UT CS/M 393N Spring 1999 -- SYLLABUS

NUMERICAL SOLUTIONS OF
ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Instructor: Dr. David M. Young, Jr (DMY)

Material is taken from the following sources
  1. HY-81: "Applied Iterative Methods" by Hageman and Young, Academic Press, 1981.
  2. Y-71: "Iterative Solution of Large Linear Systems" by David M. Young, Academic Press, 1971
  3. YG-II: "A Survey of Numerical Mathematics", Volume II, reprinted by Dover Books in 1988.
  4. WB: Workbook -- may borrow a copy for a refundable deposit from the instructor.
The following syllabus should be used as a guideline only. The amount of time spent on any particular topic may vary, and the syllabus completed after class feed-back has been taken into consideration.

Syllabus

(Last updated: April 26, 1999)

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DateTopic Handouts Sources
L1TuJan 19 Introduction Syllabus & Questionaire Handout
L2ThJan 21 Gen. Dirichlet, Review of Lin Alg., Jacobi, Gauss-Seidel 90.2 "393N Survey of Course" Handout
L3TuJan 26 Direct Sol., Splitting Matrix, SOR Jan 20, 1990: "Review of Linear Algebra" Handout
L4ThJan 28 Model Problem, LDU "Aprrox. Matrix Factorization" Sup 98.4.14;
"Assignment 99.1:Matrix Preliminaries.
Handout
L5TuFeb 02 SOR and Applications 1) "Solvers & SOR" -- sect. 3.3 of AE's dissertation,
2) Summary of Iter. Methods diagram from "Templates".
Handout
L6ThFeb 04 Choices of Splitting Matrix Q, Convergence, Extrapolation Pages -1, -2 by Anne, Feb 4, 1999;
"Convergence of Basic Iter. Methods" Sup 94.2.22.
Handout
L7TuFeb 09 Extrapolation, Variable Extrapolation, Vector Norms, Chebyshev Polynomial Assignment 99.2
Copy of today's slides
HY:Ch3.1-2,Ch4.1-2, Workbook pp 135-169, slides in back
L8ThFeb 11 Norms, Symmetrizable iter, Adaptive Chebyshev, Def. of pseudo residual, Notation for normalized Chebyshev polyn., Slides on Chebyshev Accel Copies of Slides? Slides from 1990
L9TuFeb 16 Vector norms, Conjugate Gradient 2-term formula Copies of slides? 1990 slides, Anne's notes + DMY notes
L10ThFeb 18 Conjugate Gradient -- 3-term 1990 Slides in 3-term CG; HY pp140-141
L11TuFeb 23 DMY: ITPACK 2C; ACE: MODGDP and FORTRAN 1)ITPACK 2C (TOMs article)
2)"IV.2: Subroutine MODGDP: Use w/ ITPACK 2C (same as WB pp271-276)
3)"FORTRAN FOR ITPACK USERS" by ACE Feb 23, 1999
4)"USING ITPACK 2C on UT Math Suns", by ACE Nov 19, 1998
Handouts
L12ThFeb 25 ACE: MODGDP and TOMs article on ITPACK 2C
DMY: 15 mins. on Tridiagonal Systems
"Modified Thomas Method and Block Iterative Methods, Sup 93.5.3 (incl. 2 pages on Block-Jacobi covered later) handouts
L13TuMar 02 Solutions of Tridiagonal Systems 1)"Solutions of Tridiagonal Systems (Sup 98.3.31) + extra summary sheet (attached);
2)"Assignment 99.4 on MODGDP"
Handout
L14ThMar 04 ACE: More on Line Methods, Block Jacobi;
DMY: ADI-- Example and Basic Formula (on handout)
ACE: Peaceman-Rachford
-none- Slides from 1990 Workbook
L15TuMar 09 SOR for Consistently Ordered Matrices -none- Slides in workbook pp 607-610
Y-71:Ch 5.1-6; 6.1-3
Also some material in Workbook pp77-??
L16ThMar 11 Michel Pal: Multigrid -none- Notes and handouts from Anne
--- SPRING BREAK - -
L17TuMar 23 Multigrid 2-3 handouts? Handouts
L17TuMar 23 Non-symmetrizable case -- Krylov Space Methods: Idealized Generalized CG, ORTHODIR, ORTHOMIN, ORTHORES Copy of slides -- Lect 13, 1990 HY-81: 12.3; Slides (Lect. 13, 1990)
L18TuMar 30 IGCG Special Cases 1)Chen's thesis Ch1-5.2
2) Copies of slides, Lect 14 (WB pp 637-641)
3) Assignment 99.5A: Find error(s) on p 12 of Chen's Thesis
HY-81: 12.5-6;
Slides 14.1-8,
Chen's Thesis: Ch 3;
L18ThApr 01 Conjugate residual method (Z=A^T); GCW (Q = 1/2(A + A^T)); Examples:Convection-Diffusion Eqn (A PR and Jacobi), Complex Chebyshev Handout 14.2a Slides 14.9-14.18, Chen's Thesis: Ch 4, HY-81: Ch 12.5-6, 12.2
L19TuApr 06 Lanczos/Bi-conjugate Gradient Copies of slides -- Lect 15, 1990 Chen's Thesis, Ch 4, HY-81, Ch 12
L20ThApr 08 ORTHORES -> Lanczos; NSPCG 1) ORTHORES -> ORTHORES/Lanzos (notes by ACE April '99);
2) ITPACK/NSPCG overview (notes by ACE Apr 1999);
3) CNA Report 228 -- Overview of NSPCG 4) Mini Assignment 2 (via e-mail on ELLPACK format)
Handouts, Chen's thesis
L21TuApr 13 NSPCG/ Project descriptions + overview of PIC methods - none? - CNA report on NSPCG
L22ThApr 15 Complex Chebyshev, Lanczos (review) 1) Complex Chebyshev slide copies (Apr 15, 1999 by ACE),
2) Lect Notes 15.5-15.12 incl. addendums 15.6a-c.
Handouts, HY-'81, Ch 12
L23TuApr 20 Given's rotations, GMRES overview 1)Chen's Thesis (handed out earlier),
2)Mini assigment 3 (on board -- Prob 5.1.7 in GVL p209),
3)Sect. on Householder and Given's transformations from GVL Ch 5.
Handouts, Chen's thesis Ch 5
L22TuApr 22 Dr. Linda Hayes: Finite Elements - none- Black board notes
L24TuApr 27 More on GMRES TBD -
L25TuApr 29 Dr. Linda Hayes: Block Methods and ADI TBD -
L25TuMay 04 Student presentations/ Course survey? TBD -
L25TuMay 06 LAST CLASS -- Student presentation, course survey? TBD -

Other topics (may not have time for)