method as applicable to a range of problems in physics and engineering sciences. The treatment is mathematical, but only for the purpose of clarifying the formulation. The emphasis is on coding up the formulations in a modern, open-source environment that can be expanded to other applications, subsequently.
The course includes about 45 hours of lectures covering the material I normally teach in an
introductory graduate class at University of Michigan. The treatment is mathematical, which is
natural for a topic whose roots lie deep in functional analysis and variational calculus. It is not
formal, however, because the main goal of these lectures is to turn the viewer into a
competent developer of finite element code. We do spend time in rudimentary functional
analysis, and variational calculus, but this is only to highlight the mathematical basis for the
methods, which in turn explains why they work so well. Much of the success of the Finite
Element Method as a computational framework lies in the rigor of its mathematical
foundation, and this needs to be appreciated, even if only in the elementary manner
presented here. A background in PDEs and, more importantly, linear algebra, is assumed,
although the viewer will find that we develop all the relevant ideas that are needed.
The development itself focuses on the classical forms of partial differential equations (PDEs):
elliptic, parabolic and hyperbolic. At each stage, however, we make numerous connections to
the physical phenomena represented by the PDEs. For clarity we begin with elliptic PDEs in
one dimension (linearized elasticity, steady state heat conduction and mass diffusion). We
then move on to three dimensional elliptic PDEs in scalar unknowns (heat conduction and
mass diffusion), before ending the treatment of elliptic PDEs with three dimensional problems
in vector unknowns (linearized elasticity). Parabolic PDEs in three dimensions come next
(unsteady heat conduction and mass diffusion), and the lectures end with hyperbolic PDEs in
three dimensions (linear elastodynamics). Interspersed among the lectures are responses to
questions that arose from a small group of graduate students and post-doctoral scholars who
followed the lectures live. At suitable points in the lectures, we interrupt the mathematical
development to lay out the code framework, which is entirely open source, and C++ based.
Books:
There are many books on finite element methods. This class does not have a required
textbook. However, we do recommend the following books for more detailed and broader
treatments than can be provided in any form of class:
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, T.J.R.
Hughes, Dover Publications, 2000.
The Finite Element Method: Its Basis and Fundamentals, O.C. Zienkiewicz, R.L. Taylor and
J.Z. Zhu, Butterworth-Heinemann, 2005.
A First Course in Finite Elements, J. Fish and T. Belytschko, Wiley, 2007.
Resources:
You can download the deal.ii library at dealii.org. The lectures include coding tutorials where
we list other resources that you can use if you are unable to install deal.ii on your own
computer. You will need cmake to run deal.ii. It is available at cmake.org....

Mar 13, 2017

It is very well structured and Dr Krishna Garikipati helps me understand the course in very simple manner. I would like to thank coursera community for making this course available.

Jun 21, 2018

Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).

Filtrer par :

par John F S

•May 31, 2019

Okay for learning the basics of FEM outside of a real clasroom setting. Focused too much on using their own software for actual FEM analysis. I understand that creating an actual FEM from scratch is too much to ask for an online course, but a lot of their program isn't well documented and detracts from the learning experience.

par Guilherme D

•May 21, 2019

Well structured course. It builds up from the basics of finite elements to more complex problems.

par Солин В А

•Apr 02, 2019

Это отличный курс по МКЭ. Он не легкий, совсем нет. Я пытался пройти его больше года, но в итоге осилил. Он действительно помог мне разобраться в МКЭ.

This is exxelent course about FEM. It's not easy to complete. I've managed to finish it about year. It's very usefull. It hepled me to understand FEM.

Спасибо большое за эту возможность.

Thank you for this opportunity.

par Abhishek T

•Mar 26, 2019

Very interesting course

par DEEPAK K P

•Mar 17, 2019

An exceptionally created course with every detail of the subject matter. Thanks a lot.

par Marvin T

•Jan 15, 2019

In principle, it is a good course and taught in a very understanding manner. For a five star rating, I would like to suggest that there should be additional physics, e.g. convection problems, or turbulence, featuring a CFD chapter for example with heat transfer.

par Bowei " W

•Jan 09, 2019

Thank you Prof. Garikipati and Greg for the amazing course. I have learned a lot about the FEM and am going to apply the knowledge to my research project.

par chenxi

•Jan 02, 2019

编程作业好评，如果能够出详细介绍dealii的系列就更好了。

par Vinayak V

•Dec 30, 2018

The course was was great. However, illustrative examples solving real engineering problems could be introduced in lecture.

par Houssem C

•Sep 16, 2018

very interesting course

par RAKSHITH B D

•Sep 16, 2018

The needful course for me

par 杨名

•Jul 07, 2018

Very detailed explanation and illustration. The Professor will help you revise the course material at the beginning of each video, so don't worry about forgetting things. The course is interesting and useful. Gain me a lot of insights. Assignments are great.

par Elizabeth F

•Jul 05, 2018

I like this course it is useful because have theory and the application part.

par Kapouranis I

•Jun 29, 2018

Really recommend it. There will be times when you think you should give up, but just finish it. It is worth it.

par Yuxiang W

•Jun 21, 2018

Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).

par Antonio R

•Jun 21, 2018

The course is really deep and I have to say the professor really inspired me to keep learning.It might be a little slow but the course is in general pretty good.

par Rahul S

•Jun 13, 2018

It's awesome.

par Eik U H

•May 26, 2018

Looking backward from the end of this course I know, whatever I felt during the last months, this course is really great. Thank you very much.

par Asan A

•May 15, 2018

Thank you very much that you helped me understand of the FEM. I'm so happy that I could find your online course.

You did a really very significant course which help to people easily fıgure out the FEM.

par Harold L M M

•May 12, 2018

This is an excellent course on Finite Element Method. It's a very complete one. This course includes the mathematical theory of finite elements and the practice by using deal.II C/C++ library. This course requires a lot of effort, but the gain of knowledge worth the effort.

I highly recommend it to both engineers and mathematicians interested in solving PDEs with the finite element method.

Thank you very much professor Krishna Garikipati !!!

par Mehmet A Ö

•Apr 30, 2018

Lecturer expresses anything at a snail's pace. He is really a slowcoach.

par chtld

•Mar 11, 2018

I think this course is very good for the students who first learn the fem.

par Xiong N

•Mar 03, 2018

It's a great course. It could be even better if all the quizzes and assignments can give feedback after done. e.g. explanations and such

par Congyi L

•Jan 28, 2018

Not clear on AWS setup. Easy get confused

par FRANCISCO T

•Jan 13, 2018

This is a very good course for getting introduced in the theory and practice of the finite element method. I wish there were a second part.

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