课程信息
4.6
225 个评分
50 个审阅
100% 在线

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

可灵活调整截止日期

根据您的日程表重置截止日期。
中级

中级

完成时间(小时)

完成时间大约为25 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....
可选语言

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

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

可灵活调整截止日期

根据您的日程表重置截止日期。
中级

中级

完成时间(小时)

完成时间大约为25 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....
可选语言

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(小时)
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....
Reading
11 个视频 (总计 200 分钟), 2 个阅读材料, 1 个测验
Video11 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
Reading2 个阅读材料
Help us learn more about you!10分钟
"Paper and pencil" practice assignment on strong and weak forms
Quiz1 个练习
Unit 1 Quiz8分钟
2
完成时间(小时)
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....
Reading
14 个视频 (总计 202 分钟), 1 个测验
Video14 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
Quiz1 个练习
Unit 2 Quiz6分钟
3
完成时间(小时)
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....
Reading
14 个视频 (总计 213 分钟), 2 个测验
Video14 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
Quiz1 个练习
Unit 3 Quiz6分钟
4
完成时间(小时)
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....
Reading
17 个视频 (总计 262 分钟), 1 个测验
Video17 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
Quiz1 个练习
Unit 4 Quiz8分钟
4.6
50 个审阅Chevron Right

热门审阅

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 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....

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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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