1/6: Introduction, Finite-Difference Discretization (review), HW1 distributed
1/8: Costs of Gaussian Elimination
1/11: Envelope of factorization, permutations
1/13: Graph models, Cuthill-McKee
1/15: Elimination graphs, minimum degree
1/18: Nested dissection
1/20: Intro to iterative methods
1/22: Matrix splittings, Jacobi, Gauss-Seidel, SOR
1/25: Convergence of stationary iterations
1/27: Stein-Rosenberg and Ostrowski-Reich theorems
1/29: Convergence of SOR, HW2 distributed
2/1: Incomplete Factorization
2/3: Chebyshev iteration
2/5: Convergence of Chebyshev, nonsymmetric case
2/8: Class cancelled
2/10: Class cancelled
2/12: Class cancelled
2/15: Arnoldi and GMRES, Part I
2/17: Arnoldi and GMRES, Part II
2/19: Lanczos and MINRES, HW3 distributed
2/22: Makeup Class, Conjugate Gradient
2/24: Makeup Class, Preconditioning
2/26: Makeup Class, Faber-Manteuffel Theorem, BiLanczos and BiCG
2/29: CGS and BiCGStab
3/2: Additive Schwarz
3/4: Multiplicative Schwarz, Schur Complement Methods
3/7: Overlapping DD, Restricted Additive Schwarz
3/9: Optimized Schwarz
3/11: Two-level methods, Part I
3/14: Two-level methods, Part II
3/16: Smoothing Property
3/18: Coarse-grid correction, two-grid algorithm
3/21: No class
3/23: No class
3/25: No Class: Good Friday
3/28: Multigrid V-cycle
3/30: Effectiveness of the V-cycle
4/1: Multigrid and refined meshes
4/4: Comparing domain decomposition and multigrid
4/6: Final project presentations
|