Informações sobre o curso
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Aprox. 28 horas para completar

Sugerido: 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....

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Habilidades que você terá

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

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Prazos flexíveis

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Nível intermediário

Aprox. 28 horas para completar

Sugerido: 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....

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Programa - O que você aprenderá com este curso

Semana
1
6 horas para concluir

1

This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method....
11 vídeos (total de (Total 200 mín.) min), 2 leituras, 1 teste
11 videos
01.02. Introduction. Linear elliptic partial differential equations - II 13min
01.03. Boundary conditions 22min
01.04. Constitutive relations 20min
01.05. Strong form of the partial differential equation. Analytic solution 22min
01.06. Weak form of the partial differential equation - I 12min
01.07. Weak form of the partial differential equation - II 15min
01.08. Equivalence between the strong and weak forms 24min
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21min
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19min
01.08ct.3. Intro to C++ (pointers, iterators) 14min
2 leituras
Help us learn more about you!10min
"Paper and pencil" practice assignment on strong and weak formss
1 exercício prático
Unit 1 Quiz8min
Semana
2
3 horas para concluir

2

In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem....
14 vídeos (total de (Total 202 mín.) min), 1 teste
14 videos
02.01q. Response to a question 7min
02.02. Basic Hilbert spaces - I 15min
02.03. Basic Hilbert spaces - II 9min
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22min
02.04q. Response to a question 6min
02.05. Basis functions - I 14min
02.06. Basis functions - II 14min
02.07. The bi-unit domain - I 11min
02.08. The bi-unit domain - II 16min
02.09. The finite dimensional weak form as a sum over element subdomains - I 16min
02.10. The finite dimensional weak form as a sum over element subdomains - II 12min
02.10ct.1. Intro to C++ (functions) 13min
02.10ct.2. Intro to C++ (C++ classes) 16min
1 exercício prático
Unit 2 Quiz6min
Semana
3
7 horas para concluir

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 vídeos (total de (Total 213 mín.) min), 2 testes
14 videos
03.02. The matrix-vector weak form - I - II 17min
03.03. The matrix-vector weak form - II - I 15min
03.04. The matrix-vector weak form - II - II 13min
03.05. The matrix-vector weak form - III - I 22min
03.06. The matrix-vector weak form - III - II 13min
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12min
03.06ct.2. Intro to AWS, using AWS on Windows24min
03.06ct.2c. In-Video Correction3min
03.06ct.3. Using AWS on Linux and Mac OS7min
03.07. The final finite element equations in matrix-vector form - I 22min
03.08. The final finite element equations in matrix-vector form - II 18min
03.08q. Response to a question 4min
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19min
1 exercício prático
Unit 3 Quiz6min
Semana
4
5 horas para concluir

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 vídeos (total de (Total 262 mín.) min), 1 teste
17 videos
04.02. The pure Dirichlet problem - II 17min
04.02c. In-Video Correction 1min
04.03. Higher polynomial order basis functions - I 23min
04.03c0. In-Video Correction 57s
04.03c1. In-Video Correction 34s
04.04. Higher polynomial order basis functions - I - II 16min
04.05. Higher polynomial order basis functions - II - I 13min
04.06. Higher polynomial order basis functions - III 23min
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14min
04.07. The matrix-vector equations for quadratic basis functions - I - I 21min
04.08. The matrix-vector equations for quadratic basis functions - I - II 11min
04.09. The matrix-vector equations for quadratic basis functions - II - I 19min
04.10. The matrix-vector equations for quadratic basis functions - II - II 24min
04.11. Numerical integration -- Gaussian quadrature 13min
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14min
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26min
1 exercício prático
Unit 4 Quiz8min
Semana
5
3 horas para concluir

5

This unit outlines the mathematical analysis of the finite element method....
12 vídeos (total de (Total 170 mín.) min), 1 teste
12 videos
05.01c. In-Video Correction 56s
05.01ct.1. Coding assignment 1 (functions: “solve” to “l2norm_of_error”) 10min
05.01ct.2. Visualization tools7min
05.02. Norms - II 18min
05.02. Response to a question 5min
05.03. Consistency of the finite element method 24min
05.04. The best approximation property 21min
05.05. The "Pythagorean Theorem" 13min
05.05q. Response to a question 3min
05.06. Sobolev estimates and convergence of the finite element method 23min
05.07. Finite element error estimates 22min
1 exercício prático
Unit 5 Quiz8min
Semana
6
1 hora para concluir

6

This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems....
4 vídeos (total de (Total 70 mín.) min), 1 teste
4 videos
06.02. Functionals. Free energy - II 13min
06.03. Extremization of functionals 18min
06.04. Derivation of the weak form using a variational principle 20min
1 exercício prático
Unit 6 Quiz4min
Semana
7
6 horas para concluir

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 vídeos (total de (Total 322 mín.) min), 1 teste
24 videos
07.02. The strong form of steady state heat conduction and mass diffusion - II 19min
07.02q. Response to a question 1min
07.03. The strong form, continued 19min
07.03c. In-Video Correction 42s
07.04. The weak form 24min
07.05. The finite-dimensional weak form - I 12min
07.06. The finite-dimensional weak form - II 15min
07.07. Three-dimensional hexahedral finite elements 21min
07.08. Aside: Insight to the basis functions by considering the two-dimensional case 17min
07.08c In-Video Correction 44s
07.09. Field derivatives. The Jacobian - I 12min
07.10. Field derivatives. The Jacobian - II 14min
07.11. The integrals in terms of degrees of freedom 16min
07.12. The integrals in terms of degrees of freedom - continued 20min
07.13. The matrix-vector weak form - I 17min
07.14. The matrix-vector weak form II 11min
07.15.The matrix-vector weak form, continued - I 17min
07.15c. In-Video Correction 1min
07.16. The matrix-vector weak form, continued - II 16min
07.17. The matrix vector weak form, continued further - I 17min
07.17c. In-Video Correction 47s
07.18. The matrix-vector weak form, continued further - II 20min
07.18c. In-Video Correction 3min
1 exercício prático
Unit 7 Quiz10min
Semana
8
5 horas para concluir

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 vídeos (total de (Total 108 mín.) min), 2 testes
9 videos
08.01c. In-Video Correction 1min
08.02. Lagrange basis functions in 1 through 3 dimensions - II 12min
08.02ct. Coding assignment 2 (2D problem) - I 13min
08.03. Quadrature rules in 1 through 3 dimensions 17min
08.03ct.1. Coding assignment 2 (2D problem) - II 13min
08.03ct.2. Coding assignment 2 (3D problem) 6min
08.04. Triangular and tetrahedral elements - Linears - I 6min
08.05. Triangular and tetrahedral elements - Linears - II 16min
1 exercício prático
Unit 8 Quiz6min
Semana
9
1 hora para concluir

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 vídeos (total de (Total 73 mín.) min), 1 teste
6 videos
09.02. The finite-dimensional weak form and basis functions - II 19min
09.03. The matrix-vector weak form 19min
09.03c. In-Video Correction 38s
09.04. The matrix-vector weak form - II 11min
09.04c. In-Video Correction 1min
1 exercício prático
Unit 9 Quiz4min
Semana
10
8 horas para concluir

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 vídeos (total de (Total 306 mín.) min), 2 testes
22 videos
10.02. The strong form of linearized elasticity in three dimensions - II 17min
10.02c. In-Video Correction 1min
10.03. The strong form, continued 23min
10.04. The constitutive relations of linearized elasticity 21min
10.05. The weak form - I 17min
10.05q. Response to a question 7min
10.06. The weak form - II 20min
10.07. The finite-dimensional weak form - Basis functions - I 18min
10.08. The finite-dimensional weak form - Basis functions - II 9min
10.09. Element integrals - I 20min
10.09c. In-Video Correction 53s
10.10. Element integrals - II 6min
10.11. The matrix-vector weak form - I 19min
10.12. The matrix-vector weak form - II 12min
10.13. Assembly of the global matrix-vector equations - I 20min
10.14. Assembly of the global matrix-vector equations - II 9min
10.14c. In Video Correction 2min
10.14ct.1. Coding assignment 3 - I 10min
10.14ct.2. Coding assignment 3 - II 19min
10.15. Dirichlet boundary conditions - I 21min
10.16. Dirichlet boundary conditions - II 13min
1 exercício prático
Unit 10 Quiz8min
Semana
11
9 horas para concluir

11

In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation....
27 vídeos (total de (Total 378 mín.) min), 2 testes
27 videos
11.01c In-Video Correction 43s
11.02. The weak form, and finite-dimensional weak form - I 18min
11.03. The weak form, and finite-dimensional weak form - II 10min
11.04. Basis functions, and the matrix-vector weak form - I 19min
11.04c In-Video Correction 44s
11.05. Basis functions, and the matrix-vector weak form - II 12min
11.05. Response to a question 51s
11.06. Dirichlet boundary conditions; the final matrix-vector equations 16min
11.07. Time discretization; the Euler family - I 22min
11.08. Time discretization; the Euler family - II 9min
11.09. The v-form and d-form 20min
11.09ct.1. Coding assignment 4 - I 11min
11.09ct.2. Coding assignment 4 - II 13min
11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I 17min
11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II 14min
11.11c. In-Video Correction 1min
11.12. Modal decomposition and modal equations - I 16min
11.13. Modal decomposition and modal equations - II 16min
11.14. Modal equations and stability of the time-exact single degree of freedom systems - I 10min
11.15. Modal equations and stability of the time-exact single degree of freedom systems - II 17min
11.15q. Response to a question 10min
11.16. Stability of the time-discrete single degree of freedom systems 23min
11.17. Behavior of higher-order modes; consistency - I 18min
11.18. Behavior of higher-order modes; consistency - II 19min
11.19. Convergence - I 20min
11.20. Convergence - II 16min
1 exercício prático
Unit 11 Quiz8min
Semana
12
2 horas para concluir

12

In this unit we study the problem of elastodynamics, and its finite element formulation....
9 vídeos (total de (Total 141 mín.) min), 1 teste
9 videos
12.02. The finite-dimensional and matrix-vector weak forms - I 10min
12.03. The finite-dimensional and matrix-vector weak forms - II 16min
12.04. The time-discretized equations 23min
12.05. Stability - I12min
12.06. Stability - II 14min
12.07. Behavior of higher-order modes 19min
12.08. Convergence 24min
12.08c. In-Video Correction 3min
1 exercício prático
Unit 12 Quiz4min
Semana
13
19 minutos para concluir

113

This is a wrap-up, with suggestions for future study....
1 vídeo (total de (Total 9 mín.) min), 1 leitura
1 leituras
Post-course Survey10min
4.7
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comecei uma nova carreira após concluir estes cursos

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Melhores avaliações

por 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.

por YWJun 21st 2018

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

Instrutores

Avatar

Krishna Garikipati, Ph.D.

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

Sobre Universidade de 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....

Perguntas Frequentes – FAQ

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  • Quando você adquire o Certificado, ganha acesso a todo o material do curso, incluindo avaliações com nota atribuída. Após concluir o curso, seu Certificado eletrônico será adicionado à sua página de Participações e você poderá imprimi-lo ou adicioná-lo ao seu perfil no LinkedIn. Se quiser apenas ler e assistir o conteúdo do curso, você poderá frequentá-lo como ouvinte sem custo.

  • 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.

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