Week #
Tuesday
Thursday
1
VIDEO
Video: Numerical Simulation of a Tsunami.
1
Jan172017
Martin Luther King, Jr. Day (January 16th)
Jan192017
First Meeting
[Notes #1 ]
Movies:
2
Jan242017
Hyperbolic PDEs; Introduction
[Notes #2 ]
Movies:
Jan262017
Convergence, Constistency and Stability; the
CFL Condition
[Notes #3 ]
[HW #1 ]
Movies:
3
Jan312017
Analysis of Finite Difference Schemes
[Notes #4 ]
Feb022017
Order of Accuracy of Finite Difference
Schemes
[Notes #5 ]
Movies:
4
Feb072017
Stability of LaxWendroff and CrankNicolson;
Boundary Conditions
[Notes #6 ]
[HW#2 ]
[Thomas Algorithm ]
Feb092017
Stability for Multistep Schemes
Leapfrog Scheme; General Multistep
Schemes
[Notes #7 ]
Movies:
[#1 ]
[#2 ]
[#3 ]
[#4 ]
[#5 ]
HW#1 Due (Friday)
5
Feb142017
Stability for Multistep Schemes
Schur and von Neumann Polynomials
[Notes #8 ]
Movies:
[#1 ]
[#2 ]
[#3 ]
[#4 ]
Feb162017
Dissipation and Dispersion
[Notes #9 ]
Movies:
6
Feb212017
Parabolic PDEs
Overview — Exact Solutions and
Boundary Conditions
[Notes #10 ]
Movies:
Feb232017
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 ]
HW#2 Due (Friday)
7
Feb282017
Systems of PDEs in Higher Dimensions
[Notes #12 ]
[HW #3 ]
Mar022017
The Alternating Direction Implicit Method
[Notes #13 ]
Projects and Homework
[Projects, HW#4,5,6,7 ]
8
Mar072017
Second Order Equations
[Notes #14 ]
Movies:
Mar092017
Boundary Conditions; 2D and 3D
[Notes #15 ]
Movies:
HW#3 Due (Friday)
9
Mar142017
Analysis of WellPosed and Stable Problems
[Notes #16 ]
Mar162017
Convergence Estimates for Initial Value
Problems
[Notes #17 ]
10
Mar212017
WellPosed and Stable InitialBoundary Value
Problems, Pt.1
[Notes #18 ]
Movies:
Mar232017
WellPosed and Stable InitialBoundary Value
Problems, Pt.2
[Notes #19 ]
Movies:
[#1 ]
[#2 ]
[#3 ]
[#4 ]
HW#4 Due (Friday)

Mar282017
Spring Break
Cesar Chavez Day (March 31st)
Mar302017
Spring Break
11
Apr042017
Elliptic PDEs and Difference Schemes
[Notes #20 ]
Apr062017
Finite Difference Schemes for Elliptic
Problems
[Notes #21 ]
Movies:
Project Plan Due
12
Apr112017
Elliptic Problems: Iterative Schemes
[Notes #22 ]
Movies:
Apr132017
Steepest Descent and Conjugate Gradient
[Notes #23 ]
Vortex Sheet/Dipole Simulations
[HOS1996.pdf ]
Movies:
13
Apr182017
Spectral Methods, Pt.1
[Spectral #1 ]
Movies:
Reference: Spectral
Methods in MATLAB
Apr202017
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
Apr252017
Spectral Methods, Pt.3
[Spectral #3 ]
Movies:
Apr272017
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
May022017
Project Presentations (12–15 min)
01. 12:30p Wi.By.
02. 12:45p An.Sc.
03. 01:00p Em.Ja.
__. 01:15p __.__.
__. 01:30p __.__.
May042017
Project Presentations (12–15 min)
04. 12:30p Ar.Ma.
05. 12:45p Ja.Be.
06. 01:00p __.__.
07. 01:15p __.__.
__. 01:30p __.__.
HW#7 Due (Friday)
Finals
May092017
Please verify that I have received all
your homeworks (hard or soft copy), and project (code + movies +
presentation; soft copy)
May112017
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 __.__.
__. 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