Instructor | : Chaiwoot Boonyasiriwat (chaiwoot@gmail.com) |

Class Hours | : Monday (3:00PM-4:30PM), Thursday (2:30PM-4:00PM) |

Classroom | : Computer Lab |

Objectives | : Learn how to numerically solve PDEs, and estimate medium physical properties related to geophysical problems |

Grading | : Homework 30, Participation 10, Midterm Exam 30, Final Exam 30 |

Policies |
- each homework (report and codes) must be submitted electronically to chaiwoot@gmail.com - each homework is due in one week - homework submitted after the due date will not be graded - each homework has 10 points - copying homework of others will result in a zero point |

Lecture | Date | Lecture Notes | Notifications |
---|---|---|---|

1 | Jan 25, 2016 | Class orientation, PDEs and integral equations, overview of relevant mathematical methods, introduction to Fortran programming, OpenGL Redbook codes, introduction to symplectic integration | HW1: Solving the Lotka-Volterra model using explicit, implicit, and symplectic Euler methods, MATLAB files |

2 | Jan 28, 2016 | Symplec Euler method and the derivation of Stromer-Verlet method (staggered-grid method) | |

3 | Feb 1, 2016 | Computing the Earth magnetic field from a magnetic dipole, Finite difference (FD) approximation | HW2: Earth magnetic field and charged particle motion |

4 | Feb 4, 2016 | Finite-difference solutions to Laplace, Poisson, and diffusion equations; implicit finite difference methods | HW3: Solving the 2D diffusion equation using Crank-Nicolson method |

5 | Feb 8, 2016 | Direct methods and iterative methods for solving linear systems | HW4: Solving a linear system using steepest descent and conjugate gradient methods |

6 | Feb 11, 2016 | Simulation of acoustic wave propagation using explicit FD method: regular and staggered grids | |

7 | Feb 15, 2016 | von Neumann stability analysis for an explicit scheme | |

8 | Feb 18, 2016 | Absorbing boundary conditions (ABC) and layers (ABL): Clayton-Engquist (CE) ABC, sponge ABL, perfectly matched layer (PML), hybrid methods | |

9 | Feb 25, 2016 | Frequency-domain waveform modeling, Simulation of elastic and electromagnetic wave propagation | - |

10 | Feb 29, 2016 | EM and modeling of dipole antenna | |

11 | Mar 3, 2016 | Adaptive mesh refinement, code | Berger and Oliger (1984) |

12 | Mar 7, 2016 | Introduction to finite volume method | |

13 | Mar 10, 2016 | Finite volume method (continued) | - |

14 | Mar 21, 2016 | Finite volume method (continued) | |

15 | Mar 23, 2016 | Finite volume method (continued) | - |

16 | Apr 4, 2016 | Grid generation | Read Persson and Strang (2004) |

17 | Apr 4, 2016 | Grid generation (continued) | - |

18 | Apr 18, 2016 | Artificial neural network | |

19 | Apr 18, 2016 | Artificial neural network (continued) | - |

20 | Apr 20, 2016 | Eikonal solver | |

21 | Apr 20, 2016 | Eikonal solver (continued) | - |

22 | Apr 25, 2016 | Fourier spectral method | |

23 | Apr 25, 2016 | Chebyshev spectral methods | - |

24 | Apr 27, 2016 | Introduction to finite element (FE) method and weighted residual method, FE solution to a 1D steady-state problem, Element point of view in 1D FEM, higher-order FEM, 1D time-dependent problems | |

25 | Apr 27, 2016 | FE solution to a 2D steady-state problem, 2D finite element method (continued) | - |

26 | May 4, 2016 | TBA | |

27 | May 4, 2016 | TBA | - |

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- Shearer, P., 2009, Introduction to Seismology, Cambridge University Press.
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- Abarbanel, S., and D. Gottlieb, 1988, On the construction and analysis of absorbing layers in CEM, Applied Numerical Mathematics, 27, no. 4, 331-340.
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- MIT Open Courseware: Numerical methods for partial differential equations
- Numerical methods for PDEs

Copyright © 2013-2018 Mahidol University Center for Scientific Computing. All rights reserved.

272 Rama VI Road, Room P416, Ratchathewee, Bangkok 10400, THAILAND. Tel: +66 (0)2 201 5770-1 Fax: +66 (0)2 354 7159

272 Rama VI Road, Room P416, Ratchathewee, Bangkok 10400, THAILAND. Tel: +66 (0)2 201 5770-1 Fax: +66 (0)2 354 7159