Cornell University

Department of Physics

Phys 480/680, Astro 690 April 3, 2005

Computational Physics, Spring 2005

Homework Assignment # 7

(Due Thursday, April 14)

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))));

solution of Schrodinger's equation by steepest descents.

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:

• 03/29 Lec 17: Blocked matrix multiplies; Solution of Poisson's equation in d>1 dimensions; expressive software; solution to Poisson's equation in a single line of code; choice of planewave (complex exponential) basis for periodic boundary conditions.

• 03/31 Lec 18: Form of operators and transforms in a planewave basis; octave/matlab notations; standard ordering of indices for Discrete Fourier Transforms (DFTs).

Preview of coming two weeks:

• 04/05 Lec 19: Discrete Fourier Transforms: aliasing/Nyquist frequency, Fourier factorization theorem, Fourier inversion theorem
  Reading: NR 12.0, 12.1, 12.4

• 04/07 Lec 20: Eigenvalue problems in $d>1$ dimension: variational principle, analytic continuation for constraints, minimization by steepest descents
  Reading: NR 10.0

• 04/07 Lab 7: FLOP performance of basic operations; FLOP rates in octave; Automated empirical optimization of software (AEOS): automatically tuned linear algebra software (ATLAS), fastest Fourier Transform in the West (FFTW).

• 04/12 Lec 21: DFT++ expressions for energy and gradient for multiple states

• 04/14 Lec 22: Converge of steepest descents; preconditioning; line minimization
  Reading: NR 10.2, 10.3

• 04/14 Lab 8: Spectral solution of Poisson's and Schrödinger's equations

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