Вернуться к Метод конечных элементов для решения задач в области физики

4.6
звезд
Оценки: 491
Рецензии: 97

## О курсе

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....

## Лучшие рецензии

SS

12 мар. 2017 г.

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.

RD

4 сент. 2020 г.

Well worth the time if you wish to understand the mathematical origin of the FEM methods used in solving various physical situations such as heat/mass transfer and solid mechanics

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## 76–94 из 94 отзывов о курсе Метод конечных элементов для решения задач в области физики

автор: Pierre B

17 мар. 2017 г.

This is a good intro course which introduce the Finite Element Method step by step, which suited me perfectly since I hardly coded in c++ nor did FEM before.

Nevertheless, as a graduate student, the pace is very slow, and the outline and motivation unclear, which would likely have discouraged me if I did not review video in x2, and stuck to second week lectures and onward.

I would advise to introduce more outline and motivation at the beginning of the week lecture to keep students motivated.

Apart from that, I recommand the course !

автор: Georgi H S

2 авг. 2020 г.

The course is a nice and well structured from theoretical point of view introduction to Finite Element Methods. The computational part is a little marginal in the course, but is the main for the grading. If the course had a perfect division between theory and computational part it would've been perfect. The only problem is that in theory, one does the same kind of calculations over and over again, and it's boring after few times.

автор: Marvin T

15 янв. 2019 г.

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.

автор: Sri H M

15 нояб. 2019 г.

A good primer of the theoretical fundamentals of the Finite Element Methods. The coding assignments were good too but could have benefited more with support from the mentors via the forums.

автор: Antonio R

21 июня 2018 г.

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.

автор: Vinayak V

30 дек. 2018 г.

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

автор: Kapouranis I

29 июня 2018 г.

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

автор: Guilherme D

21 мая 2019 г.

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

автор: YAN B

22 дек. 2019 г.

Good content, not easy for beginners. It may take much longer to fully understand the content covered in the lecture.

Programming exercise is somehow difficult as you have to watch dealIii tutorial videos on YouTube yourselves.

One particular drawback is that the presentation skill of the instructor should be improved as there are a lot of repetitive unnecessary and redundant writing and explanation.

автор: John F S

31 мая 2019 г.

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.

автор: George K

22 янв. 2020 г.

You will need much more time than the time listed (expectation time listed). Although you can learn

a lot!!!!! I feel grateful!

автор: LINGALA K

13 июля 2017 г.

the course is enough learn things better way to explain give notes and pdf format and doc l.

автор: Congyi L

28 янв. 2018 г.

Not clear on AWS setup. Easy get confused

автор: Mk R

24 янв. 2017 г.

good for improving skills

автор: Sachin K

5 июня 2020 г.

good exprnce

автор: M M K R

9 июля 2017 г.

good

автор: Mehmet A Ö

30 апр. 2018 г.

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

автор: Marco A M M

23 июня 2022 г.

Unfortunately i had to drop from the course during week 3 because in order to follow the coding assignments one needs to download the virtual machine. However this software is not compatible with current Mac computers (or at least I have not been able to install it).

I strongly recommend the organizers to add in the description all the requirements in order to prevent people the waste of time.

автор: Subhendu P

6 сент. 2021 г.

the video lectures are very bad quality