课程信息
41,320 次近期查看

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

中级

完成时间大约为28 小时

建议: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....

英语(English)

字幕:英语(English)

您将获得的技能

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

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

中级

完成时间大约为28 小时

建议: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....

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间为 6 小时

1

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

...
11 个视频 (总计 200 分钟), 2 个阅读材料, 1 个测验
11 个视频
01.02. Introduction. Linear elliptic partial differential equations - II 13分钟
01.03. Boundary conditions 22分钟
01.04. Constitutive relations 20分钟
01.05. Strong form of the partial differential equation. Analytic solution 22分钟
01.06. Weak form of the partial differential equation - I 12分钟
01.07. Weak form of the partial differential equation - II 15分钟
01.08. Equivalence between the strong and weak forms 24分钟
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21分钟
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19分钟
01.08ct.3. Intro to C++ (pointers, iterators) 14分钟
2 个阅读材料
Help us learn more about you!10分钟
"Paper and pencil" practice assignment on strong and weak forms2小时
1 个练习
Unit 1 Quiz8分钟
2
完成时间为 3 小时

2

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

...
14 个视频 (总计 202 分钟), 1 个测验
14 个视频
02.01q. Response to a question 7分钟
02.02. Basic Hilbert spaces - I 15分钟
02.03. Basic Hilbert spaces - II 9分钟
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22分钟
02.04q. Response to a question 6分钟
02.05. Basis functions - I 14分钟
02.06. Basis functions - II 14分钟
02.07. The bi-unit domain - I 11分钟
02.08. The bi-unit domain - II 16分钟
02.09. The finite dimensional weak form as a sum over element subdomains - I 16分钟
02.10. The finite dimensional weak form as a sum over element subdomains - II 12分钟
02.10ct.1. Intro to C++ (functions) 13分钟
02.10ct.2. Intro to C++ (C++ classes) 16分钟
1 个练习
Unit 2 Quiz6分钟
3
完成时间为 7 小时

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 个视频 (总计 213 分钟), 2 个测验
14 个视频
03.02. The matrix-vector weak form - I - II 17分钟
03.03. The matrix-vector weak form - II - I 15分钟
03.04. The matrix-vector weak form - II - II 13分钟
03.05. The matrix-vector weak form - III - I 22分钟
03.06. The matrix-vector weak form - III - II 13分钟
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12分钟
03.06ct.2. Intro to AWS, using AWS on Windows24分钟
03.06ct.2c. In-Video Correction3分钟
03.06ct.3. Using AWS on Linux and Mac OS7分钟
03.07. The final finite element equations in matrix-vector form - I 22分钟
03.08. The final finite element equations in matrix-vector form - II 18分钟
03.08q. Response to a question 4分钟
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19分钟
1 个练习
Unit 3 Quiz6分钟
4
完成时间为 5 小时

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 个视频 (总计 262 分钟), 1 个测验
17 个视频
04.02. The pure Dirichlet problem - II 17分钟
04.02c. In-Video Correction 1分钟
04.03. Higher polynomial order basis functions - I 23分钟
04.03c0. In-Video Correction 57
04.03c1. In-Video Correction 34
04.04. Higher polynomial order basis functions - I - II 16分钟
04.05. Higher polynomial order basis functions - II - I 13分钟
04.06. Higher polynomial order basis functions - III 23分钟
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14分钟
04.07. The matrix-vector equations for quadratic basis functions - I - I 21分钟
04.08. The matrix-vector equations for quadratic basis functions - I - II 11分钟
04.09. The matrix-vector equations for quadratic basis functions - II - I 19分钟
04.10. The matrix-vector equations for quadratic basis functions - II - II 24分钟
04.11. Numerical integration -- Gaussian quadrature 13分钟
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14分钟
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26分钟
1 个练习
Unit 4 Quiz8分钟
5
完成时间为 3 小时

5

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

...
12 个视频 (总计 170 分钟), 1 个测验
12 个视频
05.01c. In-Video Correction 56
05.01ct.1. Coding assignment 1 (functions: “solve” to “l2norm_of_error”) 10分钟
05.01ct.2. Visualization tools7分钟
05.02. Norms - II 18分钟
05.02. Response to a question 5分钟
05.03. Consistency of the finite element method 24分钟
05.04. The best approximation property 21分钟
05.05. The "Pythagorean Theorem" 13分钟
05.05q. Response to a question 3分钟
05.06. Sobolev estimates and convergence of the finite element method 23分钟
05.07. Finite element error estimates 22分钟
1 个练习
Unit 5 Quiz8分钟
6
完成时间为 1 小时

6

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

...
4 个视频 (总计 70 分钟), 1 个测验
4 个视频
06.02. Functionals. Free energy - II 13分钟
06.03. Extremization of functionals 18分钟
06.04. Derivation of the weak form using a variational principle 20分钟
1 个练习
Unit 6 Quiz4分钟
7
完成时间为 6 小时

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 个视频 (总计 322 分钟), 1 个测验
24 个视频
07.02. The strong form of steady state heat conduction and mass diffusion - II 19分钟
07.02q. Response to a question 1分钟
07.03. The strong form, continued 19分钟
07.03c. In-Video Correction 42
07.04. The weak form 24分钟
07.05. The finite-dimensional weak form - I 12分钟
07.06. The finite-dimensional weak form - II 15分钟
07.07. Three-dimensional hexahedral finite elements 21分钟
07.08. Aside: Insight to the basis functions by considering the two-dimensional case 17分钟
07.08c In-Video Correction 44
07.09. Field derivatives. The Jacobian - I 12分钟
07.10. Field derivatives. The Jacobian - II 14分钟
07.11. The integrals in terms of degrees of freedom 16分钟
07.12. The integrals in terms of degrees of freedom - continued 20分钟
07.13. The matrix-vector weak form - I 17分钟
07.14. The matrix-vector weak form II 11分钟
07.15.The matrix-vector weak form, continued - I 17分钟
07.15c. In-Video Correction 1分钟
07.16. The matrix-vector weak form, continued - II 16分钟
07.17. The matrix vector weak form, continued further - I 17分钟
07.17c. In-Video Correction 47
07.18. The matrix-vector weak form, continued further - II 20分钟
07.18c. In-Video Correction 3分钟
1 个练习
Unit 7 Quiz10分钟
8
完成时间为 5 小时

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 个视频 (总计 108 分钟), 2 个测验
9 个视频
08.01c. In-Video Correction 1分钟
08.02. Lagrange basis functions in 1 through 3 dimensions - II 12分钟
08.02ct. Coding assignment 2 (2D problem) - I 13分钟
08.03. Quadrature rules in 1 through 3 dimensions 17分钟
08.03ct.1. Coding assignment 2 (2D problem) - II 13分钟
08.03ct.2. Coding assignment 2 (3D problem) 6分钟
08.04. Triangular and tetrahedral elements - Linears - I 6分钟
08.05. Triangular and tetrahedral elements - Linears - II 16分钟
1 个练习
Unit 8 Quiz6分钟
9
完成时间为 1 小时

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 个视频 (总计 73 分钟), 1 个测验
6 个视频
09.02. The finite-dimensional weak form and basis functions - II 19分钟
09.03. The matrix-vector weak form 19分钟
09.03c. In-Video Correction 38
09.04. The matrix-vector weak form - II 11分钟
09.04c. In-Video Correction 1分钟
1 个练习
Unit 9 Quiz4分钟
10
完成时间为 8 小时

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 个视频 (总计 306 分钟), 2 个测验
22 个视频
10.02. The strong form of linearized elasticity in three dimensions - II 17分钟
10.02c. In-Video Correction 1分钟
10.03. The strong form, continued 23分钟
10.04. The constitutive relations of linearized elasticity 21分钟
10.05. The weak form - I 17分钟
10.05q. Response to a question 7分钟
10.06. The weak form - II 20分钟
10.07. The finite-dimensional weak form - Basis functions - I 18分钟
10.08. The finite-dimensional weak form - Basis functions - II 9分钟
10.09. Element integrals - I 20分钟
10.09c. In-Video Correction 53
10.10. Element integrals - II 6分钟
10.11. The matrix-vector weak form - I 19分钟
10.12. The matrix-vector weak form - II 12分钟
10.13. Assembly of the global matrix-vector equations - I 20分钟
10.14. Assembly of the global matrix-vector equations - II 9分钟
10.14c. In Video Correction 2分钟
10.14ct.1. Coding assignment 3 - I 10分钟
10.14ct.2. Coding assignment 3 - II 19分钟
10.15. Dirichlet boundary conditions - I 21分钟
10.16. Dirichlet boundary conditions - II 13分钟
1 个练习
Unit 10 Quiz8分钟
11
完成时间为 9 小时

11

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

...
27 个视频 (总计 378 分钟), 2 个测验
27 个视频
11.01c In-Video Correction 43
11.02. The weak form, and finite-dimensional weak form - I 18分钟
11.03. The weak form, and finite-dimensional weak form - II 10分钟
11.04. Basis functions, and the matrix-vector weak form - I 19分钟
11.04c In-Video Correction 44
11.05. Basis functions, and the matrix-vector weak form - II 12分钟
11.05. Response to a question 51
11.06. Dirichlet boundary conditions; the final matrix-vector equations 16分钟
11.07. Time discretization; the Euler family - I 22分钟
11.08. Time discretization; the Euler family - II 9分钟
11.09. The v-form and d-form 20分钟
11.09ct.1. Coding assignment 4 - I 11分钟
11.09ct.2. Coding assignment 4 - II 13分钟
11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I 17分钟
11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II 14分钟
11.11c. In-Video Correction 1分钟
11.12. Modal decomposition and modal equations - I 16分钟
11.13. Modal decomposition and modal equations - II 16分钟
11.14. Modal equations and stability of the time-exact single degree of freedom systems - I 10分钟
11.15. Modal equations and stability of the time-exact single degree of freedom systems - II 17分钟
11.15q. Response to a question 10分钟
11.16. Stability of the time-discrete single degree of freedom systems 23分钟
11.17. Behavior of higher-order modes; consistency - I 18分钟
11.18. Behavior of higher-order modes; consistency - II 19分钟
11.19. Convergence - I 20分钟
11.20. Convergence - II 16分钟
1 个练习
Unit 11 Quiz8分钟
12
完成时间为 2 小时

12

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

...
9 个视频 (总计 141 分钟), 1 个测验
9 个视频
12.02. The finite-dimensional and matrix-vector weak forms - I 10分钟
12.03. The finite-dimensional and matrix-vector weak forms - II 16分钟
12.04. The time-discretized equations 23分钟
12.05. Stability - I12分钟
12.06. Stability - II 14分钟
12.07. Behavior of higher-order modes 19分钟
12.08. Convergence 24分钟
12.08c. In-Video Correction 3分钟
1 个练习
Unit 12 Quiz4分钟
13
完成时间为 19 分钟

113

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

...
1 个视频 (总计 9 分钟), 1 个阅读材料
1 个视频
1 个阅读材料
Post-course Survey10分钟
4.7
58 个审阅Chevron Right

67%

完成这些课程后已开始新的职业生涯

67%

通过此课程获得实实在在的工作福利

来自有限元法在物理问题中的应用的热门评论

创建者 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.

创建者 YWJun 21st 2018

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

讲师

Avatar

Krishna Garikipati, Ph.D.

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

关于 密歇根大学

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....

常见问题

  • 注册以便获得证书后,您将有权访问所有视频、测验和编程作业(如果适用)。只有在您的班次开课之后,才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程,可能无法访问某些作业。

  • 您购买证书后,将有权访问所有课程材料,包括评分作业。完成课程后,您的电子课程证书将添加到您的成就页中,您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容,可以免费旁听课程。

  • 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.

还有其他问题吗?请访问 学生帮助中心