Вернуться к Метод конечных элементов для решения задач в области физики

4.6
звезд
Оценки: 491

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

Фильтр по:

51–75 из 94 отзывов о курсе Метод конечных элементов для решения задач в области физики

автор: 张宇杰

13 авг. 2020 г.

The course is arranged perfectly. I learned a lot through the coding assignment!

автор: Elizabeth F

5 июля 2018 г.

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

автор: Harsh V G

7 дек. 2017 г.

excellent course , explains stuff right from the basics.

great job overall !!

автор: chtld

11 мар. 2018 г.

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

автор: MOHD. F

19 июня 2017 г.

Exceptional!

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

автор: NISHANT S

26 мая 2020 г.

A VERY INTERESTING COURSE WITH AN ENTHUSIASTIC AND DEDICATED INSTRUCTOR

автор: LO W

31 авг. 2019 г.

It is worth to put some effort on this course. I learn alot .

автор: Prasanth s

12 июля 2017 г.

thank you sir for giving this offering of this course

автор: Ann T

9 апр. 2020 г.

Very good course, I liked everything.

автор: Xi C

2 янв. 2019 г.

автор: Bhargav E

22 сент. 2017 г.

Great we can learn many things

автор: NAGIRIMADUGU P

9 июля 2017 г.

very friendly to the students

автор: RAKSHITH B D

16 сент. 2018 г.

The needful course for me

автор: Houssem C

16 сент. 2018 г.

very interesting course

автор: Akash S

30 июля 2020 г.

Excellent Teaching

автор: NAGEPALLI N K

14 апр. 2017 г.

good for learning.

автор: Salvatore V

30 янв. 2021 г.

very good course

автор: Mukunda K

7 янв. 2020 г.

Great Lecture.

автор: Junchao

30 окт. 2017 г.

Great Course !

автор: Rahul S

13 июня 2018 г.

It's awesome.

автор: Induja P V

21 окт. 2020 г.

EXCELLENT

автор: Marco R H

23 июня 2019 г.

nice one!

автор: BHARATH K T

9 июля 2017 г.

good

автор: AKHIL L S

24 мар. 2022 г.

.

автор: Krishnakumar G

16 авг. 2019 г.

While quite mathematical in nature as opposed to a purely applied view of the method, Prof, Krishna Garikipati's teaching style and clear explanations make the material accessible to practicing engineers outside of academia. This is a great course to take for a strong introduction to the theory of FE method. The TA's explanation videos, while being helpful can sometimes be too verbose. This is a long course, and took me nearly 4 months to finish the videos. I had to go back and watch each of the videos at least 2 times over these 4 months, since some ideas are a bit mathematically dense. Upon second viewing, the ideas become clearer. Overall, a highly recommended course!