Week #
Tuesday
Thursday
1
VIDEO
Video: Numerical Simulation of a Tsunami.
1
Jan162018
Martin Luther King, Jr. Day (January 15th)
Jan182018
First Meeting
[Notes #1 ]
Movies:
2
Jan232018
Hyperbolic PDEs; Introduction
[Notes #2 ]
Movies:
Jan252018
Convergence, Constistency and Stability; the
CFL Condition
[Notes #3 ]
[HW #1 ]
Movies:
3
Jan302018
Analysis of Finite Difference Schemes
[Notes #4 ]
Feb012018
Order of Accuracy of Finite Difference
Schemes
[Notes #5 ]
Movies:
4
Feb062018
Stability of LaxWendroff and CrankNicolson;
Boundary Conditions
[Notes #6 ]
[HW#2 ]
[Thomas Algorithm ]
Feb082018
Stability for Multistep Schemes
Leapfrog Scheme; General Multistep
Schemes
[Notes #7 ]
Movies:
[#1 ]
[#2 ]
[#3 ]
[#4 ]
[#5 ]
HW#1 Due (Friday)
5
Feb132018
Stability for Multistep Schemes
Schur and von Neumann Polynomials
[Notes #8 ]
Movies:
Feb152018
Dissipation and Dispersion
[Notes #9 ]
Movies:
6
Feb202018
Parabolic PDEs
Overview — Exact Solutions and
Boundary Conditions
[Notes #10 ]
Movies:
Feb222018
Stability, Boundary Conditions,
ConvectionDiffusion, Variable Coefficients
[Notes #11 ]
Movies:
[Nx=200,
Nt=200, mu=200 ]
[Nx=200,
Nt=400, mu=100 ]
[Nx=200,
Nt=800, mu=50 ]
[Nx=200,
Nt=1600, mu=25 ]
[Nx=400,
Nt=200, mu=800 ]
[Nx=400,
Nt=400, mu=400 ]
[Nx=400,
Nt=800, mu=200 ]
[Nx=400,
Nt=1600, mu=100 ]
[Nx=800,
Nt=200, mu=3200 ]
[Nx=800,
Nt=400, mu=1600 ]
[Nx=800,
Nt=800, mu=800 ]
[Nx=800,
Nt=1600, mu=400 ]
[FTCS_conv_diff_dx0.100_dt0.0025 ]
[FTCS_conv_diff_dx0.020_dt0.0001 ]
HW#2 Due (Friday)
7
Feb272018
Systems of PDEs in Higher Dimensions
[Notes #12 ]
[HW #3 ]
Mar012018
The Alternating Direction Implicit Method
[Notes #13 ]
Projects and Homework
[Projects, HW#4,5,6,7 ]
8
Mar062018
Second Order Equations
[Notes #14 ]
Movies:
Mar082018
Boundary Conditions; 2D and 3D
[Notes #15 ]
Movies:
HW#3 Due (Friday)
9
Mar132018
Analysis of WellPosed and Stable Problems
[Notes #16 ]
Mar152018
Convergence Estimates for Initial Value
Problems
[Notes #17 ]
10
Mar202018
WellPosed and Stable InitialBoundary Value
Problems, Pt.1
[Notes #18 ]
Movies:
Mar222018
WellPosed and Stable InitialBoundary Value
Problems, Pt.2
[Notes #19 ]
Movies:
[#1 ]
[#2 ]
[#3 ]
[#4 ]
HW#4 Due (Friday)

Mar272018
Spring Break
Cesar Chavez Day (March 30th)
Mar292018
Spring Break
11
Apr032018
Elliptic PDEs and Difference Schemes
[Notes #20 ]
Apr052018
Finite Difference Schemes for Elliptic
Problems
[Notes #21 ]
Movies:
Project Plan Due
12
Apr102018
Elliptic Problems: Iterative Schemes
[Notes #22 ]
Movies:
Apr122018
Steepest Descent and Conjugate Gradient
[Notes #23 ]
Vortex Sheet/Dipole Simulations
[HOS1996.pdf ]
Movies:
13
Apr172018
Spectral Methods, Pt.1
[Spectral #1 ]
Movies:
Reference: Spectral
Methods in MATLAB
Apr192018
Spectral Methods, Pt.2
[Spectral #2 ]
Presentation Scheduling: Slots
arranged by random drawing ON THE DAY of presentation. Volunteer
for bonus / penalty for skipping.
HW#5 Due (Friday)
14
Apr242018
Spectral Methods, Pt.3
[Spectral #3 ]
Movies:
Apr262018
Mimetic Methods / MTK Toolkit
[Mimetic #1 (new) ]
[Mimetic #1 (old) ]
[Mimetic #2 (old) ]
[Mimetic #3 (old) ]
Reference: Mimetic
Discretization Methods / MTK
HW#6 Due (Friday)
15
May012018
Project Presentations (12–15 min)
01. 12:30p __.__.
02. 12:45p __.__.
03. 01:00p __.__.
__. 01:15p __.__.
__. 01:30p __.__.
May032018
Project Presentations (12–15 min)
04. 12:30p __.__.
05. 12:45p __.__.
06. 01:00p __.__.
07. 01:15p __.__.
08. 01:30p __.__.
HW#7 Due (Friday)
Finals
May082018
Please verify that I have received all
your homeworks (hard or soft copy), and project (code + movies +
presentation; soft copy)
May102018
Project Presentations (12–15 min)
09. 10:30p __.__.
10. 10:45p __.__.
11. 11:00p __.__.
12. 11:15p __.__.
13. 11:30p __.__.
14. 11:45p __.__.
15. 12:00p __.__.
16. 12:15p __.__.
Unused Modules
The Finite Element Methods
See Math542  Spring 2015
FEM: Numerics, Triangulation, Element
Stiffness Matrix
FEM: Hilbert Spaces  L_{2} (D),
H^{1} (D), and H^{1} _{0} (D)
FEM: Geometric Interpretation
Finite Element Spaces
FEM: More Spaces, C^{1} (D)
FEM: Approximation Theory
FEM: Regularity of the Exact Solution