18.086 - Computational Science and Engineering II (Spring 2014)

 

SCHEDULE

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

Semester Timeline
Date Topic Reading
Feb.04 TueIntroduction and preview. Nyquist rate; Sampling Theorem; Fourier methods for linear initial value problems. 4.1; 4.3; 4.5; 6.1
Feb.06 Th Finite difference methods 6.1 & 6.2
Feb.11 Tue Ordinary differential equations 6.2 & 6.3
Feb.13 Th Finite difference methods for the one-way wave equation; von Neumann stability analysis 6.3
Feb.18 Tue No Class. MONDAY SCHEDULE due to Presidents Day.
Feb.20 Th Wave equation, leapfrog, staggered grids 6.4 & Stability
Feb.25 TueConvection-Diffusion 6.5
Feb.27 Th Conservation Laws: characteristics, weak solutions and RH jump conditions. 6.6
Mar.04 TueConservation Laws: Lax-Wendroff Theorem, finite volumn method and entropy inequalities LeVeque's book or 16.920
Mar.06 ThConservation Laws: montone schemes, convergence and ENO schemes
Mar.11 TueIncompressible Fluids. Navier-Stokes. Fast FFT Poisson Solver. 3.5 & 6.7
Mar.13 Th Level Set Method. 6.8 & Level Set
Mar.18 Tue Pset 2 discussion.
Mar.20 ThLU, LDL, QR and SVD. Direct Method. 1.3, 1.7, & 7.1
Mar.25 TueNo Class. Spring Vacation.
Mar.28 ThNo Class. Spring Vacation.
Apr.01 TueIterative Methods: Jacobi, Gauss-Seidel, Red-Black GS. 7.2
Apr.03 ThMultigrid Method 7.3
Apr.08 TueMultigrid. 6.5 & 6.9 in Applied Numerical Linear Algebra
Apr.10 ThKrylov subspace methods. 7.4
Apr.15 TueConjugate Gradient. CG
Apr.17 ThIntroduction to optimization
Apr.22 TueNo Class. Patriots Day Vacation.
Apr.24 ThLeast Square 8.1 & 8.2
Apr.29 TueCalculus of Variation 8.3
May.01 ThCalculus of Variation; Linear Programming 8.6
May.06 TueLinear Programming; Adjoint Methods
May.08 ThNo Class
May.13 TueProject presentations
May.15 Th Project presentations