Course Information

Day One Handout

The course meets in slot 04, from 11:00-11:50 AM on Mondays, Wednesdays, and Fridays, in HH-3017. My office hours are Mondays from 1:30-2:30pm and Fridays from 9-11am.

Textbook
No textbooks are required for this course. Relevant e-books from the library's collection include:

  • Iterative methods for sparse linear systems by Saad (full text pdf available here)
  • Iterative methods for solving linear systems by Greenbaum
  • Matrix iterative analysis by Varga
  • Finite elements and fast iterative solvers with applications in incompressible fluid dynamics by Elman, Silvester, and Wathen
  • Iterative methods for linear systems: theory and applications by Olashanskii and Tyrtyshnikov
  • A multigrid tutorial by Briggs, Henson, and McCormick
  • An introduction to domain decomposition methods: algorithms, theory, and parallel implementation by Dolean, Jolivet, and Nataf

    Course Notes
  • Part one, lectures from 1/6 through 3/6
  • Part two, lectures from 3/9 through 3/20
  • Part three, lectures from 3/23 through 4/3

    D2L
    This course will not be using D2L; all material online will be posted here.
    • Approximate Schedule



  • 1/8: Introduction, Finite-Difference Discretization (review), HW1 distributed, Solutions, Solution code, Solution driver
  • 1/9: Costs of Gaussian Elimination (meet at 2pm in HH-3015)
  • 1/10: Envelope of factorization, permutations
  • 1/13: Graph models, Cuthill-McKee, HW2 distributed, Solutions
  • 1/15: Elimination graphs, minimum degree
  • Snowmageddon
  • 1/27: Nested dissection, HW1 due, HW3 distributed, Solutions, ND code, Driver
  • 1/29: Intro to iterative methods
  • 1/31: Matrix splittings, Jacobi, Gauss-Seidel, SOR, HW2 due
  • 2/3: Convergence of stationary iterations, HW4 distributed, Solutions, Solution code, Solution driver
  • 2/5: Stein-Rosenberg and Ostrowski-Reich theorems
  • 2/7: Convergence of SOR, HW3 due
  • 2/10: Incomplete Factorization, HW5 distributed, Solutions, SOR code, SOR driver, ILU driver
  • 2/12: Chebyshev iteration, HW4 due
  • 2/14: Convergence of Chebyshev, nonsymmetric case; 10-11am, SN-4083
  • 2/14: Arnoldi and GMRES, Part I
  • 2/17: Arnoldi and GMRES, Part II, HW5 due
  • 2/19: Midterm covers material through end of lecture on 2/10 and HW5. Solutions
  • 2/24: Lanczos and MINRES, HW6 distributed, Solutions, Chebyshev code, Driver
  • 2/26: Conjugate Gradient
  • 2/28: Snow day
  • 3/2: Snow day, HW7 distributed, Solutions, Sample code, Driver
  • 3/4: Preconditioning, HW6 due
  • 3/6: Faber-Manteuffel Theorem, BiLanczos and BiCG; 10-11am, SN-4083
  • 3/6: CGS and BiCGStab
  • 3/9: Additive Schwarz, HW8 distributed, Solutions, Code, Driver
  • 3/11: Multiplicative Schwarz, Schur Complement Methods, HW7 due
  • 3/13: Overlapping DD, Restricted Additive Schwarz
  • 3/16: Optimized Schwarz, HW9 distributed, Solutions, Code, Driver
  • 3/18: Two-level methods, Part I
  • 3/20: Two-level methods, Part II
  • 3/23: Smoothing Property, HW10 distributed, Solutions, DD code, DD driver, MG code, MG driver, HW8 due (revised date)
  • 3/25: Coarse-grid correction, two-grid algorithm, HW9 due
  • 3/27: The Multigrid V-cycle
  • 3/30: Effectiveness of the V-cycle
  • 4/1: Multigrid and refined meshes
  • 4/3: Comparing domain decomposition and multigrid, HW10 due
  • 4/15-17: Take-home final exam, due by 5pm on Friday, April 17.