Retour à The Finite Element Method for Problems in Physics

4.7

303 notes

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65 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.

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

Filtrer par :

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 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 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 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 DEEPAK K P

•Mar 17, 2019

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

par RAKSHITH B D

•Sep 16, 2018

The needful course for me

par Houssem C

•Sep 16, 2018

very interesting course

par Junchao

•Oct 30, 2017

Great Course !

par NAGIRIMADUGU P

•Jul 09, 2017

very friendly to the students

par benjamin j d o

•Jun 29, 2017

Absolutely amazing¡¡ Where is the other course in continuum physics in MOOC format? I can't wait.

par chtld

•Mar 11, 2018

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

par 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.

par NAGEPALLI N K

•Apr 14, 2017

good for learning.

par 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.

par 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.

par Rahul S

•Jun 13, 2018

It's awesome.

par MOHD. F

•Jun 19, 2017

Exceptional!

Need to invest a great deal of time to understand thoroughly.

par E B K

•Sep 22, 2017

Great we can learn many things

par ISAAC T

•Jul 29, 2017

Incredibly instructive, even for an industrial engineer especialzed in mechanic like me.

par Devara s

•Jul 10, 2017

it is good course it more useful to us and i learn lot information for this course thanking you giving for this opportunity

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 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.

par Harsh V G

•Dec 07, 2017

excellent course , explains stuff right from the basics.

great job overall !!

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 !!!