PHYS7412
COMPUTATIONAL PHYSICS |

- Overview
- Recommended Textbook:
Numerical Recipes (CUP)
- Assignments

- Finite-Difference Schemes

Relevant NR Section - Systems of Linear Algebraic Equations

Gaussian Elimination

Relevant NR Section - Implicit versus Explicit Schemes
- Alternating-Direction, Implicit (ADI)
Technique

Relevant NR Section (Section 19.5; starting on p. 861) - Multigrid Technique

Relevant NR Section (19.6) - Discrete Fourier Transform Technique (in context of Elliptic PDEs)

Relevant NR Section (19.4)

- Introduction to Continuum Fluid Flows

Relevant NR Section (19.1) "Flux-Conservative Initial Value Problems." - The Sod Shock-Tube Problem

- Introduction to Computer Generated Holography (CGH)
- Introduction to 1D and 2D Fast Fourier Transforms (FFTs)

Relevant NR Section (12.2) "Flux-Conservative Initial Value Problems." - Revised Discussion of Triangular Aperture

- Nonlinear Equations
- Numerical errors; Numerical Instabilities
- Efficiency; Scalability
- Boundary Conditions; Initial Conditions
- Iterative versus Direct Solutions
- Clever Finite-Difference Schemes (advection; compact)
- Assignments