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Learner Reviews & Feedback for The Finite Element Method for Problems in Physics by University of Michigan

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About the Course

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....

Top reviews

S

Nov 22, 2020

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

AI

Mar 8, 2017

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

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51 - 75 of 105 Reviews for The Finite Element Method for Problems in Physics

By Angelos M

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Feb 14, 2021

Perfect Course !

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

By Brad R

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Mar 12, 2020

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

By ISAAC T

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Jul 29, 2017

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

By Deepak P

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Mar 17, 2019

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

By 张宇杰

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Aug 13, 2020

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

By Elizabeth F

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Jul 5, 2018

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

By HARSH V G

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Dec 7, 2017

excellent course , explains stuff right from the basics.

great job overall !!

By shangyuan z

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Mar 11, 2018

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

By MOHD. F

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Jun 18, 2017

Exceptional!

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

By NISHANT S

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May 26, 2020

A VERY INTERESTING COURSE WITH AN ENTHUSIASTIC AND DEDICATED INSTRUCTOR

By LO W

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Aug 31, 2019

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

By Prasanth s

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Jul 12, 2017

thank you sir for giving this offering of this course

By Ann T

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Apr 9, 2020

Very good course, I liked everything.

By Xi C

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Jan 1, 2019

编程作业好评，如果能够出详细介绍dealii的系列就更好了。

By Bhargav E

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Sep 21, 2017

Great we can learn many things

By NAGIRIMADUGU P

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Jul 9, 2017

very friendly to the students

By Rakshith B D G

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Sep 15, 2018

The needful course for me

By Houssem C

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Sep 16, 2018

very interesting course

By Akash S

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Jul 30, 2020

Excellent Teaching

By NAGEPALLI N K

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Apr 14, 2017

good for learning.

By Salvatore V

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Jan 30, 2021

very good course

By Mukunda K

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Jan 7, 2020

Great Lecture.

By Junchao

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Oct 30, 2017

Great Course !

By Rahul S

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Jun 13, 2018

It's awesome.

By Ramy F

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Sep 4, 2022

very good