Numerical Methods for Geophysical Partial Differential Equations - SIO 239
Prerequisite: calculus and some familiarity with programming.

Yuri Fialko; 321 IGPP;; Ph. 822-5028
Lecture course, 4-units, letter grade or S/U grade, homework, class project in lieu of final exam.
Time: Mon Wed , 10:30-11:50 PM, IGPP 303 - Munk Room



Date Topic Reading/Homework Lecturer
04 JAN Introduction; Canonic PDEs and the associated boundary and initial value problems in geophysical applications Read: Notes; Ames Ch. 1 YF
06 JAN Integral transformations; solutions to PDEs in spectral domain Read: Notes
Finite differences
11 JAN Finite difference approximations; consistency, order, and convergence Read: Num Rec., Ch. 19.0 Homework 1 YF
13 JAN No class Homework 2
18 JAN No class: Martin Luther King, Jr. Holiday Read: YF
20 JAN Stability analysis (von Neumann method, matrix method); transport errors Read: Num Rec., Ch. 19.1; Hoffman Ch. 10.8
25 JAN Explicit and implicit schemes for parabolic equations; upwind and downwind differences; the Crank-Nicholson method; the Richardson (leapfrog) method Homework 3
Read: Num Rec., Ch. 19.1, Num Rec., Ch. 19.2; Hoffman Ch. 11.1-11.6
27 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 Homework 4
Read: Hoffman Ch. 12.1-12.13
Finite elements
03 FEB Weak form of PDEs; FE equations Read: Burnett, Ch. 1; FEM intro/summary I; FEM intro/summary II YF
08 FEB Weighted residual methods; basis functions Homework 5
Read: Burnett, Ch. 3, 5.2
10 FEB Assembly of element equations; 2-D FE Read: Burnett, Ch. 5.3 YF
15 FEB No class: President's Day Holiday Read: YF
17 FEB 2-D FE cont'd; Multi-dimensional variational principles Homework 6
Read: Burnett, Ch. 13
22 FEB Introduction to ABAQUS See manuals in BarnYard YF
24 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 implementation; Class notes
02 MAR Examples of BE; introduction to TWODD and DIS3D codes Read: Class notes; TWODD
Other techniques
07 MAR Multigrid and spectral methods; Monte Carlo methods Read: Notes; Num Rec., Ch. 19.4, Ch. 19.6 YF
09 MAR Class presentations YF




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.

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Last modified: Tue Jan 12 11:50:19 PST 2016