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Week 6:
Please look carefully at the Preparatory Material page for what you need to review before the course! The lectures will assume that you actually have done the preparations!
Schedule
There is a Campus map at http://www.umu.se/english/about-umu/campus-maps?languageId=1, where you can search for the rooms (e.g. NC352).
Module 4: the Finite Element Method
| Date | Content | Time | Location |
|---|---|---|---|
| Feb 6 | FEM, the general idea, short history. Mathematical background: vector calculus, integration by parts. FEM for an elliptic model problem: derivation of a variational form, the energy space. Meshing, Galerkin approximation. | 9:15-12:00 | NC352/ MA446 |
| Exercises / Computer lab | 13:15-17:00 | MA406 | |
| Feb 7 |
FEM for an elliptic model problem (cont.). Properties of the discrete problem, handling of boundary conditions. Analysis: stability, Galerkin orthogonality, error analysis. Handling of boundary conditions. Elements in 2D and 3D. More general elliptic problems. | 9:15-12:00 | NC352 |
| Computer lab | 13:15- 17:00 | MA446 | |
| Feb 8 |
Orientation about FEM for linear elasticity and for incompressible flow. | 9:15-12:00 | NC352 |
| Computer lab | 13:15-17:00 | MA446 |
Module 5: Optimization
| Date | Content | Time | Location |
|---|---|---|---|
| Feb 9 | Introduction, optimization examples. Unconstrained nonlinear optimization. Convergence rate. Multivariate Taylor series. Optimality conditions. Quadratic functions, Newton's method. Problems with basic Newton. Line search. Steepest-descent and Quasi-Newton. Non-linear least-squares. | 9:15-12:00 | NC352 |
| Computer lab | 13:15-17:00 | MA446 | |
| Feb 10 |
Optimization with constraints. Special cases: linear programming, quadratic programming. Orientation about numerical methods: penalty and barrier methods, sequential quadratic programming. | 9:15-12:00 | NC352 |
| Computer lab | 13:15-17:00 | MA446 |
For Thursday's computer lab, you need the m-files enzyme.m and enzymeRhs.m
