Cornell University

Department of Physics

Phys 480/680, Astro 690 May 4, 2004

Computational Physics, Spring 2004

Homework Assignment # 9

(Due Thursday, May 6)

Agenda and readings for the weeks of May 4-7:

Goals: Implement numerical minimization using preconditioning, steepest descents, conjugate gradient techniques; solve Kohn-Sham equations of density-functional theory.

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:

• 04/27 Lec 21: Numerical minimization: line minimization, preconditioning; difficulties with line minimization; concept of conjugate gradients (directions, actually)
  Reading: NR 10.6

• 04/29 Lec 22: Conjugate gradient algorithm

• 04/30 Lab 8: Spectral solution to Poisson's equation in octave, solution to Schrödinger's equation via steepest descent minimization

Preview of final week of class:

• 05/04 Lec 23: Derivation of gradients in algebraic notation, gradients for DFT

• 05/06 Lec 24: FFT algorithm
  Readings: NR 12.0-12.2

• 05/07 Lab 9: Performance of numerical minimization techniques, solution of Kohn-Sham equations of density-functional theory

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