MTH 655
and
MTH 659 (Numerical Analysis)
Large scale scientific computing methods
- Fall 2009
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| Labs/schedule |
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Schedule/assignment |
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Mon 1/7
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- Administration: fill out questionnaire.html
- Overview - slides in Blackboard.
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Wed 1/09
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Functional iteration and Newton's method in R: convergence. Read Chapter 5 from [Kelley]. and preliminaries, if necessary.
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Fri 1/11
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LAB 1
(MLC Kidd 108J) computer lab. You can come as early as 8:30.
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Mon 1/14
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Implementation issues for Newton's method (improve primitive algorithm).
A-posteriori estimates for error.
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Wed 1/16
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Newton's in N-dimensions. Newton-like methods: chord, secant, Broyden, inexact Newton's methods.
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Fri 1/18
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LAB 2
(MLC Kidd 108J) computer lab. You can use the primitive template newton2d.m
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Wed 1/23
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Relaxation algorithms for nonlinear problems. Newton for semismooth
functions. Application: solving problems under inequality constraints.
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Fri 1/25
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LAB 3
(MLC Kidd 108J) computer lab.
Linux for beginners
and
C-shell tutorials
Fortran tutorial
and
Fortran reference
For C tutorials - well, just
google-it up
Please read about ssh and
scp .
You must be able to use some text editor under Unix.
I suggest
emacs or vi. Please look up the basics. Or ask me.
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Mon 1/28
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More on solving problems under inequality constraints: semismooth Newton methods.
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Wed 1/30
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Jacobi, Gauss-Seidel and theor relaxation versions. Conditions on
convergence involving diagonal dominance and spectral
radius. Gershgorin circle theorem.
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Fri 2/1
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Continue
LAB 3
in (MLC Kidd 108J) computer lab.
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Mon 2/4
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Spectral properties of the "discrete laplacian". Spectrum of weighted Jacobi
iteration matrix.
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Wed 2/6
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Smoothing properties of weighted Jacobi method. Idea of coarse grid correction.
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Fri 2/8
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LAB 4
(MLC Kidd 108J computer lab). Exploration of Newton and semi-smooth
Newton methods. Stationary and relaxation iterative solvers.
You can use codes templates semicon.m and
semilinear.m.
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Mon 2/11
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Coarse grid correction wrap-up. Full multigrid idea and performance.
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Wed 2/13
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Non-stationary iterative methods: projectiob methods and Krylov subspaces.
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Fri 2/15
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LAB 5
(MLC Kidd 108J computer lab): inexact Newton-Krylov methods
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Mon 2/18
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Non-stationary iterative methods and Krylov spaces; steepeest descent
(SD), conjugate gradients (CG), and GMRES.
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Wed 2/20
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Rosenbrock banana. Preconditioning: algebraically or yusing physics based preconditioners.
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Fri 2/22
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LAB 6
(MLC Kidd 108J computer lab): preconditioning in nonstationary methods.
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Mon 2/25
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Basics of parallel computing with mypi.f example.
Presentation 655-jacobi.pdf .
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Wed 2/27
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Overview of MPI (Message Passing Interface).
Reduce and send-receive operations.
Scalability in parallel computing.
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3/1
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LAB7
(MLC Kidd 108J computer lab): working on the cluster.
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Mon 3/4
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Domain decomposition methods: overlapping: Schwarz additive method. Block Jacobi.
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Wed 3/6
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Domain decomposition methods: nonoverlapping; D-N and N-N methods.
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3/8
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(MLC Kidd 108J computer lab): finishing all assignments
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Mon 3/11
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Monte Carlo methods.
(LABS 1-4 must be turned in).
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Wed 3/13
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Introduction to statistical mechanics:
molecular dynamics and lattice methods.
(ALL LABS must be turned in).
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3/8
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LAB REVIEW
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