Peter Blomgren
San Diego State University
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Math 693b: Advanced Numerical Analysis Spring 2017
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Evolving Schedule (topics arranged by "target week.")

Week # Tuesday Thursday
1
Video: Numerical Simulation of a Tsunami.
1 Jan-17-2017

Martin Luther King, Jr. Day (January 16th)
Jan-19-2017
First Meeting
[Notes #1]
Movies:
2 Jan-24-2017
Hyperbolic PDEs; Introduction
[Notes #2]
Movies:
Jan-26-2017
Convergence, Constistency and Stability; the CFL Condition
[Notes #3] [HW #1]
Movies:
3 Jan-31-2017
Analysis of Finite Difference Schemes
[Notes #4]
Feb-02-2017
Order of Accuracy of Finite Difference Schemes
[Notes #5]
Movies:
4 Feb-07-2017
Stability of Lax-Wendroff and Crank-Nicolson; Boundary Conditions
[Notes #6] [HW#2]
[Thomas Algorithm]
Feb-09-2017
Stability for Multistep Schemes Leapfrog Scheme; General Multistep Schemes
[Notes #7]
Movies: [#1] [#2] [#3] [#4] [#5]
HW#1 Due (Friday)
5 Feb-14-2017
Stability for Multistep Schemes Schur and von Neumann Polynomials
[Notes #8]
Movies: [#1] [#2] [#3] [#4]
Feb-16-2017
Dissipation and Dispersion
[Notes #9]
Movies:
6 Feb-21-2017
Parabolic PDEs Overview — Exact Solutions and Boundary Conditions
[Notes #10]
Movies:
Feb-23-2017
Stability, Boundary Conditions, Convection-Diffusion, Variable Coefficients
[Notes #11]
Movies:
HW#2 Due (Friday)
7 Feb-28-2017
Systems of PDEs in Higher Dimensions
[Notes #12] [HW #3]
Mar-02-2017
The Alternating Direction Implicit Method
[Notes #13]
Projects and Homework
[Projects, HW#4,5,6,7]
8 Mar-07-2017
Second Order Equations
[Notes #14]
Movies:
Mar-09-2017
Boundary Conditions; 2D and 3D
[Notes #15]
Movies:
HW#3 Due (Friday)
9 Mar-14-2017
Analysis of Well-Posed and Stable Problems
[Notes #16]
Mar-16-2017
Convergence Estimates for Initial Value Problems
[Notes #17]
10 Mar-21-2017
Well-Posed and Stable Initial-Boundary Value Problems, Pt.1
[Notes #18]
Movies:
Mar-23-2017
Well-Posed and Stable Initial-Boundary Value Problems, Pt.2
[Notes #19]
Movies: [#1] [#2] [#3] [#4]
HW#4 Due (Friday)
- Mar-28-2017
Spring Break

Cesar Chavez Day (March 31st)
Mar-30-2017
Spring Break
11 Apr-04-2017
Elliptic PDEs and Difference Schemes
[Notes #20]
Apr-06-2017
Finite Difference Schemes for Elliptic Problems
[Notes #21]
Movies:
Project Plan Due
12 Apr-11-2017
Elliptic Problems: Iterative Schemes
[Notes #22]
Movies:
Apr-13-2017
Steepest Descent and Conjugate Gradient
[Notes #23]

Vortex Sheet/Dipole Simulations
[HOS-1996.pdf]
Movies:
13 Apr-18-2017
Spectral Methods, Pt.1
[Spectral #1]
Movies:
Reference: Spectral Methods in MATLAB
Apr-20-2017
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-25-2017
Spectral Methods, Pt.3
[Spectral #3]
Movies:
Apr-27-2017
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-02-2017 Project Presentations (12–15 min)
01. 12:30p  Wi.By.
02. 12:45p  An.Sc.
03. 01:00p  Em.Ja.
__. 01:15p  __.__.
__. 01:30p  __.__.
May-04-2017
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 May-09-2017

Please verify that I have received all your homeworks (hard or soft copy), and project (code + movies + presentation; soft copy)
May-11-2017
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 --- 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 © 2017 Peter Blomgren.