SCPY 486: Advanced Scientific Computing


Instructor: Chaiwoot Boonyasiriwat (chaiwoot@gmail.com)
Class Hours: Monday and Thursday (1:30PM - 3:00PM)
Class Room: TBA
Objectives: Learn mathematical methods for solving scientific problems on computers
Grading: Homework 100%
Book: book.pdf
Codes: Prof. Trefethen codes: Spectral Methods in MATLAB

Course Schedule

Week Lecture Date Topics Materials
1 1 Nov 4, 2013 PDEs, boundary conditions, finite-difference method, computational domain PDEs, FD
1 2 Nov 7, 2013 Derivation of finite difference coefficients, local and global errors, steady-state heat conduction FD, Homework 1, curve_fitting.m
2 3 Nov 11, 2013 Finite difference solution to the Laplace's equation -
2 4 Nov 14, 2013 Explicit and implicit finite-difference methods for solving the diffusion equation and the wave equation Homework 2
3 5 Nov 18, 2013 Finite element method and the weighted residual method FE
3 6 Nov 21, 2013 Finite element solution to 1D steady-state heat conduction problem -
4 7 Nov 25, 2013 Summary of finite element in one dimension -
4 8 Nov 28, 2013 Finite element in two dimensions -
5 9 Dec 2, 2013 Finite element mesh generation (continued) -
5 - Dec 5, 2013 No class -
6 - Dec 9, 2013 No class -
6 - Dec 12, 2013 No class -
7 10 Dec 16, 2013 Review of finite element method -
7 11-12 Dec 19, 2013 Grid generation methods: Voronoi diagram, Delaunay triangulation, algebraic method; Fourier Spectral method Homework 3
8 13 Dec 23, 2013 Fourier spectral collocation method Spectral Methods
8 14-15 Dec 26, 2013 Spectral and pseudo-spectral method (continued) -
9 - Dec 30, 2013 No class -
9 16 Jan 2, 2014 Finite volume method -
10 17 Jan 6, 2014 Finite volume method (continued) -
10 18 Jan 9, 2014 Inverse problems and formulation Homework 4
11 19 Jan 13, 2014 Linear vector space and functional analysis -
11 20 Jan 16, 2014 Gradient-based optimization method -
12 21 Jan 20, 2014 Gradient-based optimization method (continued) -
12 22 Jan 23, 2014 Regularization methods, Lagrange multiplier -
13 23 Jan 27, 2014 Regularization: Minimum-norm and smoothness constraints
13 24 Jan 30, 2014 Regularization: Total variation (TV) constraint -
14 25 Feb 3, 2014 Methods for choosing regularization parameters: L curve Homework 5
14 26 Feb 6, 2014 Methods for choosing regularization parameters: generalized cross validation (GCV) -
15 27 Feb 10, 2014 Least-squares Kirchhoff migration lsm.zip, lsm2.zip
15 28 Feb 13, 2014 Heuristic optimization methods: genetic algorithm (GA) -
16 29 Feb 17, 2013 Heuristic optimization methods: particle swarm optimization (PSO) -
16 30 Feb 20, 2013 Heuristic optimization methods: artificial neural network (ANN) -

References