SES # | TOPICS | KEY DATES |
---|---|---|
1 | Fundamental concepts and examples | |
2 | Well-posedness and Fourier methods for linear initial value problems | |
3 | Laplace and Poisson equation | |
4 | Heat equation, transport equation, wave equation |
Problem set 1 out Project proposal due |
5 | General finite difference approach and Poisson equation | |
6 | Elliptic equations and errors, stability, Lax equivalence theorem | |
7 | Spectral methods |
Problem set 2 out Problem set 1 due |
8 | Fast Fourier transform (guest lecture by Stephen Johnson) | |
9 | Spectral methods | |
10 | Elliptic equations and linear systems | |
11 | Efficient methods for sparse linear systems: multigrid |
Problem set 3 out Problem set 2 due |
12 | Efficient methods for sparse linear systems: Krylov methods | |
13 | Ordinary differential equations | Midterm report |
14 | Stability for ODE and von Neumann stability analysis | |
15 | Advection equation and modified equation |
Problem set 4 out Problem set 3 due |
16 | Advection equation and ENO/WENO | |
17 | Conservation laws: theory | |
18 | Conservation laws: numerical methods | |
19 | Conservation laws: high resolution methods |
Problem set 5 out Problem set 4 due |
20 | Operator splitting, fractional steps | |
21 | Systems of IVP, wave equation, leapfrog, staggered grids | |
22 | Level set method | |
23 | Navier-Stokes equation: finite difference methods | |
24 | Navier-Stokes equation: pseudospectral methods | Problem set 5 due |
25 | Particle methods | |
26 | Project presentations | Final report |