COURSE DESCRIPTION
Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes.
Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients.
Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods.
Prerequisites: 18.03 and 18.034
Text Book: Gilbert Strang, Computational Science and Engineering, Wellesley-Cambridge Press, 2007
IMPORTANT DATES
- Feb. 22: Submit project proposal by email (stoopn AT mit DOT edu). Formulate along this structure: Proposal template.
- March 28: Submit short midterm project report (max 1 page text)
- May 6: Submit written final report by email
- May 12: Project presentations
COURSE PROJECT
See above for important dates regarding course project!
The idea of this course is that you work on and present a computational project of your choice. It can be related to your research work and optimally is related to the course contents (but may also go beyond). It must have a major numerical component. No recycling of existing/old projects!
Extensive implementation/testing/comparison of methods is ok.
EXTRA MATERIAL
- FD Navier-Stokes solver (from CSE website, by B. Seibold), documentation (PDF)
- Lattice-Boltzmann code (by I. Haslam)
- mit18086_fd_transport_limiter.m Flux limiter matlab demo
- Levelset method matlab code (from CSE website)
RECENT UPDATE
[02/01/2016] Welcome to the spring semester!
