Peter Blomgren
San Diego State University
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Math 693b: Advanced Numerical Analysis Spring 2018
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Evolving Schedule (topics arranged by "target week.")

Week # Tuesday Thursday
1
Video: Numerical Simulation of a Tsunami.
1 Jan-16-2018

Martin Luther King, Jr. Day (January 15th)
Jan-18-2018
First Meeting
[Notes #1]
Movies:
2 Jan-23-2018
Hyperbolic PDEs; Introduction
[Notes #2]
Movies:
Jan-25-2018
Convergence, Constistency and Stability; the CFL Condition
[Notes #3] [HW #1]
Movies:
3 Jan-30-2018
Analysis of Finite Difference Schemes
[Notes #4]
Feb-01-2018
Order of Accuracy of Finite Difference Schemes
[Notes #5]
Movies:
4 Feb-06-2018
Stability of Lax-Wendroff and Crank-Nicolson; Boundary Conditions
[Notes #6] [HW#2]
[Thomas Algorithm]
Feb-08-2018
Stability for Multistep Schemes Leapfrog Scheme; General Multistep Schemes
[Notes #7]
Movies: [#1] [#2] [#3] [#4] [#5]
HW#1 Due (Friday)
5 Feb-13-2018
Stability for Multistep Schemes Schur and von Neumann Polynomials
[Notes #8]
Movies:
Feb-15-2018
Dissipation and Dispersion
[Notes #9]
Movies:
6 Feb-20-2018
Parabolic PDEs Overview — Exact Solutions and Boundary Conditions
[Notes #10]
Movies:
Feb-22-2018
Stability, Boundary Conditions, Convection-Diffusion, Variable Coefficients
[Notes #11]
Movies:
HW#2 Due (Friday)
7 Feb-27-2018
Systems of PDEs in Higher Dimensions
[Notes #12] [HW #3]
Mar-01-2018
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:
Mar-08-2018
Boundary Conditions; 2D and 3D
[Notes #15]
Movies:
HW#3 Due (Friday)
9 Mar-13-2018
Analysis of Well-Posed and Stable Problems
[Notes #16]
Mar-15-2018
Convergence Estimates for Initial Value Problems
[Notes #17]
10 Mar-20-2018
Well-Posed and Stable Initial-Boundary Value Problems, Pt.1
[Notes #18]
Movies:
Mar-22-2018
Well-Posed and Stable Initial-Boundary Value Problems, Pt.2
[Notes #19]
Movies: [#1] [#2] [#3] [#4]
HW#4 Due (Friday)
- Mar-27-2018
Spring Break

Cesar Chavez Day (March 30th)
Mar-29-2018
Spring Break
11 Apr-03-2018
Elliptic PDEs and Difference Schemes
[Notes #20]
Apr-05-2018
Finite Difference Schemes for Elliptic Problems
[Notes #21]
Movies:
Project Plan Due
12 Apr-10-2018
Elliptic Problems: Iterative Schemes
[Notes #22]
Movies:
Apr-12-2018
Steepest Descent and Conjugate Gradient
[Notes #23]

Vortex Sheet/Dipole Simulations
[HOS-1996.pdf]
Movies:
13 Apr-17-2018
Spectral Methods, Pt.1
[Spectral #1]
Movies:
Reference: Spectral Methods in MATLAB
Apr-19-2018
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-24-2018
Spectral Methods, Pt.3
[Spectral #3]
Movies:
Apr-26-2018
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  __.__.
May-03-2018
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  __.__.
Unused
Modules
The Finite Element Methods
See Math542 - Spring 2015

FEM: Numerics, Triangulation, Element Stiffness Matrix
FEM: Hilbert Spaces --- L2(D), H1(D), and H10(D)
FEM: Geometric Interpretation
Finite Element Spaces
FEM: More Spaces, C1(D)
FEM: Approximation Theory
FEM: Regularity of the Exact Solution

Homework and Projects will be assigned.

Copyright © 2018 Peter Blomgren.