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返回到 有限元法在物理问题中的应用

學生對 密歇根大学 提供的 有限元法在物理问题中的应用 的評價和反饋

4.6
449 個評分
93 條評論

課程概述

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....

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SS
2017年3月12日

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
2020年9月4日

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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51 - 有限元法在物理问题中的应用 的 75 個評論(共 90 個)

創建者 Elizabeth F

2018年7月5日

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

創建者 Harsh V G

2017年12月7日

excellent course , explains stuff right from the basics.

great job overall !!

創建者 chtld

2018年3月11日

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

創建者 MOHD. F

2017年6月19日

Exceptional!

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

創建者 NISHANT S

2020年5月26日

A VERY INTERESTING COURSE WITH AN ENTHUSIASTIC AND DEDICATED INSTRUCTOR

創建者 LO W

2019年8月31日

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

創建者 Prasanth s

2017年7月12日

thank you sir for giving this offering of this course

創建者 Ann T

2020年4月9日

Very good course, I liked everything.

創建者 Xi C

2019年1月2日

编程作业好评,如果能够出详细介绍dealii的系列就更好了。

創建者 Bhargav E

2017年9月22日

Great we can learn many things

創建者 NAGIRIMADUGU P

2017年7月9日

very friendly to the students

創建者 RAKSHITH B D

2018年9月16日

The needful course for me

創建者 Houssem C

2018年9月16日

very interesting course

創建者 Akash S

2020年7月30日

Excellent Teaching

創建者 NAGEPALLI N K

2017年4月14日

good for learning.

創建者 Salvatore V

2021年1月30日

very good course

創建者 Mukunda K

2020年1月7日

Great Lecture.

創建者 Junchao

2017年10月30日

Great Course !

創建者 Rahul S

2018年6月13日

It's awesome.

創建者 Induja P V

2020年10月21日

EXCELLENT

創建者 Marco R H

2019年6月23日

nice one!

創建者 BHARATH K T

2017年7月9日

good

創建者 Krishnakumar G

2019年8月16日

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!

創建者 Pierre B

2017年3月17日

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 !

創建者 Georgi H S

2020年8月2日

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.