The Finite Element Method for Problems in Physics に戻る

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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.

Jul 21, 2019

The course is great and the tutors are very helpful. I just have a suggestion that there should be more coding assignment like one for every week.\n\nThank you

フィルター：

by 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

by Benico v d W

•Aug 01, 2017

The videos are VERY long & VERY slow. It does not come to the point fast enough. It does not clearly define & explain what is to be achieved. There should be an exercise after each video. The handwriting-on-screen method is EXTREMELY slow, inefficient & frustrating. There are no handouts or textbooks. I have restarted this course 3 times - but I just can't get myself to flow with it. I like the lecturers and I can see they know their field. But this does not feel like a MOOC. It feels like varsity 25 years ago - only the chalk board is replaced by a video-recorded white screen. I try to do this in the evenings after work - but you are loosing me. Perhaps I do not have the right prerequisites, in spite of a B. Eng. degree (Mech). I am learning to use OpenFOAM & Code Aster at the moment. I also use Linux on all my computers since 2000. Yes my pde skills are a bit rusted - but so would be the pde skills of 70% of the students taking this course. I'm sorry to grade this course as a one - but in comparison with the other Moocs that I did - this one needs a lot of improvement.

by 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).

by Wei Y

•Jul 21, 2019

Need to improve his presentation skills. Most boring lectures in Cousera.

by Dimiter P

•Mar 06, 2017

Very weak presentation. Must be improved to keep attention.

by Shubham s

•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.

by Ishaan K

•Jul 21, 2019

The course is great and the tutors are very helpful. I just have a suggestion that there should be more coding assignment like one for every week.

Thank you

by 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.

by Shaik K B

•Jan 17, 2017

This is the best course as iam learning I so happy about your lecturer's

It is an wounder full experience that iam getting from you

by Abhishek T

•Mar 26, 2019

Very interesting course

by Muhammad H S

•May 20, 2017

I was expecting learning how to apply finite element as an engineer and designer, instead the course is about the mathematics & programming of the finite element method.

by Kiran A

•Dec 23, 2017

Intense development of FEM. Although its more of classroom type of teaching, its effective and Prof. Krishna has done a great job in explaining the concepts well. The assignments are good and check the understanding of the subject. Week 3 Assignment could be pushed to Week 5 may be, or it could be split into two assignments. The number of attempts for quizzes could be perhaps reduced. Presently, it is very easy to score in these quizzes. Overall a great course, and I feel confident knowing the fundamentals of FEM.

by Jose G L G

•Jun 12, 2017

A must take course if you intend to one day tackle real world finite element based Physics simulations.

There are finite element method software packages that lead us to believe that we don't need to understand the finite element method (FEM) in order to make physics simulations.

That is true if you just want to study simple academic problems. However if you want to simulate the real world you need to understand the basics of the FEM. This course will provide you with these basic tools.

by 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 !!!

by 李晨曦

•Jun 06, 2017

Instructions (in lecture and coding assignment) are clear and easy to follow. Contents of the lectures are somewhat repetitive, but I think it's OK because it allows you to go over previous materials just by watching the lecture and taking notes. Talking about potential improvement, I think it would be nice to give some more explanations to certain details, such as how the connectivity matrix is constructed.

by 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.

by Md A R F

•Mar 29, 2017

I've encountered very few courses that demonstrate the detailed connection between what we learn in theory and applying them in programming languages. The instructions on programming assignments are limpid, can get through them even with very little programming experience.

by Kumar R S

•Jan 21, 2017

Professor Garikipati provides a thorough explanation which is of immense help to a beginner in FEM like me. The course is very interesting! The practice of making entire video in form of notes is very efficient for a student to grasp everything the teacher wants to convey.

by 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.

by 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.

by Matthijs S

•Jul 11, 2017

Well-structured course with high quality lectures and slides in Galerkin FEM for problems in physics. A 'Must Take' to every professional in computer-aided design for research and concept development.

by Michael B

•Mar 05, 2017

This was a great course, I can only recommend. The tutor really explains basically all that there is to linear PDEs. What I miss, maybe as a different course is the case of nonlinear equations.

by 杨思超

•Aug 30, 2019

very good course on explaining the mathematical ground of FE and connecting it with the physical domain. Also learned a lot on the coding part of the FE modeling

by 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.

by 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.