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Über den Kurs

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-Bewertungen

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.

RD

Sep 05, 2020

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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76 - 81 von 81 Bewertungen für The Finite Element Method for Problems in Physics

von Congyi L

Jan 28, 2018

Not clear on AWS setup. Easy get confused

von Murali R

Jan 24, 2017

good for improving skills

von SACHIN K

Jun 05, 2020

good exprnce

von M M K R

Jul 09, 2017

good

von Patrick H

Dec 15, 2017

In my opinion the course material is a good base but needs further development.

This includes new recordings of old lectures which contain errors. Sometimes there is a correction video included directly in the lecture video with an additional correction video and same content placed afterwards in the timeline.

Also there should be updated version of coding assignments. As stated in the forum it was just possible to pass one assignment by 100 percent if a deal.ii version from 2015 is used. However, the provided link to the deal.ii VM provides a recent version 2017. When run the same code on the student computer with deal.ii from 2015 one could get full marks. However, using the recent version from 2017, the automatic grading just gave 80 percent. This should be for sure improved.

Additionally I would suggest to make a more even work distribution for each week. There are weeks with just 3 hours of videos and other weeks with up to 9 hours. It would be beneficial if that could be more balanced.

Coding assignment 1 is placed with a deadline in week 3. However, the required material for passing this is taught in week 4 and 5. Therefore, I would suggest to push CA1 to week 5.

von Mehmet A Ö

Apr 30, 2018

Lecturer expresses anything at a snail's pace. He is really a slowcoach.