## 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

- Farlow, S. J. 1993, Partial Differential Equations for Scientists and Engineers, Dover.
- Hughes, T. J. R., 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover.
- LeVeque, R. J. 2007, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM.
- Trefethen, L. N. 2000, Spectral Methods in MATLAB, SIAM.