Вернуться к The Finite Element Method for Problems in Physics

4.6

Оценки: 222

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Рецензии: 50

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....

автор: SS

•Mar 13, 2017

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.

автор: YW

•Jun 21, 2018

Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).

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Рецензии: 47

автор: Houssem Chkili

•Sep 16, 2018

very interesting course

автор: RAKSHITH B D

•Sep 16, 2018

The needful course for me

автор: 杨名

•Jul 07, 2018

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: Elizabeth Flores

•Jul 05, 2018

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

автор: Kapouranis Ilias

•Jun 29, 2018

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

автор: Yuxiang Wang

•Jun 21, 2018

Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).

автор: Antonio Rios

•Jun 21, 2018

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: Rahul Soni

•Jun 13, 2018

It's awesome.

автор: Eik Uwe Heine

•May 26, 2018

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: Asan Adamanov

•May 15, 2018

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.

Coursera делает лучшее в мире образование доступным каждому, предлагая онлайн-курсы от ведущих университетов и организаций.