Numerical Methods for Geophysical Partial Differential Equations - SIO 239
Prerequisite: calculus and some familiarity with programming.
Yuri Fialko; 321 IGPP; yfialko
ucsd.edu;
Ph. 822-5028
class@ucsd.edu
SYLLABUS
| Date | Topic | Reading/Homework | Lecturer |
| 09 JAN | Introduction; Canonic PDEs and the associated boundary and initial value problems in geophysical applications | Read: Notes; Ames Ch. 1 | YF |
| 11 JAN | Integral transformations; solutions to PDEs in spectral domain | Read: Notes | |
| 16 JAN | No class: Martin Luther King, Jr. Holiday | Read: | YF |
| Finite differences | |||
| 18 JAN | Finite difference approximations; consistency, order, and convergence | Read: Num Rec., Ch. 19.0 Homework 1 |
YF |
| 23 JAN | Stability analysis (von Neumann method, matrix method); transport errors | Read: Num Rec., Ch. 19.1; Hoffman Ch. 10.8 | YF |
| 25 JAN | Explicit and implicit schemes for parabolic equations; upwind and downwind differences; the Crank-Nicholson method; the Richardson (leapfrog) method |
Homework 2 Read: Num Rec., Ch. 19.1, Num Rec., Ch. 19.2; Hoffman Ch. 11.1-11.6 |
YF |
| 30 JAN | Iterative methods for elliptic equations; successive over-relaxation (SOR); the Alternating-Direction Implicit (ADI) method | Read: : Hoffman Ch. 9.4-9.8; Num Rec., Ch. 19.0 | YF |
| 01 FEB | Method of characteristics for hyberbolic equations; the Lax-Wendroff scheme; the MacCormack method | Read: Hoffman Ch. 12.1-12.13 | YF | Finite elements |
| 06 FEB | Weak form of PDEs; FE equations |
Homework 3 Read: Burnett, Ch. 1; FEM intro/summary |
YF |
| 08 FEB | Weighted residual methods; basis functions | Read: Burnett, Ch. 3, 5.2 | YF |
| 13 FEB | Assembly of element equations; 2-D FE | Read: Burnett, Ch. 5.3 | YF |
| 15 FEB | 2-D FE cont'd; Multi-dimensional variational principles |
Homework 4 Read: Burnett, Ch. 13 |
YF |
| 20 FEB | No class: President's Day Holiday | Read: | YF |
| 22 FEB | Introduction to ABAQUS | See manuals in BarnYard | YF |
| 27 FEB | Mesh generation and assembly; numerical integration; discretization errors | Read: Class notes | YF | Boundary Elements |
| 29 FEB | BEM formulation, integral equations |
Read: Crouch and Starfield, Ch. 1,3; BEM intro/summary; Class notes |
YF |
| 05 MAR | Examples of BE; introduction to TWODD and DIS3D codes | Read: Class notes; TWODD DIS3D |
YF | Other techniques |
| 07 MAR | Multigrid and spectral methods; Monte Carlo methods | Read: Notes; Num Rec., Ch. 19.4, Ch. 19.6 | YF |
| 12 MAR | Class presentations | YF | |
| 14 MAR | Class presentations (cont'd) | YF |
SIO 239 SUGGESTED BOOKS:
Textbooks:
Numerical methods for engineers and scientists, J. D. Hoffman, McGraw-Hill, 1992.
Reference Books:
Numerical Recipes/The art of scientific computing 2nd ed., W. H. Press et al., Cambridge, 1992.
Numerical methods for partial differential equations, W. F. Ames, Barnes&Noble, 1969
Finite element analysis: From concepts to applications, D. S. Burnett, Addison-Wesley, 1987.
Boundary element methods in solid mechanics, S. L. Crouch and A. M. Starfield, George Allen and Unwin, 1983.
Computer Homework:
Computer homework can be done most easily by using MATLAB
which runs on most machines. If you do not have a computer account
we will set you up.