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【国外公开课】Finite Element Methods（密歇根大学Krishna Garikipati教授）

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2018-06-06 02:39:07

转自youtube的openmichigan频道，内容是关于有限元方法的共165集系列公开课，原作者为Krishna Garikipati教授。讲座内容详细覆盖了线性有限元理论的各个方面，有一定理论深度，且还部分涉及了dealii开源代码的使用，适合于想要进一步深入了解和应用有限元方法的同学。推荐结合Belytschko或者Hughes等人的著作进行学习。

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埋头读书…

01.01. Introduction, Linear Elliptic Partial Differential Equations (Part 1)

14:46

01.02. Introduction, Linear Elliptic Partial Differential Equations (Part 2)

13:01

01.03. Boundary Conditions

22:19

01.04. Constitutive relations

20:07

01.05. Strong Form of the Partial Differential Equation, Analytic Solution

22:45

01.06. Weak Form of the Partial Differential Equation (Part 1)

12:29

01.07. Weak Form of the Partial Differential Equation (Part 2)

15:05

01.08. Equivalence Between the Strong and Weak Forms (Part 1)

24:20

01.08ct. 1. Intro to C++ (Running Your Code, Basic Structure, Number Types, Vect

21:09

01.08ct. 2. Intro to C++ (Conditional Statements, _for_ Loops, Scope)

19:28

01.08ct. 3. Intro to C++ (Pointers, Iterators)

14:01

02.01. The Galerkin, or finite dimensional weak form

23:15

02.02. Basic Hilbert Spaces (Part 1)

15:52

02.03. Basic Hilbert Spaces (Part 2)

09:29

02.04. FEM for the One Dimensional, Linear Elliptic PDE

22:54

02.04. Response to a question

06:22

02.05. Basis Functions (Part 1)

14:56

02.06. Basis Functions (Part 2)

14:44

02.07. The Bi-Unit Domain (Part 1)

11:44

02.08. The Bi-Unit Domain (Part 2)

16:20

02.09. Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 1)

16:08

02.10. Finite Dimensional Weak Form as a Sum Over Element Subdomains (Part 2)

12:24

02.10ct. 1. Intro to C++ (Functions)

13:27

02.10ct. 2. Intro to C++ (C++ Classes)

16:44

03.01. The Matrix-Vector Weak Form - I (Part 1)

16:27

03.02. The Matrix-Vector Weak Form - I (Part 2)

17:45

03.03. The Matrix-Vector Weak Form - II (Part 1)

15:38

03.04. The Matrix-Vector Weak Form - II (Part 2)

13:52

03.05. The Matrix-Vector Weak Form - III (Part 1)

22:32

03.06. The Matrix-Vector Weak Form - III (Part 2)

13:23

03.06ct1 Dealii.org, Running Deal.II on a Virtual Machine with Oracle Virtualbox

13:00

03.06ct. 2. Intro to AWS; Using AWS on Windows

24:44

03.06ct2. Correction

03:32

03.06ct. 3. Using AWS on Linux and Mac OS

07:43

03.07. The Final Finite Element Equations in Matrix-Vector form (Part 1)

22:05

03.08. The Final Finite Element Equations in Matrix-Vector form (Part 2)

18:24

03.08. Response to a question

04:36

03.08ct Coding Assignment 1 (main1.cc, Overview of C++ Class in FEM1.h)

19:35

04.01. The Pure Dirichlet Problem (Part 1)

18:16

04.02. The Pure Dirichlet Problem (Part 2)

17:42

04.02. Correction to boardwork

01:01

04.03. Higher Polynomial Order Basis Functions - I

22:56

04.03. Correction to boardwork

00:58

04.04. Higher Polynomial Order Basis Functions - 1 (Part 2)

16:39

04.05. Higher Polynomial Order Basis Functions - II (Part 1)

13:39

04.06. Higher Polynomial Order Basis Functions - III

23:24

04.06ct. Coding Assignment 1 (Functions_ Class Constructor to

14:41

04.07. The Matrix Vector Equations for Quadratic Basis Functions - I (Part 1)

21:20

04.08. The Matrix Vector Equations for Quadratic Basis Functions - I (Part 2)

11:54

04.09. The Matrix Vector Equations for Quadratic Basis Functions - II (Part 1)

19:10

04.10. The Matrix Vector Equations for Quadratic Basis Functions - II (Part 2)

24:09

04.11. Numerical Integration -- Gaussian Quadrature

13:58

04.11ct. 1. Coding Assignment 1 (Functions_

14:22

04.11ct.2. Coding Assignment 1 (Functions_

26:59

05.01. Norms (Part 1)

18:23

05.01. Correction to boardwork

00:57

05.01ct. 1. Coding Assignment 1 (Functions_ _solve_ to _I2norm_of_error_)

10:58

05.01ct.2. Visualization Tools

07:18

05.02. Norms (Part 2)

18:22

05.02. Response to a question

05:46

05.03. Consistency of the Finite Element Method

24:28

05.04. The Best Approximation Property

21:33

05.05. The Pythagorean Theorem

13:15

05.05. Response to a question

03:32

05.06. Sobolev Estimates and Convergence of the Finite Element Method

23:51

05.07. Finite Element Error Estimates

22:08

06.01. Functionals, Free Energy (Part 1)

17:39

06.02. Functionals, Free Energy (Part 2)

13:21

06.03. Extremization of Functionals

18:31

06.04. Derivation of the Weak Form Using a Variational Principle

20:10

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