À propos de ce cours
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Niveau intermédiaire

Approx. 27 heures pour terminer

Recommandé : 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....

Anglais

Sous-titres : Anglais

Compétences que vous acquerrez

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

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau intermédiaire

Approx. 27 heures pour terminer

Recommandé : 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....

Anglais

Sous-titres : Anglais

Programme du cours : ce que vous apprendrez dans ce cours

Semaine
1
6 heures pour terminer

1

This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method....
11 vidéos (Total 200 min), 2 lectures, 1 quiz
11 vidéos
01.02. Introduction. Linear elliptic partial differential equations - II 13 min
01.03. Boundary conditions 22 min
01.04. Constitutive relations 20 min
01.05. Strong form of the partial differential equation. Analytic solution 22 min
01.06. Weak form of the partial differential equation - I 12 min
01.07. Weak form of the partial differential equation - II 15 min
01.08. Equivalence between the strong and weak forms 24 min
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21 min
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19 min
01.08ct.3. Intro to C++ (pointers, iterators) 14 min
2 lectures
Help us learn more about you!10 min
"Paper and pencil" practice assignment on strong and weak formss
1 exercice pour s'entraîner
Unit 1 Quiz8 min
Semaine
2
3 heures pour terminer

2

In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem....
14 vidéos (Total 202 min), 1 quiz
14 vidéos
02.01q. Response to a question 7 min
02.02. Basic Hilbert spaces - I 15 min
02.03. Basic Hilbert spaces - II 9 min
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22 min
02.04q. Response to a question 6 min
02.05. Basis functions - I 14 min
02.06. Basis functions - II 14 min
02.07. The bi-unit domain - I 11 min
02.08. The bi-unit domain - II 16 min
02.09. The finite dimensional weak form as a sum over element subdomains - I 16 min
02.10. The finite dimensional weak form as a sum over element subdomains - II 12 min
02.10ct.1. Intro to C++ (functions) 13 min
02.10ct.2. Intro to C++ (C++ classes) 16 min
1 exercice pour s'entraîner
Unit 2 Quiz6 min
Semaine
3
7 heures pour terminer

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 vidéos (Total 213 min), 2 quiz
14 vidéos
03.02. The matrix-vector weak form - I - II 17 min
03.03. The matrix-vector weak form - II - I 15 min
03.04. The matrix-vector weak form - II - II 13 min
03.05. The matrix-vector weak form - III - I 22 min
03.06. The matrix-vector weak form - III - II 13 min
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12 min
03.06ct.2. Intro to AWS, using AWS on Windows24 min
03.06ct.2c. In-Video Correction3 min
03.06ct.3. Using AWS on Linux and Mac OS7 min
03.07. The final finite element equations in matrix-vector form - I 22 min
03.08. The final finite element equations in matrix-vector form - II 18 min
03.08q. Response to a question 4 min
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19 min
1 exercice pour s'entraîner
Unit 3 Quiz6 min
Semaine
4
5 heures pour terminer

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 vidéos (Total 262 min), 1 quiz
17 vidéos
04.02. The pure Dirichlet problem - II 17 min
04.02c. In-Video Correction 1 min
04.03. Higher polynomial order basis functions - I 23 min
04.03c0. In-Video Correction 57s
04.03c1. In-Video Correction 34s
04.04. Higher polynomial order basis functions - I - II 16 min
04.05. Higher polynomial order basis functions - II - I 13 min
04.06. Higher polynomial order basis functions - III 23 min
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14 min
04.07. The matrix-vector equations for quadratic basis functions - I - I 21 min
04.08. The matrix-vector equations for quadratic basis functions - I - II 11 min
04.09. The matrix-vector equations for quadratic basis functions - II - I 19 min
04.10. The matrix-vector equations for quadratic basis functions - II - II 24 min
04.11. Numerical integration -- Gaussian quadrature 13 min
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14 min
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26 min
1 exercice pour s'entraîner
Unit 4 Quiz8 min
Semaine
5
3 heures pour terminer

5

This unit outlines the mathematical analysis of the finite element method....
12 vidéos (Total 170 min), 1 quiz
12 vidéos
05.01c. In-Video Correction 56s
05.01ct.1. Coding assignment 1 (functions: “solve” to “l2norm_of_error”) 10 min
05.01ct.2. Visualization tools7 min
05.02. Norms - II 18 min
05.02. Response to a question 5 min
05.03. Consistency of the finite element method 24 min
05.04. The best approximation property 21 min
05.05. The "Pythagorean Theorem" 13 min
05.05q. Response to a question 3 min
05.06. Sobolev estimates and convergence of the finite element method 23 min
05.07. Finite element error estimates 22 min
1 exercice pour s'entraîner
Unit 5 Quiz8 min
Semaine
6
1 heure pour terminer

6

This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems....
4 vidéos (Total 70 min), 1 quiz
4 vidéos
06.02. Functionals. Free energy - II 13 min
06.03. Extremization of functionals 18 min
06.04. Derivation of the weak form using a variational principle 20 min
1 exercice pour s'entraîner
Unit 6 Quiz4 min
Semaine
7
6 heures pour terminer

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 vidéos (Total 322 min), 1 quiz
24 vidéos
07.02. The strong form of steady state heat conduction and mass diffusion - II 19 min
07.02q. Response to a question 1 min
07.03. The strong form, continued 19 min
07.03c. In-Video Correction 42s
07.04. The weak form 24 min
07.05. The finite-dimensional weak form - I 12 min
07.06. The finite-dimensional weak form - II 15 min
07.07. Three-dimensional hexahedral finite elements 21 min
07.08. Aside: Insight to the basis functions by considering the two-dimensional case 17 min
07.08c In-Video Correction 44s
07.09. Field derivatives. The Jacobian - I 12 min
07.10. Field derivatives. The Jacobian - II 14 min
07.11. The integrals in terms of degrees of freedom 16 min
07.12. The integrals in terms of degrees of freedom - continued 20 min
07.13. The matrix-vector weak form - I 17 min
07.14. The matrix-vector weak form II 11 min
07.15.The matrix-vector weak form, continued - I 17 min
07.15c. In-Video Correction 1 min
07.16. The matrix-vector weak form, continued - II 16 min
07.17. The matrix vector weak form, continued further - I 17 min
07.17c. In-Video Correction 47s
07.18. The matrix-vector weak form, continued further - II 20 min
07.18c. In-Video Correction 3 min
1 exercice pour s'entraîner
Unit 7 Quiz10 min
Semaine
8
5 heures pour terminer

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 vidéos (Total 108 min), 2 quiz
9 vidéos
08.01c. In-Video Correction 1 min
08.02. Lagrange basis functions in 1 through 3 dimensions - II 12 min
08.02ct. Coding assignment 2 (2D problem) - I 13 min
08.03. Quadrature rules in 1 through 3 dimensions 17 min
08.03ct.1. Coding assignment 2 (2D problem) - II 13 min
08.03ct.2. Coding assignment 2 (3D problem) 6 min
08.04. Triangular and tetrahedral elements - Linears - I 6 min
08.05. Triangular and tetrahedral elements - Linears - II 16 min
1 exercice pour s'entraîner
Unit 8 Quiz6 min
Semaine
9
1 heure pour terminer

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 vidéos (Total 73 min), 1 quiz
6 vidéos
09.02. The finite-dimensional weak form and basis functions - II 19 min
09.03. The matrix-vector weak form 19 min
09.03c. In-Video Correction 38s
09.04. The matrix-vector weak form - II 11 min
09.04c. In-Video Correction 1 min
1 exercice pour s'entraîner
Unit 9 Quiz4 min
Semaine
10
8 heures pour terminer

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 vidéos (Total 306 min), 2 quiz
22 vidéos
10.02. The strong form of linearized elasticity in three dimensions - II 17 min
10.02c. In-Video Correction 1 min
10.03. The strong form, continued 23 min
10.04. The constitutive relations of linearized elasticity 21 min
10.05. The weak form - I 17 min
10.05q. Response to a question 7 min
10.06. The weak form - II 20 min
10.07. The finite-dimensional weak form - Basis functions - I 18 min
10.08. The finite-dimensional weak form - Basis functions - II 9 min
10.09. Element integrals - I 20 min
10.09c. In-Video Correction 53s
10.10. Element integrals - II 6 min
10.11. The matrix-vector weak form - I 19 min
10.12. The matrix-vector weak form - II 12 min
10.13. Assembly of the global matrix-vector equations - I 20 min
10.14. Assembly of the global matrix-vector equations - II 9 min
10.14c. In Video Correction 2 min
10.14ct.1. Coding assignment 3 - I 10 min
10.14ct.2. Coding assignment 3 - II 19 min
10.15. Dirichlet boundary conditions - I 21 min
10.16. Dirichlet boundary conditions - II 13 min
1 exercice pour s'entraîner
Unit 10 Quiz8 min
Semaine
11
9 heures pour terminer

11

In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation....
27 vidéos (Total 378 min), 2 quiz
27 vidéos
11.01c In-Video Correction 43s
11.02. The weak form, and finite-dimensional weak form - I 18 min
11.03. The weak form, and finite-dimensional weak form - II 10 min
11.04. Basis functions, and the matrix-vector weak form - I 19 min
11.04c In-Video Correction 44s
11.05. Basis functions, and the matrix-vector weak form - II 12 min
11.05. Response to a question 51s
11.06. Dirichlet boundary conditions; the final matrix-vector equations 16 min
11.07. Time discretization; the Euler family - I 22 min
11.08. Time discretization; the Euler family - II 9 min
11.09. The v-form and d-form 20 min
11.09ct.1. Coding assignment 4 - I 11 min
11.09ct.2. Coding assignment 4 - II 13 min
11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I 17 min
11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II 14 min
11.11c. In-Video Correction 1 min
11.12. Modal decomposition and modal equations - I 16 min
11.13. Modal decomposition and modal equations - II 16 min
11.14. Modal equations and stability of the time-exact single degree of freedom systems - I 10 min
11.15. Modal equations and stability of the time-exact single degree of freedom systems - II 17 min
11.15q. Response to a question 10 min
11.16. Stability of the time-discrete single degree of freedom systems 23 min
11.17. Behavior of higher-order modes; consistency - I 18 min
11.18. Behavior of higher-order modes; consistency - II 19 min
11.19. Convergence - I 20 min
11.20. Convergence - II 16 min
1 exercice pour s'entraîner
Unit 11 Quiz8 min
Semaine
12
2 heures pour terminer

12

In this unit we study the problem of elastodynamics, and its finite element formulation....
9 vidéos (Total 141 min), 1 quiz
9 vidéos
12.02. The finite-dimensional and matrix-vector weak forms - I 10 min
12.03. The finite-dimensional and matrix-vector weak forms - II 16 min
12.04. The time-discretized equations 23 min
12.05. Stability - I12 min
12.06. Stability - II 14 min
12.07. Behavior of higher-order modes 19 min
12.08. Convergence 24 min
12.08c. In-Video Correction 3 min
1 exercice pour s'entraîner
Unit 12 Quiz4 min
Semaine
13
19 minutes pour terminer

113

This is a wrap-up, with suggestions for future study....
1 vidéo (Total 9 min), 1 lecture
1 lecture
Post-course Survey10 min
4.7
57 avisChevron Right

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a commencé une nouvelle carrière après avoir terminé ces cours

67%

a bénéficié d'un avantage concret dans sa carrière grâce à ce cours

Meilleurs avis

par 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.

par YWJun 21st 2018

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

Enseignant

Avatar

Krishna Garikipati, Ph.D.

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

À propos de Université du 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....

Foire Aux Questions

  • Une fois que vous êtes inscrit(e) pour un Certificat, vous pouvez accéder à toutes les vidéos de cours, et à tous les quiz et exercices de programmation (le cas échéant). Vous pouvez soumettre des devoirs à examiner par vos pairs et en examiner vous-même uniquement après le début de votre session. Si vous préférez explorer le cours sans l'acheter, vous ne serez peut-être pas en mesure d'accéder à certains devoirs.

  • Lorsque vous achetez un Certificat, vous bénéficiez d'un accès à tout le contenu du cours, y compris les devoirs notés. Lorsque vous avez terminé et réussi le cours, votre Certificat électronique est ajouté à votre page Accomplissements. À partir de cette page, vous pouvez imprimer votre Certificat ou l'ajouter à votre profil LinkedIn. Si vous souhaitez seulement lire et visualiser le contenu du cours, vous pouvez accéder gratuitement au cours en tant qu'auditeur libre.

  • 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.

D'autres questions ? Visitez le Centre d'Aide pour les Etudiants.