Course Information

Day One Handout

The course meets in slot 18, from 10:30-11:45am on Tuesdays and Thursdays, in HH 3013. My office hours are on Tuesdays, from 9-10:20 AM, and Wednesdays, from 10:30AM - noon, in HH-2019.

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

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

  • 1/4: Introduction, Finite-Difference Discretization (review), Dense Gaussian Elimination, HW1 distributed, Q1 Code, Q2 Code, Q3 Code, Q4 Code
  • 1/9: Banded Gaussian Elimination, envelope of factorization, permutations
  • 1/11: Graph models, Cuthill-McKee, Elimination graphs, HW2 distributed, Solutions
  • 1/16: Minimum degree, Nested Dissection, HW1 due
  • 1/18: Intro to iterative methods, matrix splittings, HW3 distributed, Nested Dissection code, driver
  • 1/23: Convergence of stationary iterations, HW2 due
  • 1/25: Convergence of stationary iterations, part 2, HW4 distributed, Solutions, Jacobi code, GS code, SOR code, Driver
  • 1/30: Incomplete factorizations, HW3 due
  • 2/1: Chebyshev Iteration
  • 2/6: Nonsymmetric matrices, Arnoldi and GMRES, HW4 due, HW5 distributed, Solutions, Q1 Driver, GS code, Chebyshev driver, Chebyshev
  • 2/8: Arnoldi and GMRES, Part II, Lanczos
  • 2/13: No class
  • 2/15: No class
  • 2/20: Winter Break
  • 2/22: Winter Break
  • 2/26: Makeup class (HH3017, 9AM) MINRES and CG, HW6 distributed, Solutions
  • 2/27: Snow day
  • 2/28: Makeup class (HH3017, 9AM) Preconditioning, Faber-Manteuffel Theorem, HW5 due
  • 3/1: BiLanczos and BiCGStab, HW7 distributed, Solutions, Driver code
  • 3/6: Schwarz Methods, HW6 due
  • 3/8: Overlapping DD, Restricted Additive Schwarz, HW8 distributed, Driver, Matrix, Subdomain setup, Additive, Multiplicative
  • 3/13: Optimized Schwarz, HW7 due
  • 3/15: 2-level methods, HW9 distributed
  • 3/20: Smoothing property, coarse-grid correction, HW8 due
  • 3/22: 2-grid and V-cycle algorithms
  • 3/27: No class
  • 3/29: No class
  • 4/3: Multigrid theory, non-uniform meshes, HW9 due
  • 4/5: Algebraic Multigrid, comparing MG and DD
  • 4/5: Final project presentations, 2-3pm in SN4068
  • 4/13: Final Exam, 12:00 - 2:30pm, HH-3013