3450:730 Advanced Numerical Solution of Partial Differential Equations
Spring 2012
Policy sheet
Course outline
Spring Schedule -- subject to updates
Homework Sets
Homework 1, due Thursday 12 January
Homework 2, due Thursday 19 January
Sample1.f (standard format for explicit codes)
Sample2.f (standard format for explicit codes with memory saving and intermediate outputs)
Homework 3, due Thursday 26 January
Homework 4 and 5, due Tuesday 31 January
Homework 6,7,8, due Thursday 2 February
Homework 9, due Tuesday 7 February
Homework 10, due Thursday 23 February
Homework 11, due Thursday 22 March
Homework 12, 13, due Thursday 5 April
Homework 14, due Tuesday 17 April
Computer Projects
CP1: Crank-Nicolson, due Thursday 16 February
CP2: Nonlinear Parabolic Equation, Crank-Nicolson with Successive Approximations, due Tuesday 6 March
CP3: Block SOR, due Thursday 12 April
CP4: Kurganov-Tadmor MUSCL, due Tuesday 24 April
FORTRAN Issues
The Force 2.0
FORTRAN compiler
Information about
installing Windows applications on a Mac
A FORTRAN manual
FORTRAN programming issues
How to write to a file in FORTRAN
Building the spatial grid in a code
Saving memory in arrays
Handling the time variable
Creating file names to save data
Routines chan3 and ooutfn for cut and paste
Handling different cases in a code
A tridiagonal solver (FORTRAN)
A tridiagonal solver (C)
Using the tridiagonal solver
A barebones pentadiagonal solver
MATLAB file to input a 2d array for line plotting
MATLAB file to input a set of 2d files for multiple line plotting
MATLAB file to input a 3d array for surface plotting
Chapter 1 Introduction and Notation
MATLAB example of instability
Chapter 2 Parabolic PDEs
Crank-Nicolson, ghost points versus row reduction
2d parabolic code, full Gauss Elimination
2d parabolic code, block SOR
MATLAB example of SOR iteration
Bottom BC
Top BC
Left BC
Right BC
Chapter 3 Hyperbolic PDEs
MATLAB example of travelling waves
First wave
Second wave
MATLAB example of a discontinuity in an advection equation
MATLAB example of numercial dispersion
MATLAB example of physical dispersion with numercial dispersion
MATLAB example of dispersion in the upwind scheme
Exact solution
function file for upwind scheme movie (MATLAB)
Lele JCP 1992 Compact Finite Difference Schemes with
Spectral-like Resolution
MUSCL code