Main Content
Evolving Schedule (topics arranged by "target week.")
Week
Monday
Wednesday
Video: Numerical Simulation of a Tsunami.
1
Jan-16-2018
Martin Luther King, Jr. Day (January 15th)
Martin Luther King, Jr. Day (January 15th)
Jan-18-2018
First Meeting
[Notes #1]
Movies:
First Meeting
[Notes #1]
Movies:
- [heat] [alt]
- [hmovie2d-ic6] [alt]
- [wmovie2d-ic3] [alt]
- [smovie-fn7] [alt]
- [kdv-2soliton] [alt]
- [kdv-sin] [alt]
- [fokker-planck-dark-matter] [alt]
- [fokker-planck-dark-matter]
- [fokker-planck-landau]
2
Jan-23-2018
Hyperbolic PDEs; Introduction
[Notes #2]
Movies:
Hyperbolic PDEs; Introduction
[Notes #2]
Movies:
- [Hyperbolic]
- [LF λ=0.80 dx=0.10] [error]
- [LF λ=0.80 dx=0.05] [error]
- [LF λ=0.95 dx=0.10] [error]
- [LF λ=0.95 dx=0.05] [error]
- [LF λ=1.02 dx=0.10] [error]
- [LF λ=1.02 dx=0.05] [error]
Video: Visualization of solutions to the one-way
wave equation using the FTCS, FTBS, Lax-Friedrichs, and Leapfrog
schemes. The grid spacing is fixed at dx=0.05,
and λ=0.9. [Generated in
Python, using
matplotlib; reencoded using
ffmpeg.]
3
4
Feb-06-2018
Stability of Lax-Wendroff and Crank-Nicolson; Boundary Conditions
[Notes #6] [HW#2]
[Thomas Algorithm]
Stability of Lax-Wendroff and Crank-Nicolson; Boundary Conditions
[Notes #6] [HW#2]
[Thomas Algorithm]
5
6
Feb-20-2018
Parabolic PDEs Overview — Exact Solutions and Boundary Conditions
[Notes #10]
Movies:
Parabolic PDEs Overview — Exact Solutions and Boundary Conditions
[Notes #10]
Movies:
- [G(t,x,y=0,b=1) (std)]
- [G(t,x,y=0,b=1) (semilog)]
- [multisource]
- [heat_1D (x-t, 0 BC)]
- [dff_stab]
Feb-22-2018
Stability, Boundary Conditions, Convection-Diffusion, Variable Coefficients
[Notes #11]
Movies:
Stability, Boundary Conditions, Convection-Diffusion, 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]
7
Mar-01-2018
The Alternating Direction Implicit Method
[Notes #13]
Projects and Homework
[Projects, HW#4,5,6,7]
The Alternating Direction Implicit Method
[Notes #13]
Projects and Homework
[Projects, HW#4,5,6,7]
8
Mar-06-2018
Second Order Equations
[Notes #14]
Movies:
Second Order Equations
[Notes #14]
Movies:
- [domain]
- [wave#1]
- [wave#2]
- [wave#3]
- CTCS Full Wave:
- [(xmax=2.0)]
- [(xmax=3.0)]
- [(xmax=4.0)]
- [(xmax=5.0)]
- [(xmax=6.0)]
- [(xmax=7.0)]
- [(xmax=8.0)]
- [(xmax=9.0)]
- [(xmax=10.0)]
- [(xmax=15.0)]
- [(xmax=15.0, a+)]
- [(xmax=15.0, a-)]
- [FastBox]
- [obstacle]
- [wall01]
- [wall02]
- [wall03]
- [beach]
9
10
Mar-27-2018
Spring Break
Cesar Chavez Day (March 30th)
Spring Break
Cesar Chavez Day (March 30th)
Mar-29-2018
Spring Break
Spring Break
11
12
13
Apr-19-2018
Spectral Methods, Pt.2
[Spectral #2]
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
Apr-26-2018
Mimetic Methods / MTK Toolkit
[Mimetic #1 (new)]
[Mimetic #1 (old)]
[Mimetic #2 (old)]
[Mimetic #3 (old)]
Reference: Mimetic Discretization Methods / MTK
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
May-01-2018
Project Presentations (12–15 min)
01. 12:30p __.__.
02. 12:45p __.__.
03. 01:00p __.__.
__. 01:15p __.__.
__. 01:30p __.__.
01. 12:30p __.__.
02. 12:45p __.__.
03. 01:00p __.__.
__. 01:15p __.__.
__. 01:30p __.__.
May-03-2018
Project Presentations (12–15 min)
04. 12:30p __.__.
05. 12:45p __.__.
06. 01:00p __.__.
07. 01:15p __.__.
08. 01:30p __.__.
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
May-08-2018
Please verify that I have received all
your homeworks (hard or soft copy), and project (code + movies +
presentation; soft copy)
May-10-2018
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 __.__.
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 Method
[FEM #1] Introduction
[FEM #2] The Finite Element Method #2
[FEM #3] Triangulation; Element Stiffness Matrix; Hilbert Spaces --- L2(D), H1(D), and H10(D); Geometric Interpretation
[FEM #4] Finite Element Spaces
[FEM #5] FEM: More Spaces, C1(D)
[FEM #6] FEM: Approximation Theory
[FEM #7] FEM: Regularity of the Exact Solution