Cornell University
Department of Physics
Phys 480/680, Astro 690 April 26, 2006
Computational Physics, Spring 2006
Homework Assignment # 8
(Due Wednesday, April 19)
Agenda and readings for the weeks of April 18-22:
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
edition (in C). Readings
marked LN are from the course lecture notes to be found at
http://www.muchomas.lassp.cornell.edu/P480.
Recap:
- 04/06 Lec 19: Discrete Fourier Transforms: standard ordering
of indices, aliasing/Nyquist frequency,
Fourier factorization theorem
Reading: NR
12.0, 12.1, 12.4
- 04/11 Lec 20: Fourier inversion theorem; Eigenvalue problems in
dimension: variational principle, analytic continuation for
constraints, minimization by steepest descents; DFT++ expressions for energy for multiple states.
Reading: NR 10.0
Preview:
- 04/13 Lec 21: DFT++ expressions for energy and gradient for multiple
states and for density functional theory
Reading: Sections 1-4 of
http://arxiv.org/abs/cond-mat/9909130
- 04/13 Lab 7: FLOP rates; Spectral solution of Poisson's equation
- 04/18 Lec 22: Convergence of steepest descents; preconditioning; line
minimization; motivation for conjugate gradients
Reading: NR 10.2, 10.3. 10.5
- 04/20 Lec 23: Conjugate gradient algorithm
Reading: 10.6
- 04/20 Lab 8: Spectral solution of Schrödinger's equation and
Kohn-Sham equations for simple harmonic oscillator.
- 04/25 Lec 24: FFT
Reading: 12.2
- 04/27 Lec 25: Further optimizations for spectral methods; ab initio pseudopotentials
- 04/27 Lab 9: Performance of numerical minimization techniques;
preconditioner for quantum calculations, H
molecule
- 05/02 Lec 26: Extraction of eigenstates from variational principle
- 05/04 Lab 10: Physics of harmonic oscillator, H2 molecule and
germanium solid
Tomas Arias
2006-04-26
