PHYS7412 COMPUTATIONAL PHYSICS

• Overview
• Recommended Textbook: Numerical Recipes (CUP)

• Assignments

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1^st Third of the Semester

• 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)

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2^nd Third of the Semester

• Introduction to Continuum Fluid Flows
  Relevant NR Section (19.1) "Flux-Conservative Initial Value Problems."
• The Sod Shock-Tube Problem

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3^rd Third of the Semester

• 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

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General Concepts to be Covered

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

• Assignments