AMSC 661 / CMSC 661 Scientific Computing II (Section 0101)

Information for Spring 2010


Dianne P. O'Leary

Reminder: Normal office hours through May 17, and also on May 21, but not on May 18.

oleary@cs.umd.edu

When and Where: Monday, 4pm - 7pm (CSI 2107) (CSI is the Computer Science Classroom building, attached to A.V. Williams and behind the Wind Tunnel.)

Office Hours: Monday 3-3:40, Tuesday 12:30-1:20, Friday 8:45-10, and by appointment, in AVW 3271.

Topics: Numerical solution of partial differential equations using finite element and finite difference methods. Solution of sparse systems of linear equations. Wavelet and fast transform methods.

Textbook: Stig Larsson and Vidar Thomee, Partial Differential Equations with Numerical Methods, Springer 2003: ISBN 3-540-01772-0.

Known typos in the textbook

Programming language: We will use Matlab for the programming assignments.

Grading:

  • Quizzes: 140 points. Nine quizzes will each be 20 minutes long, The lowest two scores will be dropped.
  • Assignments: approx. 160 points. This will involve a mix of written work, programming, and analysis of results.
  • Term project: 100 points. Each student will be given a manuscript. The project will be to write a review of the manuscript and test the numerical method that it discusses.
  • Exams: none.

    • CMSC Masters Comprehensive Exam grade: based on quiz grades

    Questions? Please contact me.

    Basic Information:

  • Final Grades as of 05-19-2010
  • 2010 Course Information and Syllabus
  • UMCP Code of Academic Integrity
  • Information about computer accounts. For your assignments, you may use GRACE or any other machine with Matlab access.
  • 02-16-2010 Accessing Matlab on the GRACE machines, with graphics Thanks to Nick for presenting this information.
  • Notes for CMSC 460. Use these if you find that your background is lacking.
  • How Not to go about a programming assignment by Agustín Cernuda del Río
  • Survival Guide for Scientific Computing
  • Guidelines on Writing and Documenting Scientific Computing Software Read this before you submit any programming assignment.
  • Documentation for Matlab's PDE Toolbox

    • Accommodations: If you require academic accommodations due to a religious obligation or a disability, please provide documentation by the end of the 2nd week of the semester.

    Tentative Schedule for Spring 2010:

    01 Jan 25 Preliminaries, ODE BVP
    02 Feb 1 Quiz 1 ODE BVP Homework 1 assigned.
    03 Feb 8 Snow Day
    04 Feb 15 Quiz 2 ODE BVP / Elliptic PDEs
    05 Feb 22 Quiz 3 Elliptic PDEs Homework 1 due
    06 Mar 1 Quiz 4 Fourier, Wavelet methods Homework 2 assigned.
    07 Mar 8 Colloquium, Sparse Matrices
    Mar 15 Spring Break No class
    08 Mar 22 Sparse Matrices Homework 2 due. Homework 3 assigned.
    09 Mar 29 ODE IVP, Parabolic PDE Passover
    10 Apr 5 Quiz 5 Parabolic PDE Homework 3 due. Term project topics announced.
    11 Apr 12 Quiz 6 Parabolic PDE Homework 4 assigned.
    12 Apr 19 Quiz 7 Hyperbolic PDE Term project decision due.
    13 Apr 26 Quiz 8 Hyperbolic PDE, Eigenproblem Homework 4 due.
    May 3 No class
    14 May 10 Quiz 9 Eigenproblem, Multipole
    May 17 4:00 pm Term project due.

    Lecture Notes

  • 01-25-2010 Introduction
  • Solution of ordinary differential equations, boundary value problems
  • 01-25-2010 Notes Part 1: Some theory
  • 01-20-2010 Notes Part 2: Computational methods
  • Solution of elliptic partial differential equations
  • 02-01-2010 Notes Part 1: Some theory
  • 02-01-2010 Notes Part 2: Computational methods
  • 02-22-2010 slit.m Adaptive mesh example
  • 04-19-2010 Notes Part 3: Eigenvalue problems
  • 05-10-2010 Tacoma Narrows Bridge collapse
  • 05-10-2010 Hearing the shape of a drum Wikipedia entry
  • 05-10-2010 Vibrational Modes of a Membrane demo by Daniel A. Russell
  • Solution of sparse linear systems of equations
  • 03-01-2010 Notes Part 1: Direct methods
  • spar5.m Demo: reordering the 5-point operator using various algorithms. (The documentation is not good.)
  • Notes Part 2: Iterative methods
  • Notes Supplement: Convergence of SIMs
  • Solution of parabolic differential equations
  • 03-23-2010 Notes on initial value problems for ODEs
  • 03-23-2010 Notes on theory for parabolic problems
  • 03-23-2010 Notes on numerical methods for parabolic problems
  • Solution of hyperbolic differential equations
  • 04-07-2010 Notes on theory for hyperbolic problems
  • 04-07-2010 Notes on numerical methods for hyperbolic problems
  • 04-26-2010 pdedemo2.m (Mathworks demo)
  • 04-26-2010 some documentation for pdedemo2
  • 04-26-2010 pdedemo6.m (Mathworks demo)
  • 04-26-2010 pdedemo2movie.mat (result of Mathworks demo)
  • 04-26-2010 pdedemo6movie.mat (result of Mathworks demo)
  • Fourier transforms, wavelets, and fast multipole algorithms
  • 02-23-2010 Notes on Fast Poisson Solvers
  • 02-23-2010 Notes on Transforms and Wavelets
  • 03-01-2010 Two wavelet figures from Kammler's book
  • 02-23-2010 waveletsigdemo.m
  • 02-26-2010 waveletimagedemo.m
  • 02-26-2010 elk.jpg image used by waveletimagedemo.m
  • 02-26-2010 Supplementary Notes on Transforms and Wavelets
  • Multipole article by Sun and Pitsianis (This link should work from the umd.edu domain.) (SIAM Review Vol 43, No 2, pp 289-300)
  • 04-27-2010 Notes on the Fast Multipole Method

    • Homework

  • 02-01-2010 Information about Homework 1
  • 03-03-2010 Sample solution to Homework 1 Use the username and password from the top of Quiz 2.
  • 03-01-2010 Information about Homework 2 Watch the FAQs for updates.
  • Comments on the Solution to Homework 2
  • Information about Homework 3 including comments on solution (04-15-2010)
  • 04-15-2010 Information about Homework 4 05-10-2010: Partial solution posted.
  • Term Project: Due 4pm, May 17, 2010.
  • 03-29-2010 2010 Description of the project.
  • 04-05-2010 List of papers from which to choose.

    • Quizzes: 2010. Hints should appear on the Tuesday before the quiz.

  • quiz 1: Hints. L&T Problems 2.1 - 2.4, in case you don't yet have a copy of the textbook. Quiz Questions and Answers . Mean = 18, Median = 17.
  • quiz 2: Hints. Quiz Questions and Answers . Mean=16, Median=16.
  • quiz 3: Hints. Quiz Questions and Answers . Mean=17, Median=17.
  • quiz 4: Hints. Quiz Questions and Answers . Mean = 18, Median = 18.
  • quiz 5: Hints. Quiz Questions and Answers . Mean = 15, Median = 15.
  • quiz 6: Hints. Quiz Questions and Answers . Mean = 15, Median = 15.
  • quiz 7: Hints. Quiz Questions and Answers . Mean = 12, Median = 14.
  • quiz 8: Hints. Quiz Questions and Answers . Mean=15, Median = 16.
  • quiz 9: Hints. Quiz 05-10-2010 Questions and Answers .

    • Quizzes: 2005

  • quiz 1: Hints. Quiz Questions and Answers .
  • quiz 2: Hints. Quiz Questions and Answers .
  • quiz 3: Hints. Quiz Questions and Answers .
  • quiz 4: Hints. Quiz Questions and Answers .
  • quiz 5: Hints. Quiz Questions and Answers .
  • quiz 6: Hints. Quiz Questions and Answers .
  • quiz 7: Hints. Quiz Questions and Answers .
  • quiz 8: Hints. Quiz Questions and Answers .
  • quiz 9: Hints. Quiz Questions and Answers .

    • References other than the textbook: One-third of the course material (sparse matrix computation and FFT/wavelet) will be taken from other references:

  • Chapter 23 and Unit VII (Sparse Matrix Computations) of Scientific Computing with Case Studies by Dianne P. O'Leary, SIAM Press, 2009. If you don't already own this book, variants of the relevant chapters can be downloaded (free, using the University's license) from the IEEE/AIP magazine called Computing in Science and Engineering:
  • Chapter 23: Dianne P. O'Leary, ``Finite Differences and Finite Elements: Getting to Know You," Computing in Science and Engineering.
    Project: Vol. 7, No. 3, May/June 2005, pp. 20-23.
    Solution: Vol. 7, No. 4, July/August 2005, pp. 71-75.
  • Chapter 27: Dianne P. O'Leary, ``Solving Sparse Linear Systems: Taking the Direct Approach," Computing in Science and Engineering.
    Project: Vol. 7, No. 5, September/October 2005, pp. 62-67.
    Solution: Vol. 7, No. 6, November/December 2005, pp. 77-80.
  • Chapter 28: Dianne P. O'Leary, ``Iterative Methods for Linear Systems: Following the Meandering Way," Computing in Science and Engineering.
    Project: Vol. 8, No. 4, July/August 2006, pp. 74-78.
    Solution: Vol. 8, No. 5, September/October 2006, pp. 91-93.
  • Chapter 29: Dianne P. O'Leary, ``Elastoplastic Torsion: Twist and Stress," Computing in Science and Engineering.
    Project: Vol. 6, No. 4, July/August 2004, pp. 74-76.
    Solution: Vol. 6, No. 5, September/October 2004. pp. 63-65.
  • Chapter 30: Dianne P. O'Leary, ``Fast Solvers and Sylvester Equations: Both Sides Now," Computing in Science and Engineering.
    Project: Vol. 7, No. 6, November/December 2005, pp. 74-77.
    Solution: Vol. 8, No. 1, January/February 2006, pp. 81-83.
  • Chapter 31: Dianne P. O'Leary, ``Eigenvalues: Valuable Principles," Computing in Science and Engineering.
    Project: Vol. 7, No. 4, July/August 2005, pp. 68-70.
    Solution: Vol. 7, No. 5, September/October 2005, pp. 67-70.
  • Chapter 32: Dianne P. O'Leary, ``Multigrid Methods: Managing Massive Meshes," Computing in Science and Engineering.
    Project: Vol. 8, No. 5, September/October 2006, pp. 86-90.
    Solution: Vol. 8, No. 6, November/December 2006, pp. 89-91.
    • For solutions, it is better to use those found at the book's website.
  • Tutorials on Fourier and wavelet methods.
  • one
  • two
  • (added 05-10-2010) Life beyond bases: The advent of frames (Part I), J. Kovacevic, J. and A. Chebira, IEEE Signal Processing Magazine, Vol. 24, No. 4, 2007, pp. 86--104.
  • (added 05-10-2010) Ingrid Daubechies, Ten Lectures on Wavelets, SIAM, 1992. Chapter 1.
  • (added 05-10-2010) Wavelets and Applications, John J. Benedetto and Michael W. Frazier, CRC Press, 1993. Chapters 3 and 7.
  • Xiaobai Sun and Nikos P. Pitsianis, ``A Matrix Version of the Fast Multipole Method," SIAM Review 43 (2001) 289-300.

    • Old lecture notes