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.

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

D2L
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