CS 550

Iterative & Multigrid Solvrs

Course Info

Time: 11:00am-12:15pm Tuesday/Thursday
Location: 1304 SC
Instructor: Luke Olson (lukeo)
Text: Iterative Methods for Sparse Linear Systems, Second Edition by Yousef Saad.
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Course Description

A comprehensive treatment of algebraic and multigrid iterative solvers for systems of equations, primarily linear equations arising from discretization of partial differential equations. Same as CSE 511. Prerequisite: CS 450.

Course Format

(tentative)

The course will follow a lecture format covering

1/5Sparse Computation Fundamentals
2/5Krylov Methods and Preconditioning
2/5Multigrid (mainly algebraic)

Biweekly assignments covering both theory and computation is expected. One goal is to develop a comprehensive library of methods we (intend to) cover over the semester. The text will be followed for a most of the course, but supplemental materials will be handed out for parts of the algebraic mutligrid section. The midterm and final exams will be in the form of projects we develop over the semester.

The grading will be based on 3 components:
Homework: 40%
Project I: 20% (with HW4)
Project II: 40% (includes presentation)

Lectures

Datetopicmaterial
January 16, 2007 Course Intro, Sparse Matrices [.pdf] [.print.pdf]
January 18, 2007 Sparse Matrices [.pdf] [.print.pdf]
January 25, 2007 Projection Methods [.pdf] [.print.pdf]
January 30, 2007 One Dimensional Projection Methods [.pdf] [.print.pdf] [algSD.m] [algMR.m] [algRNSD.m] [onedim.m]
February 1, 2007 Krylov [.pdf] [.print.pdf]
February 15, 2007 Krylov [.pdf] [.pdf]
February 17, 2007 bi-conjugates [.pdf] [.pdf]
February 17, 2007 bi-conjugates [.pdf] [.m] [.m] [.m]
March 1, 2007 J,GS,SOR,SSOR [.pdf] [.pdf] [.pdf] [.pdf]
March 1, 2007 PCG/PGMRES [.pdf] [.pdf]
March 13, 2007 GMG [.pdf]
April 3, 2007 AMG [.pdf]

Homeworks

#Due Datematerial
1Tuesday February 6, 2007 [.pdf] [.tex]
2Thursday February 22, 2007 [.pdf] [.tex]
3Tuesday March 13, 2007 [.pdf] [.tex]
4Thursday, March 29, 2007 [.pdf] [.tex] [.m] [.m] [.m] [.m]
5Thursday, April 12, 2007 [.pdf] [.tex]
finalSaturday, May 5, 2007 [.pdf] [.tex]

Schedule

Date Topic Section Notes
Tue, Jan 16, 07 Introduction 1.x General overview
Thu, Jan 18, 07 Sparse Matrices 3.4,3.5 COO, CSR, LL
Tue, Jan 23, 07 Basic Methods 4.1,4.2 Motivate projection methods. HW1 released
Thu, Jan 25, 07 Projection Methods 5.1,5.2 basic techniques
Tue, Jan 30, 07 Projection Methods 5.3 one-dimensional methods
Thu, Feb 1, 07 Arnoldi 6.1-6.4 Arnoldi, FOM, and variants
Tue, Feb 6, 07 GMRES 6.5 in-depth look HW1 due
Thu, Feb 8, 07 Lanczos 6.6 derive triple recursion HW2 released
Tue, Feb 13, 07 snow -

Thu, Feb 15, 07 CG types, Faber-Manteuffel 6.7-6.10 some theory here
Tue, Feb 20, 07 Lanczos bi-orthogonalization 7.1-7.2 unsymmetric case
Thu, Feb 22, 07 BCG, QMR, CGS, TFQMR 7.1,7.2 unsymmetric methods HW2 due
Tue, Feb 27, 07 Intro to preconditioning 9.1-9.2 basic preconditioning
Thu, Mar 1, 07 PGMRES, PCG 9.3-9.4 Krylov preconditioning HW3 released
Tue, Mar 6, 07 ILU
idea and implementation, PCG
Thu, Mar 8, 07 SPAI

HW4=project I released
Tue, Mar 13, 07 MG

HW3 due
Thu, Mar 15, 07 MG


Tue, Mar 27, 07 MG

HW4 due
Thu, Mar 29, 07 MG

HW5 released
Tue, Apr 3, 07 MG


Thu, Apr 5, 07 MG


Tue, Apr 10, 07 MG


Thu, Apr 12, 07 MG

HW5 due
Tue, Apr 17, 07 MG


Thu, Apr 19, 07 Presentation


Tue, Apr 24, 07 Presentation


Thu, Apr 26, 07 Presentation

Tue, May 1, 07 Presentation

Sat, May 5, 07 Presentation

Project II due