Homework | Day | Date | Lectures |
Out | Due | Nr | Topic | Reading |
1 | | Wed | 02/06 | 1 | Introduction & motivation | |
| | Fri | 02/08 | 2 | Fourier methods for linear initial value problems | 6.1 |
| | Mon | 02/11 | 3 | Finite difference methods & ordinary differential equations | 6.2 |
| | Wed | 02/13 | 4 | Von Neumann stability analysis | 6.1 & 6.2 |
| | Fri | 02/15 | 5 | Finite difference methods for the one-way wave equation | 6.3 |
| project proposal | Tue | 02/19 | 6 | Modified equation | LeVeque |
| | Wed | 02/20 | 7 | Lax equivalence theorem | 6.3 |
2 | 1 | Fri | 02/22 | 8 | Numerical error analysis & convection-diffusion problems | 6.5 |
| | Mon | 02/25 | 9 | Wave equation, leapfrog, staggered grids | 6.4 |
| | Wed | 02/27 | 10 | Conservation laws: examples, method of characteristics | 6.6 |
| | Fri | 02/29 | 11 | Conservation laws: weak solutions | 6.6 |
| | Mon | 03/03 | 12 | Conservation laws: high resolution shock capturing | 6.6 |
| | Wed | 03/05 | 13 | Conservation laws: finite volume & particle methods | 6.6 |
3 | 2 | Fri | 03/07 | 14 | Higher space dimensions | |
| | Mon | 03/10 | 15 | Systems of initial value problems | |
| | Wed | 03/12 | 16 | Level set method | 6.8 |
| | Fri | 03/14 | 17 | Navier-Stokes equation | 6.7 |
| | Mon | 03/17 | 18 | Navier-Stokes equation | 6.7 |
| | Wed | 03/19 | 19 | Generating sparse matrices | |
| 3, midterm report | Fri | 03/21 | 20 | Elimination with reordering | 7.1 |
| | 03/24-03/28 | Spring break |
4 | | Mon | 03/31 | 21 | ILU, preconditioning, iterative methods | 7.1 & 7.2 |
| | Wed | 04/02 | 22 | Iterative methods | 7.2 |
| | Fri | 04/04 | 23 | Multigrid methods | 7.3 |
| | Mon | 04/07 | 24 | Multigrid methods | 7.3 |
| | Wed | 04/09 | 25 | Krylov subspace methods | 7.4 |
| | Fri | 04/11 | 26 | Krylov subspace methods | 7.4 |
| | Mon | 04/14 | 27 | Least squares problems | 8.1 |
| | Wed | 04/16 | 28 | Weighted least squares & duality | 8.1 |
5 | 4 | Fri | 04/18 | 29 | Minimization with constraints | 8.1 |
| | 04/21-04/22 | Patriot's vacation |
| | Wed | 04/23 | 30 | Regularization & pseudoinverse | 8.2 |
| | Fri | 04/25 | 31 | Inverse problems | 8.2 |
| | Mon | 04/28 | 32 | Tychonov regularization & ill posed operators in function spaces | 8.2 |
| | Wed | 04/30 | 33 | Calculus of variations | 8.3 |
| 5 | Fri | 05/02 | 34 | Calculus of variations | 8.3 |
| | Mon | 05/05 | 35 | Saddle point Stokes problem | 8.5 |
| | Wed | 05/07 | 36 | Linear programming | 8.6 |
| | Fri | 05/09 | 37 | Linear programming | 8.6 |
| final report | Mon | 05/12 | 38 | Adjoint methods | 8.7 |
| | Wed | 05/14 | 39 | Project presentations | |