| Instructor | Chaiwoot Boonyasiriwat |
| Assessment | homework 60%, project 40% |
| Online learning | ZOOM |
| Homework Files | hw.pdf |
| Homework submission | submit your homework file here |
| Date | Time | Topics |
|---|---|---|
| Jun 30, 2025 | 9.00-12.00 |
Course introduction, numerical differentiation and finite difference (FD) method, numerical integration and rectangular rules, Euler method Code: numerical differentiation of sin(x) [exercise1.ipynb] Example: radioactive decay Lecture: lecture1.pdf Video: 2025-06-30.mp4 |
| Jul 3, 2025 | 9.00-12.00 |
Euler method, Taylor series method, Heun method, Runge-Kutta methods Code: [exercise2.ipynb], [exercise3.ipynb] Lecture: lecture2.pdf Video: 2025-07-03.mp4 |
| Jul 7, 2025 | 9.00-12.00 |
Explicit and implicit methods, explicit Runge-Kutta methods, 4th-order Runge-Kutta method (RK4) Code: [exercise4.ipynb], [exercise5.ipynb] Lecture: lecture3.pdf Video: 2025-07-07.mp4 |
| Jul 14, 2025 | 9.00-12.00 | Embedded method, solving the linear, driven, damped oscillation problem using RK4, phase space, stroboscopic map, nondimensionalization Code: [exercise6.ipynb] Lecture: lecture4.pdf Video: 2025-07-14.mp4 |
| Jul 18, 2025 | 9.00-12.00 | Interpolation, boundary value problems, shooting method Code: [exercise7.ipynb] Lecture: lecture5.pdf Video: 2025-07-18.mp4 |
| Jul 21, 2025 | 9.00-12.00 | Finite difference method, Thomas algorithm, Numerov's method, physical phenomena governed by the Laplace and Poisson equations Lecture: lecture6.pdf Video: 2025-07-21.mp4 |
| Jul 24, 2025 | 9.00-12.00 | Iterative methods for solving a sparse linear system of algebraic equations, solving 2D Poisson equation using the Jacobi method Code: [exercise8.ipynb] Lecture: lecture7.pdf Video: 2025-07-24.mp4 |
| Jul 30, 2025 | 9.00-12.00 | Solving 2D Poisson equation using the Gauss-Seidel and SOR methods, solving the diffusion equation using the FD method: implicit and explicit schemes, von Neuman stability analysis Code: [exercise9.ipynb] Lecture: lecture8.pdf Video: 2025-07-30.mp4 |
| Aug 1, 2025 | 9.00-12.00 | Implicit methods for diffusion equation, Crank-Nicolson method, alternating-direction implicit (ADI) method, explicit scheme for 1D scalar wave equation, dispersion relation Code: [exercise10.ipynb] Lecture: lecture9.pdf Video: 2025-08-01.mp4 |
| Aug 7, 2025 | 13.00-15.00 | Numerical dispersion, dispersion relation and stability analysis of an explicit FD scheme for 1D scalar wave equation, CFL condition Code: [exercise11.ipynb] Lecture: lecture10.pdf Video: 2025-08-07.mp4 |
| Aug 13, 2025 | 13.00-15.00 | Solving first-order coupled acoustic wave equations on regular and staggered grids, stability analysis of an explicit FD scheme on a staggered grid Code: [exercise12.ipynb] |
| Aug 21, 2025 | 13.00-15.00 | Maxwell's equations in free space and in matters, staggered grids for modeling EM wave propagations, elastic wave equations: P-SV, P-SH stress-velocity formulations Lecture: lecture12.pdf Video: 2025-08-21.mp4 |
| Aug 28, 2025 | 13.00-15.00 | FD schemes for modeling EM and elastic waves on staggered grids, modeling wave propagation in unbounded domains Code: [exercise13.ipynb] Lecture: lecture13.pdf Video: 2025-08-28.mp4 |
| Sep 4, 2025 | 13.00-15.00 | Implementation of ADI for 2D diffusion equation, Engquist-Majda absorbing boundary conditions Lecture: lecture14.pdf Video: 2025-09-04.mp4 |
| Sep 11, 2025 | 13.00-15.00 | Solving the Helmholtz equation, linear advection equation, and inviscid Burgers' equation, method of characteristics Lecture: lecture15.pdf Video: 2025-09-11.mp4 |
| Sep 18, 2025 | 13.00-15.00 | Solving ray tracing equations and the eikonal equation Lecture: lecture16.pdf Video: 2025-09-18.mp4 |
| Sep 25, 2025 | 13.00-15.00 | Solving the diffusion-advection equation and Schrodinger equation, higher-order FD methods |
| Oct 9, 2025 | 13.00-15.00 | Solving PDEs in other coordinate systems |
| Oct 16, 2025 | 13.00-15.00 | Solving PDEs using spectral methods |
| Oct 23, 2025 | 13.00-15.00 | Solving PDEs using the finite-element method |
| Oct 30, 2025 | 13.00-15.00 | Solving PDEs using the finite-element method (continued) |
| Dec 11, 2025 | 9.00-12.00 | Project presentation |