18.086 - Computational Science And Engineering II (Spring 2016)



Note: The schedule is subject to change. Check back for changes and updates

Semester Timeline
Date Topic Reading  
Feb. 2, TIntroduction, Fourier methods, Intro to FD4.1, 4.3, 4.5, 6.1, slides
Feb. 4, ThFinite Differences6.1, 6.2, 6.3, slides
Feb. 9, TFinite Differences for 1-way wave equation (advection eq)6.3
Feb. 11, ThModified equationsslides lectures 3-4, notes
Feb. 16, TPresident's day - Monday schedule (no class)
Feb. 18, ThLax equivalence theorem, Leapfrog6.4, slides
Feb. 23, TStaggered grids, heat equation6.4, 6.5, slides
Feb. 25, ThAdvection-diffusion, nonlinear transport6.5, 6.6, slides
Mar. 1, TBrownian motion, SDE6.5, notes, matlab files
Mar. 3, ThSDE application to finance6.5, notes
Mar. 8, TConservation laws, weak solutions6.6
Mar. 10, ThConserved schemes, Flux Limiter6.6, slides (Lect.10/11)
Mar. 15, TNavier-Stokes, Lattice-Boltzmann methodslides, LBcode.m, mit18086_navierstokes.m (documentation)
Mar. 22, TSpring break
Mar. 24, ThSpring break
Mar. 29, TLevelset method, Matrix factorization (LU), Gaussian eliminationslides, mit18086_levelset_front.m
Mar. 31, ThCholesky factorization, Fill-in, Graph reorderingslides, mit18086_fillin.m
Apr. 5, TIterative methods, Multigridslides
Apr. 7, ThMultigrid methodsslides
Apr. 12, TKrylov subspaces, Conjugate gradientsslides
Apr. 14, ThConjugate gradient method, Introduction to optimization problems 
Apr. 19, TNo class (holiday adjustment) 
Apr. 21, ThOptimization problems: Ordinary least squares, weighted LSQ, duality, KKT matrices8.1
Apr. 26, TMinimization with constraints: Nullspace method; Regularization8.1
Apr. 28, ThRegularisation; inverse problems8.2, slides
May 3, TCalculus of variations8.3
May 5, ThIntroduction to Finite ElementsSlides, A gentle introduction to the Finite Element method (by Francisco-Javier Sayas
May 10, TNonlinear optimizationSlides
May 12, ThProject presentations