Iterative and Multigrid Methods

CS556 :: Fall 2024

Instructor: Paul Fischer
Class Time/Place: 9:30-10:45, Tu/Th, 1302 Siebel Center
Office Hours: 2:00-3:30, Wed, 4320 Seibel Center
Syllabus: Syllabus

About the Course

Course page under construction. The following is subject to change.

sparse matrix

The course is divided roughly into three parts: the basics of numerical linear algebra, iterative methods (such as CG, GMRES, BiCGStab, etc), and multilevel methods (for example Schwarz and multigrid). We will primarily follow the text of Yousef Saad.

Course-work includes homework (usually bi-weekly) and a final project focussed on multigrid. We will have weekly in class quizzes. There is also a strong participation grade based on your attendence (informal) and ability to keep up with handouts and other tasks. The tentative grade breakdown is:

Quizzes 15
Homework 50
Midterm Project 15
Final Project 15
Attendance and handouts 5

Lectures

Lecture	Date	Material
	08-27	lec1.pdf quiz1.pdf quiz1
	08-29	hpc_experiments.pdf hpc_results.pdf lin_alg1.pdf hw1.pdf quiz2.pdf quiz2 hw1
	09-03	lec3a.pdf
	09-05	lec4.pdf nest_diss_notes.pdf george_1973_nest_diss.pdf martinsson_nest_diss_2014.pdf schmitz_ying_2014_nested.pdf cartesian_nested_src.tar quiz3
	09-10	lec5.pdf
	09-12	lec6.pdf lec6b.pdf fdm_demo.tar quiz4.pdf hw2.pdf quiz4 hw2
	09-17	lec7a.pdf lec7b.pdf jacobi_demo.tar
	09-19	projection1.pdf projection2.pdf takeaways.pdf
	09-24	projection2a.pdf steep.pdf quiz5.pdf quiz5
	09-26	projection2b.pdf
	10-01	precond_crs.pdf hw3.pdf hw3_v2.pdf lin_interp2.m
	10-03	fem1.pdf hw1_soln.pdf hw2_soln.pdf
	10-08	fem2.pdf hw3
	10-10	fem_test.tar quiz6.pdf quiz6
	10-15	Lecture on Eigenvalues pcg_eigenvalues.pdf hw4
	10-17	schwarz_notes.pdf
	10-22	schwarz24b.pdf
	10-24	toselli_widlund.pdf olson_numpdes.pdf
	10-29	mgrid.pdf taubin-sg95.pdf taubin-golub.pdf quiz7_files.tar quiz7.pdf quiz7
	11-05	mgrid2.pdf midterm.pdf
	11-12	aggregate.pdf livne_brandt_lamg_2012.pdf
	11-14	adi_slides.pdf peaceman_rachford_1955.pdf fem_data_files.tar

Books

We will be using Saad's book Iterative methods for sparse linear systems

In addition, there are several other helpful texts (optional):

Computing

We will be using matlab (Octave) and Python with the libraries numpy, scipy and matplotlib for assignments.

The majority of examples will be in matlab. Octave is the free version of matlab. If you don't have matlab, you should install octave on your laptop. Bring your laptop to class in order to be able to work on the in-class examples that will be presented daily. This is a relatively small class, so we can make it interactive.

Python and Numpy Help

Python tutorial
Facts and myths about Python names and values
Dive into Python 3
Project Euler (Lots of practice problems)
Introduction to Python for Science
The SciPy lectures
The Numpy User Guide by Travis Oliphant
Numpy/Scipy documentation
More in this reddit thread
Spyder (a Python IDE, like Matlab) is installed in the virtual machine. (Applications Menu > Development > Spyder)
An introduction to Numpy and SciPy
100 Numpy exercises