AA+372+Syllabus

The purpose of computing is insight, not numbers. - Richard W. Hamming computer architecture: hierarchical memory, pipelines, etc.; Moore's law tools: programming languages, software, libraries, MPI, openMP, visualization, publicly available codes; need to know what's available examples: N-body, hydrodynamics/MHD, adaptive meshes || Hennessy & Patterson; @http://top500.org/ effect of cache branch prediction || || || Errors: truncation, round-off Stability (von-Neumann's linear stability analysis), Convergence, Consistency Interpolation || Thomas Algorithm for Tridiagonal System The choice of u, v here for Sherman-Morrison formula is not appropriate. A better choice is u'=(1,0,..,0,c_n) & v'=(1,0,...,0,a_1). || ||  || Root-finding || A set of notes from Aarhus University detailing the Romberg method:  ||  ||  || Slides based on "A Multigrid Tutorial" || || matlab code to set up different rate coefficients:
 * Date || Topic || Refs. || Slides || Homework ||
 * week 1 || Overview: what will be covered? frequently-used basic tools
 * week 2 || Taylor series expansion: simple examples
 * week 3 || Numerical integration &
 * week 4 || System of linear equations; tridiagonal system; LAPACK || Extremely lucid article on Conjugate-Gradient method: [[file:painless-conjugate-gradient.pdf]]

fortran program to create a logarithmic grid: just use logspace(1,log10(200),100) in matlab

this is how the mach number vs. radius plot looks like for an isothermal Parker wind with T=1.e6 K: || ODEs: boundary value problems: shooting methods, relaxation methods || matlab files for solving the nonlinear pendulum: x'' + w0^2 sin(x) = 0 via Euler, RK2,RK4, Leap-Frog:
 * week 5 || ODEs: initial value problems: Runge-Kutta methods, explicit vs. implicit methods, stiff problems

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 * week 6 || PDEs: elliptic equations, Poisson's equation; Operator/directional splitting ||  || [[file:lec7.pdf]] || [[file:hw6_na.pdf]] ||
 * week 7 || PDEs: hyperbolic/parabolic equations; advection equation, FTCS, Lax-Wendroff, Godunov schemes; Crank-Nicolson method || Leveque ||  ||   ||
 * week 8 || Random numbers and Monte Carlo methods ||  ||   ||   ||
 * week 9 || Fourier/spectral methods ||  ||   ||   ||