Вернуться к Метод конечных элементов для решения задач в области физики

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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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## 26–50 из 94 отзывов о курсе Метод конечных элементов для решения задач в области физики

автор: Rohan S

21 янв. 2017 г.

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.

автор: Josiel C T

30 нояб. 2020 г.

The course was very interesting and helped me to understand the mathematical basis of the Finite element method. Besides, Professor Krishna Garikipati makes the concepts very easy to understand. Due to this course, I am very motivated to go through more advance topics.

автор: 杨名

7 июля 2018 г.

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.

автор: Gabriel D L C

27 апр. 2021 г.

Excellent course on the foundations of the Finite Element Method. The mathematical concepts are very well presented so that it enables the learners to use current finite element software consciously without facing it as a black box.

автор: Patel P

21 мая 2020 г.

Professor is very clear with explanation, and meticulous with accuracy to the highest degree possible. Assignment at first seems daunting, but Gregory Teichert explains very clearly and then it seems like only a typing job.

автор: pavankumar j

16 июня 2021 г.

An exceptional course for people pursuing career in Mechanical Engineering and need a deeper understanding of Finite Element Method fundamentals. Huge respect for Sir Krishna Garikipati for the kind simplified explanation.

автор: DILAN T S

19 окт. 2020 г.

I got the fundamental knowledge of the finite element method also experienced C++ programming for simulating a simple system using the finite element method. Course content and programming is interest to me.

автор: Asan

15 мая 2018 г.

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.

автор: Matthijs S

11 июля 2017 г.

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.

автор: Michael B

5 мар. 2017 г.

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.

автор: Rahul B D

5 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

автор: 杨思超

30 авг. 2019 г.

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

автор: MEHMET A

8 сент. 2020 г.

This course is really didactic course. If you are interested in FEM, please take this course. Thank you Professor Krishna Garikipat.

Sincerely....

автор: Eik U H

26 мая 2018 г.

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.

автор: FRANCISCO T

13 янв. 2018 г.

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.

автор: Sumedh S

23 нояб. 2020 г.

Excellent course, subject matter is presented very methodically, and the instructor's command over the subject taught is outstanding.

автор: Devara s

10 июля 2017 г.

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

автор: Aamir i

9 мар. 2017 г.

A rigorous and organized introduction to the subject with the additional benefit of learning through implementation.

автор: LUIS A P C

17 сент. 2020 г.

This should be the standard way for teaching Finite Element Methods in Engineering in colleges and universities

автор: benjamin j d o

29 июня 2017 г.

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

автор: Diego V

24 мар. 2021 г.

Excelente para personas con conocimiento básico o nulo de elementos finitos. Super recomendado :)

автор: Angelos M

14 февр. 2021 г.

Perfect Course !

I recommend it to everyone who is interested in mathematics and physics.

12 мар. 2020 г.

Very well organized and presented from an instructor who is clearly quite knowledgeable.

автор: ISAAC T

29 июля 2017 г.

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

автор: Deepak P

17 мар. 2019 г.

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