|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|
|18 JAN||Finite difference approximations; consistency, order, and convergence||Read: Num Rec., Ch. 19.0
|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||
Read: Num Rec., Ch. 19.1, Num Rec., Ch. 19.2; Hoffman Ch. 11.1-11.6
|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||
Read: Burnett, Ch. 1; FEM intro/summary
|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||
Read: Burnett, Ch. 13
|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
|05 MAR||Examples of BE; introduction to TWODD and DIS3D codes||Read: Class notes; TWODD
|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|
Numerical methods for engineers and scientists, J. D. Hoffman, McGraw-Hill, 1992.
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 can be done most easily by using MATLAB
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