Schedule
This schedule is not final but this is the anticipated curriculum of TMA4212.
Teaching material
Main material:
Additional material
Prerequisites
| Subject | Topics | Subtopics |
| Linear algebra | Basics | Vector and matrix norms; Symmetric Positive Definite matrices; Inner product spaces; Linear independence; basis of a vector space; orthonormal basis. |
| | Matrix factorizations | Diagonalization and orthogonal diagonalization of matrices; LU decomposition (Gaussian elimination, pivoting); Cholesky factorization; QR factorization; SVD; Jordan Canonical form; Schur factorization. |
| | Topics of interest in numerical linear algebra | Spectral radius; Gershgoring's theorem; Condition number; Neumann series. |
| | Iterative methods | Newton method; fixed point iteration; convergence of the basic iterative methods (Jacobi, Gauss-Seidel and SOR) for linear systems. |
| Calculus | Taylor theorem | |
Schedule
| Week | Date | Teaching material | Subject |
| 2 | 11.01, | TMA4212-Introduction | Introduction to TMA4212. Examples of numerical solution of real world PDEs |
| 3 | 18.01, 20.01 | Owren2017tns: 1,2,3. Owren2017tns: 4.1–4.2 | Difference operators and difference formulae. Classification of linear PDEs. Methods for parabolic problems. Heat equation |
| 4 | 25.01, 27.01 | Owren2017tns: 4.3–4.5, 5 | Heat equation. Stability, consistence and convergence. |
| 5 | 01.02, 03.02 | TMA4212_Presentations_20210201. Owren2017tns: 6.1-6.6 | Numerical examples, convergence studies, manufactured solutions. Elliptic equations. |
| 6 | 08.02, 10.02 | TMA4212_Presentations_20210210. Owren2017tns: 6.7-6.11 | Numerical examples, convergence studies, adaptive grids. How to write technical reports Elliptic equations. |
| 7 | 15.02, 17.02 | Owren2017tns: 7 | Hyperbolic equations. |
| 8 | 22.02, 24.02 | JCS2004fds: Ch 13&14 | Numerical solution of linear systems. |
| 9 | 01.03, 03.03 | Curry2018tp2: 1 -4 | Introduction to FEM. BVPs and the Galerkin method, Variational problems, Stability and convergence of Galerkin method |
| 10 | 08.03, 10.03 | Curry2018tp2: 5. TMA4212_Presentations_20210309 | 2D Poisson equation, Convergence studies for heat equation |
| 11 | 15.03, 17.03 | | Project work - No lectures |
| 12 | 22.03, 24.03 | | Project work - No lectures |
| 13 | 27.03, 29.03 | | Easter holiday. |
| 14 | , 07.04 | | Project work - No lectures |
| 15 | 12.04, 14.04 | | Project work - No lectures |
| 16 | 19.04, 21.04 | | Project work - No lectures |
| 17 | 26.04, | | Info and questions related to the Project |