Об этом курсе
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Прибл. 28 часа на выполнение

Предполагаемая нагрузка: 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....

Английский

Субтитры: Английский

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

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Прибл. 28 часа на выполнение

Предполагаемая нагрузка: 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....

Английский

Субтитры: Английский

Программа курса: что вы изучите

Неделя
1
6 ч. на завершение

1

This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method.

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11 видео ((всего 200 мин.)), 2 материалов для самостоятельного изучения, 1 тест
11 видео
01.02. Introduction. Linear elliptic partial differential equations - II 13мин
01.03. Boundary conditions 22мин
01.04. Constitutive relations 20мин
01.05. Strong form of the partial differential equation. Analytic solution 22мин
01.06. Weak form of the partial differential equation - I 12мин
01.07. Weak form of the partial differential equation - II 15мин
01.08. Equivalence between the strong and weak forms 24мин
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21мин
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19мин
01.08ct.3. Intro to C++ (pointers, iterators) 14мин
2 материала для самостоятельного изучения
Help us learn more about you!10мин
"Paper and pencil" practice assignment on strong and weak forms
1 практическое упражнение
Unit 1 Quiz8мин
Неделя
2
3 ч. на завершение

2

In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem.

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14 видео ((всего 202 мин.)), 1 тест
14 видео
02.01q. Response to a question 7мин
02.02. Basic Hilbert spaces - I 15мин
02.03. Basic Hilbert spaces - II 9мин
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22мин
02.04q. Response to a question 6мин
02.05. Basis functions - I 14мин
02.06. Basis functions - II 14мин
02.07. The bi-unit domain - I 11мин
02.08. The bi-unit domain - II 16мин
02.09. The finite dimensional weak form as a sum over element subdomains - I 16мин
02.10. The finite dimensional weak form as a sum over element subdomains - II 12мин
02.10ct.1. Intro to C++ (functions) 13мин
02.10ct.2. Intro to C++ (C++ classes) 16мин
1 практическое упражнение
Unit 2 Quiz6мин
Неделя
3
7 ч. на завершение

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.

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14 видео ((всего 213 мин.)), 2 тестов
14 видео
03.02. The matrix-vector weak form - I - II 17мин
03.03. The matrix-vector weak form - II - I 15мин
03.04. The matrix-vector weak form - II - II 13мин
03.05. The matrix-vector weak form - III - I 22мин
03.06. The matrix-vector weak form - III - II 13мин
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12мин
03.06ct.2. Intro to AWS, using AWS on Windows24мин
03.06ct.2c. In-Video Correction3мин
03.06ct.3. Using AWS on Linux and Mac OS7мин
03.07. The final finite element equations in matrix-vector form - I 22мин
03.08. The final finite element equations in matrix-vector form - II 18мин
03.08q. Response to a question 4мин
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19мин
1 практическое упражнение
Unit 3 Quiz6мин
Неделя
4
5 ч. на завершение

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.

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17 видео ((всего 262 мин.)), 1 тест
17 видео
04.02. The pure Dirichlet problem - II 17мин
04.02c. In-Video Correction 1мин
04.03. Higher polynomial order basis functions - I 23мин
04.03c0. In-Video Correction 57
04.03c1. In-Video Correction 34
04.04. Higher polynomial order basis functions - I - II 16мин
04.05. Higher polynomial order basis functions - II - I 13мин
04.06. Higher polynomial order basis functions - III 23мин
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14мин
04.07. The matrix-vector equations for quadratic basis functions - I - I 21мин
04.08. The matrix-vector equations for quadratic basis functions - I - II 11мин
04.09. The matrix-vector equations for quadratic basis functions - II - I 19мин
04.10. The matrix-vector equations for quadratic basis functions - II - II 24мин
04.11. Numerical integration -- Gaussian quadrature 13мин
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14мин
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26мин
1 практическое упражнение
Unit 4 Quiz8мин
Неделя
5
3 ч. на завершение

5

This unit outlines the mathematical analysis of the finite element method.

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12 видео ((всего 170 мин.)), 1 тест
12 видео
05.01c. In-Video Correction 56
05.01ct.1. Coding assignment 1 (functions: “solve” to “l2norm_of_error”) 10мин
05.01ct.2. Visualization tools7мин
05.02. Norms - II 18мин
05.02. Response to a question 5мин
05.03. Consistency of the finite element method 24мин
05.04. The best approximation property 21мин
05.05. The "Pythagorean Theorem" 13мин
05.05q. Response to a question 3мин
05.06. Sobolev estimates and convergence of the finite element method 23мин
05.07. Finite element error estimates 22мин
1 практическое упражнение
Unit 5 Quiz8мин
Неделя
6
1 ч. на завершение

6

This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems.

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4 видео ((всего 70 мин.)), 1 тест
4 видео
06.02. Functionals. Free energy - II 13мин
06.03. Extremization of functionals 18мин
06.04. Derivation of the weak form using a variational principle 20мин
1 практическое упражнение
Unit 6 Quiz4мин
Неделя
7
6 ч. на завершение

7

In this unit, we develop the finite element method for three-dimensional scalar problems, such as the heat conduction or mass diffusion problems.

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24 видео ((всего 322 мин.)), 1 тест
24 видео
07.02. The strong form of steady state heat conduction and mass diffusion - II 19мин
07.02q. Response to a question 1мин
07.03. The strong form, continued 19мин
07.03c. In-Video Correction 42
07.04. The weak form 24мин
07.05. The finite-dimensional weak form - I 12мин
07.06. The finite-dimensional weak form - II 15мин
07.07. Three-dimensional hexahedral finite elements 21мин
07.08. Aside: Insight to the basis functions by considering the two-dimensional case 17мин
07.08c In-Video Correction 44
07.09. Field derivatives. The Jacobian - I 12мин
07.10. Field derivatives. The Jacobian - II 14мин
07.11. The integrals in terms of degrees of freedom 16мин
07.12. The integrals in terms of degrees of freedom - continued 20мин
07.13. The matrix-vector weak form - I 17мин
07.14. The matrix-vector weak form II 11мин
07.15.The matrix-vector weak form, continued - I 17мин
07.15c. In-Video Correction 1мин
07.16. The matrix-vector weak form, continued - II 16мин
07.17. The matrix vector weak form, continued further - I 17мин
07.17c. In-Video Correction 47
07.18. The matrix-vector weak form, continued further - II 20мин
07.18c. In-Video Correction 3мин
1 практическое упражнение
Unit 7 Quiz10мин
Неделя
8
5 ч. на завершение

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.

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9 видео ((всего 108 мин.)), 2 тестов
9 видео
08.01c. In-Video Correction 1мин
08.02. Lagrange basis functions in 1 through 3 dimensions - II 12мин
08.02ct. Coding assignment 2 (2D problem) - I 13мин
08.03. Quadrature rules in 1 through 3 dimensions 17мин
08.03ct.1. Coding assignment 2 (2D problem) - II 13мин
08.03ct.2. Coding assignment 2 (3D problem) 6мин
08.04. Triangular and tetrahedral elements - Linears - I 6мин
08.05. Triangular and tetrahedral elements - Linears - II 16мин
1 практическое упражнение
Unit 8 Quiz6мин
Неделя
9
1 ч. на завершение

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.

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6 видео ((всего 73 мин.)), 1 тест
6 видео
09.02. The finite-dimensional weak form and basis functions - II 19мин
09.03. The matrix-vector weak form 19мин
09.03c. In-Video Correction 38
09.04. The matrix-vector weak form - II 11мин
09.04c. In-Video Correction 1мин
1 практическое упражнение
Unit 9 Quiz4мин
Неделя
10
8 ч. на завершение

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.

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22 видео ((всего 306 мин.)), 2 тестов
22 видео
10.02. The strong form of linearized elasticity in three dimensions - II 17мин
10.02c. In-Video Correction 1мин
10.03. The strong form, continued 23мин
10.04. The constitutive relations of linearized elasticity 21мин
10.05. The weak form - I 17мин
10.05q. Response to a question 7мин
10.06. The weak form - II 20мин
10.07. The finite-dimensional weak form - Basis functions - I 18мин
10.08. The finite-dimensional weak form - Basis functions - II 9мин
10.09. Element integrals - I 20мин
10.09c. In-Video Correction 53
10.10. Element integrals - II 6мин
10.11. The matrix-vector weak form - I 19мин
10.12. The matrix-vector weak form - II 12мин
10.13. Assembly of the global matrix-vector equations - I 20мин
10.14. Assembly of the global matrix-vector equations - II 9мин
10.14c. In Video Correction 2мин
10.14ct.1. Coding assignment 3 - I 10мин
10.14ct.2. Coding assignment 3 - II 19мин
10.15. Dirichlet boundary conditions - I 21мин
10.16. Dirichlet boundary conditions - II 13мин
1 практическое упражнение
Unit 10 Quiz8мин
Неделя
11
9 ч. на завершение

11

In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation.

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27 видео ((всего 378 мин.)), 2 тестов
27 видео
11.01c In-Video Correction 43
11.02. The weak form, and finite-dimensional weak form - I 18мин
11.03. The weak form, and finite-dimensional weak form - II 10мин
11.04. Basis functions, and the matrix-vector weak form - I 19мин
11.04c In-Video Correction 44
11.05. Basis functions, and the matrix-vector weak form - II 12мин
11.05. Response to a question 51
11.06. Dirichlet boundary conditions; the final matrix-vector equations 16мин
11.07. Time discretization; the Euler family - I 22мин
11.08. Time discretization; the Euler family - II 9мин
11.09. The v-form and d-form 20мин
11.09ct.1. Coding assignment 4 - I 11мин
11.09ct.2. Coding assignment 4 - II 13мин
11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I 17мин
11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II 14мин
11.11c. In-Video Correction 1мин
11.12. Modal decomposition and modal equations - I 16мин
11.13. Modal decomposition and modal equations - II 16мин
11.14. Modal equations and stability of the time-exact single degree of freedom systems - I 10мин
11.15. Modal equations and stability of the time-exact single degree of freedom systems - II 17мин
11.15q. Response to a question 10мин
11.16. Stability of the time-discrete single degree of freedom systems 23мин
11.17. Behavior of higher-order modes; consistency - I 18мин
11.18. Behavior of higher-order modes; consistency - II 19мин
11.19. Convergence - I 20мин
11.20. Convergence - II 16мин
1 практическое упражнение
Unit 11 Quiz8мин
Неделя
12
2 ч. на завершение

12

In this unit we study the problem of elastodynamics, and its finite element formulation.

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9 видео ((всего 141 мин.)), 1 тест
9 видео
12.02. The finite-dimensional and matrix-vector weak forms - I 10мин
12.03. The finite-dimensional and matrix-vector weak forms - II 16мин
12.04. The time-discretized equations 23мин
12.05. Stability - I12мин
12.06. Stability - II 14мин
12.07. Behavior of higher-order modes 19мин
12.08. Convergence 24мин
12.08c. In-Video Correction 3мин
1 практическое упражнение
Unit 12 Quiz4мин
Неделя
13
19 минуты на завершение

113

This is a wrap-up, with suggestions for future study.

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1 видео ((всего 9 мин.)), 1 материал для самостоятельного изучения
1 видео
1 материал для самостоятельного изучения
Post-course Survey10мин
4.7
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Лучшие отзывы о курсе Метод конечных элементов для решения задач в области физики

автор: 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.

автор: YWJun 21st 2018

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

Преподаватели

Avatar

Krishna Garikipati, Ph.D.

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

О Мичиганский университет

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....

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  • Зарегистрировавшись на сертификацию, вы получите доступ ко всем видео, тестам и заданиям по программированию (если они предусмотрены). Задания по взаимной оценке сокурсниками можно сдавать и проверять только после начала сессии. Если вы проходите курс без оплаты, некоторые задания могут быть недоступны.

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  • 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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