課程信息
4.6
219 個評分
50 個審閱
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中級

中級

完成時間(小時)

完成時間大約為24 小時

建議: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....
可選語言

英語(English)

字幕:英語(English)...

您將獲得的技能

Finite DifferencesC++C Sharp (C#) (Programming Language)Matrices
100% online

100% online

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為24 小時

建議: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....
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 6 小時

1

This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method....
Reading
11 個視頻(共 200 分鐘), 2 個閱讀材料, 1 個測驗
Video11 個視頻
01.02. Introduction. Linear elliptic partial differential equations - II 13分鐘
01.03. Boundary conditions 22分鐘
01.04. Constitutive relations 20分鐘
01.05. Strong form of the partial differential equation. Analytic solution 22分鐘
01.06. Weak form of the partial differential equation - I 12分鐘
01.07. Weak form of the partial differential equation - II 15分鐘
01.08. Equivalence between the strong and weak forms 24分鐘
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21分鐘
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19分鐘
01.08ct.3. Intro to C++ (pointers, iterators) 14分鐘
Reading2 個閱讀材料
Help us learn more about you!10分鐘
"Paper and pencil" practice assignment on strong and weak forms分鐘
Quiz1 個練習
Unit 1 Quiz8分鐘
2
完成時間(小時)
完成時間為 3 小時

2

In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem....
Reading
14 個視頻(共 202 分鐘), 1 個測驗
Video14 個視頻
02.01q. Response to a question 7分鐘
02.02. Basic Hilbert spaces - I 15分鐘
02.03. Basic Hilbert spaces - II 9分鐘
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22分鐘
02.04q. Response to a question 6分鐘
02.05. Basis functions - I 14分鐘
02.06. Basis functions - II 14分鐘
02.07. The bi-unit domain - I 11分鐘
02.08. The bi-unit domain - II 16分鐘
02.09. The finite dimensional weak form as a sum over element subdomains - I 16分鐘
02.10. The finite dimensional weak form as a sum over element subdomains - II 12分鐘
02.10ct.1. Intro to C++ (functions) 13分鐘
02.10ct.2. Intro to C++ (C++ classes) 16分鐘
Quiz1 個練習
Unit 2 Quiz6分鐘
3
完成時間(小時)
完成時間為 7 小時

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 個視頻(共 213 分鐘), 2 個測驗
Video14 個視頻
03.02. The matrix-vector weak form - I - II 17分鐘
03.03. The matrix-vector weak form - II - I 15分鐘
03.04. The matrix-vector weak form - II - II 13分鐘
03.05. The matrix-vector weak form - III - I 22分鐘
03.06. The matrix-vector weak form - III - II 13分鐘
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12分鐘
03.06ct.2. Intro to AWS, using AWS on Windows24分鐘
03.06ct.2c. In-Video Correction3分鐘
03.06ct.3. Using AWS on Linux and Mac OS7分鐘
03.07. The final finite element equations in matrix-vector form - I 22分鐘
03.08. The final finite element equations in matrix-vector form - II 18分鐘
03.08q. Response to a question 4分鐘
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19分鐘
Quiz1 個練習
Unit 3 Quiz6分鐘
4
完成時間(小時)
完成時間為 5 小時

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 個視頻(共 262 分鐘), 1 個測驗
Video17 個視頻
04.02. The pure Dirichlet problem - II 17分鐘
04.02c. In-Video Correction 1分鐘
04.03. Higher polynomial order basis functions - I 23分鐘
04.03c0. In-Video Correction 分鐘
04.03c1. In-Video Correction 分鐘
04.04. Higher polynomial order basis functions - I - II 16分鐘
04.05. Higher polynomial order basis functions - II - I 13分鐘
04.06. Higher polynomial order basis functions - III 23分鐘
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14分鐘
04.07. The matrix-vector equations for quadratic basis functions - I - I 21分鐘
04.08. The matrix-vector equations for quadratic basis functions - I - II 11分鐘
04.09. The matrix-vector equations for quadratic basis functions - II - I 19分鐘
04.10. The matrix-vector equations for quadratic basis functions - II - II 24分鐘
04.11. Numerical integration -- Gaussian quadrature 13分鐘
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14分鐘
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26分鐘
Quiz1 個練習
Unit 4 Quiz8分鐘
4.6
50 個審閱Chevron Right

熱門審閱

創建者 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.

創建者 YWJun 21st 2018

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

講師

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Krishna Garikipati, Ph.D.

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

關於 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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