About this Course
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Intermediate Level

Approx. 27 hours to complete

Suggested: You should expect to watch about 3 hours of video lectures a week. Apart from the lectures, expect to put in between 3 and 5 hours a week....

English

Subtitles: English

Skills you will gain

Finite DifferencesC++C Sharp (C#) (Programming Language)Matrices

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 27 hours to complete

Suggested: You should expect to watch about 3 hours of video lectures a week. Apart from the lectures, expect to put in between 3 and 5 hours a week....

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
6 hours to complete

1

This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method....
11 videos (Total 200 min), 2 readings, 1 quiz
11 videos
01.02. Introduction. Linear elliptic partial differential equations - II 13m
01.03. Boundary conditions 22m
01.04. Constitutive relations 20m
01.05. Strong form of the partial differential equation. Analytic solution 22m
01.06. Weak form of the partial differential equation - I 12m
01.07. Weak form of the partial differential equation - II 15m
01.08. Equivalence between the strong and weak forms 24m
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21m
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19m
01.08ct.3. Intro to C++ (pointers, iterators) 14m
2 readings
Help us learn more about you!10m
"Paper and pencil" practice assignment on strong and weak formss
1 practice exercise
Unit 1 Quiz8m
Week
2
3 hours to complete

2

In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem....
14 videos (Total 202 min), 1 quiz
14 videos
02.01q. Response to a question 7m
02.02. Basic Hilbert spaces - I 15m
02.03. Basic Hilbert spaces - II 9m
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22m
02.04q. Response to a question 6m
02.05. Basis functions - I 14m
02.06. Basis functions - II 14m
02.07. The bi-unit domain - I 11m
02.08. The bi-unit domain - II 16m
02.09. The finite dimensional weak form as a sum over element subdomains - I 16m
02.10. The finite dimensional weak form as a sum over element subdomains - II 12m
02.10ct.1. Intro to C++ (functions) 13m
02.10ct.2. Intro to C++ (C++ classes) 16m
1 practice exercise
Unit 2 Quiz6m
Week
3
7 hours to complete

3

In this unit, you will write the finite-dimensional weak form in a matrix-vector form. You also will be introduced to coding in the deal.ii framework....
14 videos (Total 213 min), 2 quizzes
14 videos
03.02. The matrix-vector weak form - I - II 17m
03.03. The matrix-vector weak form - II - I 15m
03.04. The matrix-vector weak form - II - II 13m
03.05. The matrix-vector weak form - III - I 22m
03.06. The matrix-vector weak form - III - II 13m
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12m
03.06ct.2. Intro to AWS, using AWS on Windows24m
03.06ct.2c. In-Video Correction3m
03.06ct.3. Using AWS on Linux and Mac OS7m
03.07. The final finite element equations in matrix-vector form - I 22m
03.08. The final finite element equations in matrix-vector form - II 18m
03.08q. Response to a question 4m
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19m
1 practice exercise
Unit 3 Quiz6m
Week
4
5 hours to complete

4

This unit develops further details on boundary conditions, higher-order basis functions, and numerical quadrature. You also will learn about the templates for the first coding assignment....
17 videos (Total 262 min), 1 quiz
17 videos
04.02. The pure Dirichlet problem - II 17m
04.02c. In-Video Correction 1m
04.03. Higher polynomial order basis functions - I 23m
04.03c0. In-Video Correction 57s
04.03c1. In-Video Correction 34s
04.04. Higher polynomial order basis functions - I - II 16m
04.05. Higher polynomial order basis functions - II - I 13m
04.06. Higher polynomial order basis functions - III 23m
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14m
04.07. The matrix-vector equations for quadratic basis functions - I - I 21m
04.08. The matrix-vector equations for quadratic basis functions - I - II 11m
04.09. The matrix-vector equations for quadratic basis functions - II - I 19m
04.10. The matrix-vector equations for quadratic basis functions - II - II 24m
04.11. Numerical integration -- Gaussian quadrature 13m
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14m
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26m
1 practice exercise
Unit 4 Quiz8m
Week
5
3 hours to complete

5

This unit outlines the mathematical analysis of the finite element method....
12 videos (Total 170 min), 1 quiz
12 videos
05.01c. In-Video Correction 56s
05.01ct.1. Coding assignment 1 (functions: “solve” to “l2norm_of_error”) 10m
05.01ct.2. Visualization tools7m
05.02. Norms - II 18m
05.02. Response to a question 5m
05.03. Consistency of the finite element method 24m
05.04. The best approximation property 21m
05.05. The "Pythagorean Theorem" 13m
05.05q. Response to a question 3m
05.06. Sobolev estimates and convergence of the finite element method 23m
05.07. Finite element error estimates 22m
1 practice exercise
Unit 5 Quiz8m
Week
6
1 hour to complete

6

This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems....
4 videos (Total 70 min), 1 quiz
4 videos
06.02. Functionals. Free energy - II 13m
06.03. Extremization of functionals 18m
06.04. Derivation of the weak form using a variational principle 20m
1 practice exercise
Unit 6 Quiz4m
Week
7
6 hours to complete

7

In this unit, we develop the finite element method for three-dimensional scalar problems, such as the heat conduction or mass diffusion problems....
24 videos (Total 322 min), 1 quiz
24 videos
07.02. The strong form of steady state heat conduction and mass diffusion - II 19m
07.02q. Response to a question 1m
07.03. The strong form, continued 19m
07.03c. In-Video Correction 42s
07.04. The weak form 24m
07.05. The finite-dimensional weak form - I 12m
07.06. The finite-dimensional weak form - II 15m
07.07. Three-dimensional hexahedral finite elements 21m
07.08. Aside: Insight to the basis functions by considering the two-dimensional case 17m
07.08c In-Video Correction 44s
07.09. Field derivatives. The Jacobian - I 12m
07.10. Field derivatives. The Jacobian - II 14m
07.11. The integrals in terms of degrees of freedom 16m
07.12. The integrals in terms of degrees of freedom - continued 20m
07.13. The matrix-vector weak form - I 17m
07.14. The matrix-vector weak form II 11m
07.15.The matrix-vector weak form, continued - I 17m
07.15c. In-Video Correction 1m
07.16. The matrix-vector weak form, continued - II 16m
07.17. The matrix vector weak form, continued further - I 17m
07.17c. In-Video Correction 47s
07.18. The matrix-vector weak form, continued further - II 20m
07.18c. In-Video Correction 3m
1 practice exercise
Unit 7 Quiz10m
Week
8
5 hours to complete

8

In this unit, you will complete some details of the three-dimensional formulation that depend on the choice of basis functions, as well as be introduced to the second coding assignment....
9 videos (Total 108 min), 2 quizzes
9 videos
08.01c. In-Video Correction 1m
08.02. Lagrange basis functions in 1 through 3 dimensions - II 12m
08.02ct. Coding assignment 2 (2D problem) - I 13m
08.03. Quadrature rules in 1 through 3 dimensions 17m
08.03ct.1. Coding assignment 2 (2D problem) - II 13m
08.03ct.2. Coding assignment 2 (3D problem) 6m
08.04. Triangular and tetrahedral elements - Linears - I 6m
08.05. Triangular and tetrahedral elements - Linears - II 16m
1 practice exercise
Unit 8 Quiz6m
Week
9
1 hour to complete

9

In this unit, we take a detour to study the two-dimensional formulation for scalar problems, such as the steady state heat or diffusion equations....
6 videos (Total 73 min), 1 quiz
6 videos
09.02. The finite-dimensional weak form and basis functions - II 19m
09.03. The matrix-vector weak form 19m
09.03c. In-Video Correction 38s
09.04. The matrix-vector weak form - II 11m
09.04c. In-Video Correction 1m
1 practice exercise
Unit 9 Quiz4m
Week
10
8 hours to complete

10

This unit introduces the problem of three-dimensional, linearized elasticity at steady state, and also develops the finite element method for this problem. Aspects of the code templates are also examined....
22 videos (Total 306 min), 2 quizzes
22 videos
10.02. The strong form of linearized elasticity in three dimensions - II 17m
10.02c. In-Video Correction 1m
10.03. The strong form, continued 23m
10.04. The constitutive relations of linearized elasticity 21m
10.05. The weak form - I 17m
10.05q. Response to a question 7m
10.06. The weak form - II 20m
10.07. The finite-dimensional weak form - Basis functions - I 18m
10.08. The finite-dimensional weak form - Basis functions - II 9m
10.09. Element integrals - I 20m
10.09c. In-Video Correction 53s
10.10. Element integrals - II 6m
10.11. The matrix-vector weak form - I 19m
10.12. The matrix-vector weak form - II 12m
10.13. Assembly of the global matrix-vector equations - I 20m
10.14. Assembly of the global matrix-vector equations - II 9m
10.14c. In Video Correction 2m
10.14ct.1. Coding assignment 3 - I 10m
10.14ct.2. Coding assignment 3 - II 19m
10.15. Dirichlet boundary conditions - I 21m
10.16. Dirichlet boundary conditions - II 13m
1 practice exercise
Unit 10 Quiz8m
Week
11
9 hours to complete

11

In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation....
27 videos (Total 378 min), 2 quizzes
27 videos
11.01c In-Video Correction 43s
11.02. The weak form, and finite-dimensional weak form - I 18m
11.03. The weak form, and finite-dimensional weak form - II 10m
11.04. Basis functions, and the matrix-vector weak form - I 19m
11.04c In-Video Correction 44s
11.05. Basis functions, and the matrix-vector weak form - II 12m
11.05. Response to a question 51s
11.06. Dirichlet boundary conditions; the final matrix-vector equations 16m
11.07. Time discretization; the Euler family - I 22m
11.08. Time discretization; the Euler family - II 9m
11.09. The v-form and d-form 20m
11.09ct.1. Coding assignment 4 - I 11m
11.09ct.2. Coding assignment 4 - II 13m
11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I 17m
11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II 14m
11.11c. In-Video Correction 1m
11.12. Modal decomposition and modal equations - I 16m
11.13. Modal decomposition and modal equations - II 16m
11.14. Modal equations and stability of the time-exact single degree of freedom systems - I 10m
11.15. Modal equations and stability of the time-exact single degree of freedom systems - II 17m
11.15q. Response to a question 10m
11.16. Stability of the time-discrete single degree of freedom systems 23m
11.17. Behavior of higher-order modes; consistency - I 18m
11.18. Behavior of higher-order modes; consistency - II 19m
11.19. Convergence - I 20m
11.20. Convergence - II 16m
1 practice exercise
Unit 11 Quiz8m
Week
12
2 hours to complete

12

In this unit we study the problem of elastodynamics, and its finite element formulation....
9 videos (Total 141 min), 1 quiz
9 videos
12.02. The finite-dimensional and matrix-vector weak forms - I 10m
12.03. The finite-dimensional and matrix-vector weak forms - II 16m
12.04. The time-discretized equations 23m
12.05. Stability - I12m
12.06. Stability - II 14m
12.07. Behavior of higher-order modes 19m
12.08. Convergence 24m
12.08c. In-Video Correction 3m
1 practice exercise
Unit 12 Quiz4m
Week
13
19 minutes to complete

113

This is a wrap-up, with suggestions for future study....
1 video (Total 9 min), 1 reading
1 reading
Post-course Survey10m
4.7
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Top Reviews

By SSMar 13th 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.

By YWJun 21st 2018

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

Instructor

Avatar

Krishna Garikipati, Ph.D.

Professor of Mechanical Engineering, College of Engineering - Professor of Mathematics, College of Literature, Science and the Arts

About University of Michigan

The mission of the University of Michigan is to serve the people of Michigan and the world through preeminence in creating, communicating, preserving and applying knowledge, art, and academic values, and in developing leaders and citizens who will challenge the present and enrich the future....

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

  • You will need computing resources sufficient to install the code and run it. Depending on the type of installation this could be between a 13MB download of a tarred and gzipped file, to 45MB for a serial MacOSX binary and 192MB for a parallel MacOSX binary. Additionally, you will need a specific visualization program that we recommend. Altogether, if you have 1GB you should be fine. Alternately, you could download a Virtual Machine Interface.

  • You will be able to write code that simulates some of the most beautiful problems in physics, and visualize that physics.

  • You will need to know about matrices and vectors. Having seen partial differential equations will be very helpful. The code is in C++, but you don't need to know C++ at the outset. We will point you to resources that will teach you enough C++ for this class. However, you will need to have done some programming (Matlab, Fortran, C, Python, C++ should all do).

  • Apart from the lectures, expect to put in between 5 and 10 hours a week.

More questions? Visit the Learner Help Center.