SCHEDULE
Note: The schedule is subject to change. Check back for changes and updates
| Date | Topic | Reading | |
|---|---|---|---|
| Feb. 2, T | Introduction, Fourier methods, Intro to FD | 4.1, 4.3, 4.5, 6.1, slides | |
| Feb. 4, Th | Finite Differences | 6.1, 6.2, 6.3, slides | |
| Feb. 9, T | Finite Differences for 1-way wave equation (advection eq) | 6.3 | |
| Feb. 11, Th | Modified equations | slides lectures 3-4, notes | |
| Feb. 16, T | President's day - Monday schedule (no class) | ||
| Feb. 18, Th | Lax equivalence theorem, Leapfrog | 6.4, slides | |
| Feb. 23, T | Staggered grids, heat equation | 6.4, 6.5, slides | |
| Feb. 25, Th | Advection-diffusion, nonlinear transport | 6.5, 6.6, slides | |
| Mar. 1, T | Brownian motion, SDE | 6.5, notes, matlab files | |
| Mar. 3, Th | SDE application to finance | 6.5, notes | |
| Mar. 8, T | Conservation laws, weak solutions | 6.6 | |
| Mar. 10, Th | Conserved schemes, Flux Limiter | 6.6, slides (Lect.10/11) | |
| Mar. 15, T | Navier-Stokes, Lattice-Boltzmann method | slides, LBcode.m, mit18086_navierstokes.m (documentation) | |
| Mar. 22, T | Spring break | ||
| Mar. 24, Th | Spring break | ||
| Mar. 29, T | Levelset method, Matrix factorization (LU), Gaussian elimination | slides, mit18086_levelset_front.m | |
| Mar. 31, Th | Cholesky factorization, Fill-in, Graph reordering | slides, mit18086_fillin.m | |
| Apr. 5, T | Iterative methods, Multigrid | slides | |
| Apr. 7, Th | Multigrid methods | slides | |
| Apr. 12, T | Krylov subspaces, Conjugate gradients | slides | |
| Apr. 14, Th | Conjugate gradient method, Introduction to optimization problems | ||
| Apr. 19, T | No class (holiday adjustment) | ||
| Apr. 21, Th | Optimization problems: Ordinary least squares, weighted LSQ, duality, KKT matrices | 8.1 | |
| Apr. 26, T | Minimization with constraints: Nullspace method; Regularization | 8.1 | |
| Apr. 28, Th | Regularisation; inverse problems | 8.2, slides | |
| May 3, T | Calculus of variations | 8.3 | |
| May 5, Th | Introduction to Finite Elements | Slides, A gentle introduction to the Finite Element method (by Francisco-Javier Sayas | |
| May 10, T | Nonlinear optimization | Slides | |
| May 12, Th | Project presentations |
