APPM 5720 - Spring 2011

Open Topics in Applied Mathematics: Fast Methods in Scientific Computing, Spring 2011 (APPM 4720/5720)

Meeting times: MWF 11.00 - 11.50, KOBL 255.

Instructor: Gunnar Martinsson. ECOT 233.

Course notes: Download the notes here. (The notes will be updated as the class proceeds.)

Office Hours: Monday 3pm - 5pm and Wednesday 10am -- 11am. (ECOT 233)

Homeworks: Please submit a hard copy in class on the due date. Group homeworks are permitted and encouraged. Undergraduate students may work in groups of three, and graduate students in groups of two.

Reference homeworks: Each student (not each group) should pick two problems (not "sets") during the course of the semester and submit a solution that is clean enough to be posted on this web-page. Please attach matlab-code when appropriate. To avoid that one problem is picked by more than one student, please sign up on the spreadsheet (the url was emailed to you).

Projects: If you find some part of the class particularly relevant to your academic interests, you have the option to propose an individual or a group project on that subject. Depending on the size of the project, this will count against one or two homeworks (i.e. you will be not be required to hand in those homeworks).

Various documents: Syllabus. Outline.

Notes:

Week:
Homework:
Material covered:

1 (Jan 10)
Introduction - overview of elliptic PDEs. Notes
Quadrature and the FFT.

2 (Jan 17)
No class Monday (MLK day).
The Laplace and Poisson equations - mathematical properties and basic solution strategies.

3 (Jan 24) Homework 1 due on Wednesday.
The file lgwt.m.
Solution to 1.2: pdf. m-file.
Solution to 1.3: pdf. m-file.
Laplace and Poisson problems ... continued.
The N-body problem.

4 (Jan 31)
Multipole expansions and fast summation. Notes

5 (Feb 7)
Homework 2 due on Monday. Multipole expansions and fast summation. Notes
On Friday, please attend the Biros seminar (Benson 180 at 2pm) instead of the regular lecture.

6 (Feb 14)
Fast summation, continued.
Boundary Integral Equation methods.

7 (Feb 21) Homework 3 due on Monday. Boundary Integral Equation methods.

8 (Feb 28)
Mon/Wed: Guest lectures on Radial Basis Functions (Thanks Bengt Fornberg!)
Fri: Boundary Integral Equation methods.

9 (Mar 7) Homework 4 due on Wednesday. Boundary Integral Equation methods.

10 (Mar 14)
Mon/Wed: Guest lectures on Gaussian Basis Functions (Thanks Greg Beylkin!)
Fri: Boundary Integral Equation methods.

Spring Break

11 (Mar 28) Homework 5 due on Wednesday. Randomized methods for large scale linear algebra.
Slides for lectures this week.

12 (Apr 4)
Mon: Randomized methods for large scale linear algebra, continued.
Wed/Fri: Krylov space methods (GMRES, Lanczos, etc.).
Sections 32 and 33 of Numerical Linear Algebra by Trefethen and Bau.

13 (Apr 11) No formal homework this week.
For anyone short on "reference homeworks" your task is this:
Device a homework problem on randomized NLA, and solve it! Krylov space methods (GMRES, Lanczos, etc.).
Sections 34, 35, and 36 of Numerical Linear Algebra by Trefethen and Bau.

14 (Apr 18)
Krylov space methods (GMRES, Lanczos, etc.).
Sections 37 and 38 of Numerical Linear Algebra by Trefethen and Bau.

15 (Apr 25) Homework 7 due on Wednesday.
The file main_hw07.m. Final lecture.

Finals week

Codes for the Fast Multipole Method:

protofmm.zip
This is a zip-file containing all files.

README.txt
Read this first - it describes the various files.

main_simplefmm.m

main_simplefmm_visualize.m

main_fmm.m

main_fmm_timing.m
main_T_ops_are_fun.m

Week:	Homework:	Material covered:
1 (Jan 10)		Introduction - overview of elliptic PDEs. Notes Quadrature and the FFT.
2 (Jan 17)		No class Monday (MLK day). The Laplace and Poisson equations - mathematical properties and basic solution strategies.
3 (Jan 24)	Homework 1 due on Wednesday. The file lgwt.m. Solution to 1.2: pdf. m-file. Solution to 1.3: pdf. m-file.	Laplace and Poisson problems ... continued. The N-body problem.
4 (Jan 31)		Multipole expansions and fast summation. Notes
5 (Feb 7)	Homework 2 due on Monday.	Multipole expansions and fast summation. Notes On Friday, please attend the Biros seminar (Benson 180 at 2pm) instead of the regular lecture.
6 (Feb 14)		Fast summation, continued. Boundary Integral Equation methods.
7 (Feb 21)	Homework 3 due on Monday.	Boundary Integral Equation methods.
8 (Feb 28)		Mon/Wed: Guest lectures on Radial Basis Functions (Thanks Bengt Fornberg!) Fri: Boundary Integral Equation methods.
9 (Mar 7)	Homework 4 due on Wednesday.	Boundary Integral Equation methods.
10 (Mar 14)		Mon/Wed: Guest lectures on Gaussian Basis Functions (Thanks Greg Beylkin!) Fri: Boundary Integral Equation methods.
Spring Break
11 (Mar 28)	Homework 5 due on Wednesday.	Randomized methods for large scale linear algebra. Slides for lectures this week.
12 (Apr 4)		Mon: Randomized methods for large scale linear algebra, continued. Wed/Fri: Krylov space methods (GMRES, Lanczos, etc.). Sections 32 and 33 of Numerical Linear Algebra by Trefethen and Bau.
13 (Apr 11)	No formal homework this week. For anyone short on "reference homeworks" your task is this: Device a homework problem on randomized NLA, and solve it!	Krylov space methods (GMRES, Lanczos, etc.). Sections 34, 35, and 36 of Numerical Linear Algebra by Trefethen and Bau.
14 (Apr 18)		Krylov space methods (GMRES, Lanczos, etc.). Sections 37 and 38 of Numerical Linear Algebra by Trefethen and Bau.
15 (Apr 25)	Homework 7 due on Wednesday. The file main_hw07.m.	Final lecture.
Finals week