The integrals in terms of degrees of freedom (16:25), 07.12. Coding Assignment 4 - I (11:10), 11.09ct. Its development can be traced back to the work by A. Hrennikoff and R. Courant in the early 1940s. Field derivatives. The matrix-vector weak form - II - II (13:50), 03.05. The strong form, continued (23:54), 10.04. Boundary value problems are also called field problems. 1. Coding Assignment 1 (Functions: "generate_mesh" to "setup_system") (14:21), 04.11ct.2. The matrix-vector weak form - I - II (17:44), 03.03. Assembly of the global matrix-vector equations - I (20:40), 10.14. The finite-dimensional weak form - I (12:35), 07.06. The matrix-vector equations for quadratic basis functions - II - I (19:09), 04.10. 2. The matrix-vector weak form - I - I (16:26), 03.02. Much of the success of the Finite Element Method as a computational framework lies in the rigor of its mathematical foundation, and this needs to be appreciated, even if only in the elementary manner presented here. Intro to C++ (Running Your Code, Basic Structure, Number Types, Vectors) (21:09), 01.08ct. Articles about Massively Open Online Classes (MOOCs) had been rocking the academic world (at least gently), and it seemed that your writer had scarcely experimented with teaching methods. Then, with appropriate loadings, boundary, and initial conditions applied to the elements/nodes, the local element equations for all the finite elements are assembled together and solved Weak form of the partial differential equation - II (15:05), 01.08. Lagrange basis functions in 1 through 3 dimensions - I (18:58), 08.02. Taylor. Unit 05: Analysis of the finite element method. The strong form of linearized elasticity in three dimensions - I (09:58), 10.02. Functionals. It is hoped that these lectures on Finite Element Methods will complement the series on Continuum Physics to provide a point of departure from which the seasoned researcher or advanced graduate student can embark on work in (continuum) computational physics. Some of the key mathematical assumptions in the method (without going into detailed derivation) will be presented. Welcome to Finite Element Methods. Intro to C++ (C++ Classes) (16:43), 03.01. Quadrature rules in 1 through 3 dimensions (17:03), 08.03ct. I first had to take a detour through another subject, Continuum Physics, for which video lectures also are available, and whose recording in this format served as a trial run for the present series of lectures on Finite Element Methods. 1. Coding Assignment 2 (2D Problem) - II (13:50), 08.03ct. The finite-dimensional and matrix-vector weak forms - II (16:00), 12.04. The idea for an online version of Finite Element Methods first came a little more than a year ago. 1. The Galerkin, or finite-dimensional weak form (23:14), 02.04. 4.1.2 Principles of Finite Element Method. The strong form of steady state heat conduction and mass diffusion - I (18:24), 07.02. Three-dimensional hexahedral finite elements (21:30), 07.08. Triangular and tetrahedral elements - Linears - II (16:29), 09.01. Weak form of the partial differential equation - I (12:29), 01.07. Coding Assignment 03 Template, 11.09ct. Coding Assignment 1 (Functions: "assemble_system") (26:58), 05.01ct. Linear elliptic partial differential equations - II (13:01), 01.05. At each stage, however, we make numerous connections to the physical phenomena represented by the PDEs. Behavior of higher-order modes; consistency - I (18:57), 11.18. The field is the domain of interest and most often represents a physical structure. Triangular and tetrahedral elements - Linears - I (10:25), 08.05. There are a number of people that I need to thank: Shiva Rudraraju and Greg Teichert for their work on the coding framework, Tim O'Brien for organizing the recordings, Walter Lin and Alex Hancook for their camera work and post-production editing, and Scott Mahler for making the studios available. The matrix-vector weak form, continued further - II (17:18), 08.01. Introduction. Unit 02: Approximation. Strong form of the partial differential equation. Intro to C++ (Pointers, Iterators) (14:01), 02.01. From there to the video lectures that you are about to view took nearly a year. Modal equations and stability of the time-exact single degree of freedom systems - I (10:49), 11.15. Particularly compelling was the fact that there already had been some successes reported with computer programming classes in the online format, especially as MOOCs. Krishna Garikipati The constitutive relations of linearized elasticity (21:09), 10.07. Unit 03: Linear algebra; the matrix-vector form. basis functions defined within each subdomain. The weak form, and finite-dimensional weak form - II (10:15), 11.04. Dirichlet boundary conditions; the final matrix-vector equations (16:57), 11.07. The matrix-vector weak form - III - II (13:22), 03.06ct. At suitable points in the lectures, we interrupt the mathematical development to lay out the code framework, which is entirely open source, and C++ based. Equivalence between the strong and weak forms - 1 (25:10), 01.08ct. The matrix-vector weak form - I (17:19), 07.14. The finite-dimensional and matrix-vector weak forms - I (10:37), 12.03. The finite dimensional weak form as a sum over element subdomains - I (16:08), 02.10. 2. Then, the assembly of subdomains, which is based on the process of putting the finite elements back into their original positions, results in a discrete set of equations which are system of equations. Coding Assignment 2 (3D Problem), 08.04. During the finite element analysis, errors can be introduced due to the approximations of the domain discretization, the solutions of the element equations, and the solution of the assembled The treatment is mathematical, which is natural for a topic whose roots lie deep in functional analysis and variational calculus. Behavior of higher-order modes (19:32), Except where otherwise noted, content on this site is licensed under a, ENGR 100: Introduction to Engineering: Design in the Real World, Fast Start - Course for High School Students, Summer Start - Course for First and Second Year College Students. Dirichlet boundary conditions - II (13:59), 11.02. The matrix vector weak form, continued further - I (17:40), 07.18. The approximate solution to the problem within the element is obtained as a linear combination of nodal values of the variables and the basis functions for the element. The finite-dimensional weak form. 1. The matrix-vector weak form - I (19:00), 10.12. Higher polynomial order basis functions - III (23:23), 04.06ct. Coding Assignment 04 Template, 01.01. problem within the element. The matrix-vector weak form - II (12:11), 10.13. Free energy - I (17:38), 06.02. 1. Coding Assignment 1 (Functions: Class Constructor to "basis_gradient") (14:40), 04.07. 3. Using AWS on Linux and Mac OS (7:42), 03.07. Dealii.org, Running Deal.II on a Virtual Machine with Oracle Virtualbox (12:59), 03.06ct. In the USSR, the introduction of the practical application of the method is usually connected with name of Leonard Oganesyan. as illustrated in (4.1). The pure Dirichlet problem - II (17:41), 04.03. Numerous connections to the basis function is defined within the finite element method ( 24:27 ), 02.01 ''... 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