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自分のスケジュールですぐに学習を始めてください。

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約28時間で修了

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

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

中級レベル

約28時間で修了

推奨: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....

英語

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シラバス - 本コースの学習内容

1
6時間で修了

1

This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method....
11件のビデオ (合計200分), 2 readings, 1 quiz
11件のビデオ
01.02. Introduction. Linear elliptic partial differential equations - II 13 分
01.03. Boundary conditions 22 分
01.04. Constitutive relations 20 分
01.05. Strong form of the partial differential equation. Analytic solution 22 分
01.06. Weak form of the partial differential equation - I 12 分
01.07. Weak form of the partial differential equation - II 15 分
01.08. Equivalence between the strong and weak forms 24 分
01.08ct.1. Intro to C++ (running your code, basic structure, number types, vectors) 21 分
01.08ct.2. Intro to C++ (conditional statements, “for” loops, scope) 19 分
01.08ct.3. Intro to C++ (pointers, iterators) 14 分
2件の学習用教材
Help us learn more about you!10 分
"Paper and pencil" practice assignment on strong and weak forms
1の練習問題
Unit 1 Quiz8 分
2
3時間で修了

2

In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem....
14件のビデオ (合計202分), 1 quiz
14件のビデオ
02.01q. Response to a question 7 分
02.02. Basic Hilbert spaces - I 15 分
02.03. Basic Hilbert spaces - II 9 分
02.04. The finite element method for the one-dimensional, linear, elliptic partial differential equation 22 分
02.04q. Response to a question 6 分
02.05. Basis functions - I 14 分
02.06. Basis functions - II 14 分
02.07. The bi-unit domain - I 11 分
02.08. The bi-unit domain - II 16 分
02.09. The finite dimensional weak form as a sum over element subdomains - I 16 分
02.10. The finite dimensional weak form as a sum over element subdomains - II 12 分
02.10ct.1. Intro to C++ (functions) 13 分
02.10ct.2. Intro to C++ (C++ classes) 16 分
1の練習問題
Unit 2 Quiz6 分
3
7時間で修了

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件のビデオ (合計213分), 2 quizzes
14件のビデオ
03.02. The matrix-vector weak form - I - II 17 分
03.03. The matrix-vector weak form - II - I 15 分
03.04. The matrix-vector weak form - II - II 13 分
03.05. The matrix-vector weak form - III - I 22 分
03.06. The matrix-vector weak form - III - II 13 分
03.06ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox12 分
03.06ct.2. Intro to AWS, using AWS on Windows24 分
03.06ct.2c. In-Video Correction3 分
03.06ct.3. Using AWS on Linux and Mac OS7 分
03.07. The final finite element equations in matrix-vector form - I 22 分
03.08. The final finite element equations in matrix-vector form - II 18 分
03.08q. Response to a question 4 分
03.08ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h) 19 分
1の練習問題
Unit 3 Quiz6 分
4
5時間で修了

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件のビデオ (合計262分), 1 quiz
17件のビデオ
04.02. The pure Dirichlet problem - II 17 分
04.02c. In-Video Correction 1 分
04.03. Higher polynomial order basis functions - I 23 分
04.03c0. In-Video Correction 57
04.03c1. In-Video Correction 34
04.04. Higher polynomial order basis functions - I - II 16 分
04.05. Higher polynomial order basis functions - II - I 13 分
04.06. Higher polynomial order basis functions - III 23 分
04.06ct. Coding assignment 1 (functions: class constructor to “basis_gradient”) 14 分
04.07. The matrix-vector equations for quadratic basis functions - I - I 21 分
04.08. The matrix-vector equations for quadratic basis functions - I - II 11 分
04.09. The matrix-vector equations for quadratic basis functions - II - I 19 分
04.10. The matrix-vector equations for quadratic basis functions - II - II 24 分
04.11. Numerical integration -- Gaussian quadrature 13 分
04.11ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”) 14 分
04.11ct.2. Coding assignment 1 (functions: “assemble_system”) 26 分
1の練習問題
Unit 4 Quiz8 分
5
3時間で修了

5

This unit outlines the mathematical analysis of the finite element method....
12件のビデオ (合計170分), 1 quiz
12件のビデオ
05.01c. In-Video Correction 56
05.01ct.1. Coding assignment 1 (functions: “solve” to “l2norm_of_error”) 10 分
05.01ct.2. Visualization tools7 分
05.02. Norms - II 18 分
05.02. Response to a question 5 分
05.03. Consistency of the finite element method 24 分
05.04. The best approximation property 21 分
05.05. The "Pythagorean Theorem" 13 分
05.05q. Response to a question 3 分
05.06. Sobolev estimates and convergence of the finite element method 23 分
05.07. Finite element error estimates 22 分
1の練習問題
Unit 5 Quiz8 分
6
1時間で修了

6

This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems....
4件のビデオ (合計70分), 1 quiz
4件のビデオ
06.02. Functionals. Free energy - II 13 分
06.03. Extremization of functionals 18 分
06.04. Derivation of the weak form using a variational principle 20 分
1の練習問題
Unit 6 Quiz4 分
7
6時間で修了

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件のビデオ (合計322分), 1 quiz
24件のビデオ
07.02. The strong form of steady state heat conduction and mass diffusion - II 19 分
07.02q. Response to a question 1 分
07.03. The strong form, continued 19 分
07.03c. In-Video Correction 42
07.04. The weak form 24 分
07.05. The finite-dimensional weak form - I 12 分
07.06. The finite-dimensional weak form - II 15 分
07.07. Three-dimensional hexahedral finite elements 21 分
07.08. Aside: Insight to the basis functions by considering the two-dimensional case 17 分
07.08c In-Video Correction 44
07.09. Field derivatives. The Jacobian - I 12 分
07.10. Field derivatives. The Jacobian - II 14 分
07.11. The integrals in terms of degrees of freedom 16 分
07.12. The integrals in terms of degrees of freedom - continued 20 分
07.13. The matrix-vector weak form - I 17 分
07.14. The matrix-vector weak form II 11 分
07.15.The matrix-vector weak form, continued - I 17 分
07.15c. In-Video Correction 1 分
07.16. The matrix-vector weak form, continued - II 16 分
07.17. The matrix vector weak form, continued further - I 17 分
07.17c. In-Video Correction 47
07.18. The matrix-vector weak form, continued further - II 20 分
07.18c. In-Video Correction 3 分
1の練習問題
Unit 7 Quiz10 分
8
5時間で修了

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件のビデオ (合計108分), 2 quizzes
9件のビデオ
08.01c. In-Video Correction 1 分
08.02. Lagrange basis functions in 1 through 3 dimensions - II 12 分
08.02ct. Coding assignment 2 (2D problem) - I 13 分
08.03. Quadrature rules in 1 through 3 dimensions 17 分
08.03ct.1. Coding assignment 2 (2D problem) - II 13 分
08.03ct.2. Coding assignment 2 (3D problem) 6 分
08.04. Triangular and tetrahedral elements - Linears - I 6 分
08.05. Triangular and tetrahedral elements - Linears - II 16 分
1の練習問題
Unit 8 Quiz6 分
9
1時間で修了

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件のビデオ (合計73分), 1 quiz
6件のビデオ
09.02. The finite-dimensional weak form and basis functions - II 19 分
09.03. The matrix-vector weak form 19 分
09.03c. In-Video Correction 38
09.04. The matrix-vector weak form - II 11 分
09.04c. In-Video Correction 1 分
1の練習問題
Unit 9 Quiz4 分
10
8時間で修了

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件のビデオ (合計306分), 2 quizzes
22件のビデオ
10.02. The strong form of linearized elasticity in three dimensions - II 17 分
10.02c. In-Video Correction 1 分
10.03. The strong form, continued 23 分
10.04. The constitutive relations of linearized elasticity 21 分
10.05. The weak form - I 17 分
10.05q. Response to a question 7 分
10.06. The weak form - II 20 分
10.07. The finite-dimensional weak form - Basis functions - I 18 分
10.08. The finite-dimensional weak form - Basis functions - II 9 分
10.09. Element integrals - I 20 分
10.09c. In-Video Correction 53
10.10. Element integrals - II 6 分
10.11. The matrix-vector weak form - I 19 分
10.12. The matrix-vector weak form - II 12 分
10.13. Assembly of the global matrix-vector equations - I 20 分
10.14. Assembly of the global matrix-vector equations - II 9 分
10.14c. In Video Correction 2 分
10.14ct.1. Coding assignment 3 - I 10 分
10.14ct.2. Coding assignment 3 - II 19 分
10.15. Dirichlet boundary conditions - I 21 分
10.16. Dirichlet boundary conditions - II 13 分
1の練習問題
Unit 10 Quiz8 分
11
9時間で修了

11

In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation....
27件のビデオ (合計378分), 2 quizzes
27件のビデオ
11.01c In-Video Correction 43
11.02. The weak form, and finite-dimensional weak form - I 18 分
11.03. The weak form, and finite-dimensional weak form - II 10 分
11.04. Basis functions, and the matrix-vector weak form - I 19 分
11.04c In-Video Correction 44
11.05. Basis functions, and the matrix-vector weak form - II 12 分
11.05. Response to a question 51
11.06. Dirichlet boundary conditions; the final matrix-vector equations 16 分
11.07. Time discretization; the Euler family - I 22 分
11.08. Time discretization; the Euler family - II 9 分
11.09. The v-form and d-form 20 分
11.09ct.1. Coding assignment 4 - I 11 分
11.09ct.2. Coding assignment 4 - II 13 分
11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I 17 分
11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II 14 分
11.11c. In-Video Correction 1 分
11.12. Modal decomposition and modal equations - I 16 分
11.13. Modal decomposition and modal equations - II 16 分
11.14. Modal equations and stability of the time-exact single degree of freedom systems - I 10 分
11.15. Modal equations and stability of the time-exact single degree of freedom systems - II 17 分
11.15q. Response to a question 10 分
11.16. Stability of the time-discrete single degree of freedom systems 23 分
11.17. Behavior of higher-order modes; consistency - I 18 分
11.18. Behavior of higher-order modes; consistency - II 19 分
11.19. Convergence - I 20 分
11.20. Convergence - II 16 分
1の練習問題
Unit 11 Quiz8 分
12
2時間で修了

12

In this unit we study the problem of elastodynamics, and its finite element formulation....
9件のビデオ (合計141分), 1 quiz
9件のビデオ
12.02. The finite-dimensional and matrix-vector weak forms - I 10 分
12.03. The finite-dimensional and matrix-vector weak forms - II 16 分
12.04. The time-discretized equations 23 分
12.05. Stability - I12 分
12.06. Stability - II 14 分
12.07. Behavior of higher-order modes 19 分
12.08. Convergence 24 分
12.08c. In-Video Correction 3 分
1の練習問題
Unit 12 Quiz4 分
13
19分で修了

113

This is a wrap-up, with suggestions for future study....
1件のビデオ (合計9分), 1 reading
1件のビデオ
1件の学習用教材
Post-course Survey10 分
4.7
58件のレビューChevron Right

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人気のレビュー

by 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.

by 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

ミシガン大学(University of Michigan)について

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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