Autumn 2019
Prof. PJ Guruprasad
Author: Sakshi Dayal
Pre-requisite courses: AE 227, AE 238
Pre-requisite skills: Basic MATLAB coding. (Code template was given, you need to just complete missing sections according to the question)
Course Content:
- Basics of finite element method (for motivation)
- Standard discrete spring-mass-damper system
- Variational methods of approximation (derivations)
- Rayleigh- Ritz method and Method of Weighted Residuals
- Weak Forms of Finite Element Approximation
- 1D, 2D, 3D FEM models (bar, Euler-Bernoulli beam, Timoshenko beam)
- Reduced Numerical integration
- Introduction to finite element method in dynamics and vibrations
- Computer implementation of the finite element models
Motivation to take up the course: I had been using ANSYS and other simulation software mindlessly, but during my intern I realised we must know the background algorithms to avoid committing blunders. Also, FEM is an integral part of structures and if one is seeking to do projects or pursue career in this field, one will definitely require basic FEM knowledge.
Information about Projects/Assignments:
Two quizzes (10% each)
Assignments (10%)
Midsem (30%)
Endsem (40%)
This was declared in the beginning of the course, but changed drastically as semester proceeded. Weightage for assignments was increased and there was no midsem. Assignments are given a week in advance and have deadline a day prior to quiz. Completing and understanding each concept covered in the assignment is beneficial for quiz preparation. Quizzes are quite straightforward, mostly based on tutorial problems covered in class. Endsem was of medium difficulty. Formulae are provided during exams, no need of memorizing, just knowing how to attempt and reduce the question is important. There is a lot of scope of doing silly mistakes, so make sure you complete the questions till the very end while practicing.
Quizzes/Midsem/Endsem papers Difficulty: 2/5
Overall Course Difficulty: Moderate
Average Time Commitment: (Apart from lectures and tutorials) Less than 3 hrs
Attendance Policy: There was no attendance policy, but it is recommended to attend lectures (especially tutorials)
General funda: Attempt tutorial questions and assignments on your own, and till the very last step. Use a calculator and discover your own tricks to solve questions in less time and with more accuracy.
Grading stats:
| AA | 4 |
| AB | 16 |
| BB | 11 |
| BC and below | 14 |
| FR | 1 |
Professor’s Teaching Style: Asking doubts personally from the professor helps a lot. Raise questions and ask to repeat if you don’t understand some step. Reading and attempting derivations by oneself using lecture notes is helpful.
Should you do this course?: Anyone in third year or above can take this course. One should be comfortable with numerical methods, structure courses, and basic MATLAB coding. Scoring 8-9 is easy if you follow the course regularly, a 10 needs extra efforts. But for the utility of the course content, I highly recommend taking up this course, you won’t regret.
Autumn 2022
Prof. Amuthan Ramabathiran
Author: Vishnu Sankar
Pre-requisite skills: Python programming, Basic Calculus
Course Content:
- Part 1 - 1D FEM
- Basic FEM algorithm for second order ODEs.
- Implementation of FEM in Python.
- Introduction to Sobolev spaces.
- Modern mathematical perspective of FEM.
- A-priori and a-posteriori error estimates.
- Part 2 - FEM for 2D elliptic PDEs
- Variational theory of elliptic PDEs.
- Abstract FE methodology.
- Introduction to Fenics.
- Application to heat conduction and elasticity using Fenics
- Part 3 - Advanced Topics
- Decriminalizing variational crimes.
- Mixed finite elements: application to the Stokes problem.
- Locking phenomenon.
- Relationship between P1 finite elements and ReLU Deep Neural Networks.
- FEM for parabolic PDEs
Motivation to take up the course: Wanted to expand my knowledge of solving PDEs and wanted to experience one of the kind teaching style of Prof. Amuthan once again (first being AE 102)
Information about Projects/Assignments:
- Assignments - 20%
- Midsem - 30%
- Endsem - 50%
- Project (optional) - 10%
- Class wiki: Scribe for each lecture (optional) - 2% for each
Quizzes/Midsem/Endsem papers Difficulty: 4/5
Projects/Assignments Difficulty: 4/5
General funda: This course presents a new way of abstract thinking that you might have hardly encountered before in any of the core/elective courses, so you need to put in some effort to get hold of the mathematical jargons and abstract thinking. The midsem is a pure programming, open book & open internet exam for 3 hrs. Assignments also involve fair amount of programming. The endsem exam is a mix of both numerical problems and programming. Soon after the midsem, professor Amuthan introduces you to a python framework called FEMTO (which he is currently developing). The course is fast paced after midsems, and you need to catch up to his teaching, devote enough time to understand OOPs concepts in Python and his code FEMTO. This is inevitable as you will have to use FEMTO in the assignments and endsem exams. The prof is chill with the grading, but you need to work towards it. Try to scribe as many class wiki’s as possible as you will understand concepts better when you write them down for others to understand (and also you get bonus 2% for each class wiki)
Professor’s Teaching Style: Prof Amuthan’s teaching is so fluid and immersive, this course is pretty mathematical in nature, but the Prof makes it quite simple to understand. Thankfully, he doesn’t grill you with such mathematical questions in the exams. He conducted three demo lectures on advanced topics (not for exams/evaluation purpose): Introduction to open-source FEM packages such as FREEFEM and Fenics, Application of FEM to fluid problems, and relationship between FEM and ReLU Deep Neural Networks. The prof is also very accommodating of student requests such as deadline extensions etc. You also get to taste Prof. Amuthan’s humor sense at time :)
Should you do this course?: Anyone interested in solving PDEs through numerical computations in general can take up this course. The framework can be used for both Fluids and Structures, though in industry it is widely used only for structures problems. Recent research in the topic in the Fluid community involve hybrid FEM and FVM methods for fluid problems. If you want to get a sneak peek of modern mathematical formulation to solve PDEs/ODEs along with an immersive hands on Python programming experience, you should definitely take this course.
References:
- Claes Johnson - Numerical Solutions Of Partial Differential Equations By The Finite Element Method
- Johnson - Numerical Solutions of PDE by FEM