Cornell University

Department of Physics

Phys 480/680, Astro 690 April 8, 2004

Computational Physics, Spring 2004

Homework Assignment # 7

(Due Thursday, April 22)

Agenda and readings for the weeks of April 6-23:

Goal: Learn to use the octave linear algebraic language to express scientific algorithms succinctly; solution of Poisson's equation in a single line of code:

  phi=cI(Linv(-4*pi*O(cJ(n))));

Readings marked NR are from Numerical Recipes: The Art of Scientific Computing, 2$^{\mathrm nd}$ edition (in C). Readings marked LN are from the course lecture notes to be found at http://www.muchomas.lassp.cornell.edu/P480.

Recap of last week of class:

• 04/06 Lec 18: Spectral methods (use of the DFT/FFT to implement plane wave bases), expressive software notation, octave syntax, O and L operators
• 04/08 Lec 19: Transform operators (${\cal I}$, ${\cal J}$), indexing of three dimensional objects
  Reading: NR 12.0, 12.1
• 04/09 Lab 7: FLOP performance of basic operations; FLOP rates in octave.

Preview of coming two weeks:

• 04/13 Lec 18: Aliasing/Nyquist frequency, Fourier factorization theorem; Fourier inversion theorem; Eigenvalue problems in $d>1$ dimension, variational principle, analytic continuation for constraints
  Reading: NR 12.0, 12.4
• 04/15 NO CLASS
• 04/16 NO LAB
• 04/20 Lec 19: Algebraic formulation for energy for Schrödinger's equation; Numerical minimization: steepest descents
  Reading: NR 10.0

• 04/22 Lec 20: Gradient of energy for Schrödinger's equation; Numerical minimization: line minimization, preconditioning; difficulties with line minimization; concept of conjugate gradients (directions, actually)
  Reading: NR 10.6

• 04/23 Lab 8: Spectral solution to Poisson's equation in octave

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