Cornell University

Department of Physics

Phys 480/680, Astro 690 April 15, 2001

Computational Physics, Spring 2001

Homework Assignment # 8

(Due Friday, April 20 at 8:00 am in Computer Lab.)

Agenda and readings for the weeks of April 2 & 9:

Goals: Solution of single particle Schrödinger equation using unconstrained minimization techniques; minimization using steepest descents, line minimization, preconditioning and conjugate gradients; solution of the harmonic oscillator in d=3 dimensions.

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 of last week:

• Lec16, 04/02 [1 hr]: Solution of linear equations through LU decomposition; Crout's algorithm (without pivoting)
  Reading: NR 2.3
• Lec17, 04/04 [1 hr]: Crout's algorithm with pivoting
  Reading: NR 2.3
• Lec18, 04/05 [1 hr: evening, Clark 710]: Solution of Poisson's equation in d>1 dimensions; expressive software/DFT++
• Lec19, 04/06 [1 hr]: Use of the DFT/FFT to implement plane wave bases
  Reading: NR 12.0,1,4
• Lec20, 04/09 [1 hr]: Fourier factorization theorem, Fourier inversion theorem, Aliasing/Nyquist frequency.
• Lec21, 04/10 [1 hr: evening, Clark 710]: Coding in C++
• Lec22, 04/11 [1 hr]: Optimization; Amdahl's Law; inner loop tricks
• Lab7, 04/13 [1 hr]: More on flop rates; solution of Poisson's equation in d>1 dimensions. Introduction to cache

Preview of coming week:

• Lec23, 04/16 [1 hr]: Cache optimization; avoiding cache misses; BLAS1-3; blocked matrix multiplies; Eigenvalue problems in d>1 dimension, variational principle.
• Lec24, 04/17 [1 hr: evening, Clark 710]: Schrödinger's energy and gradient, steepest descents minimization, algebra of complex vectors.
• Lec22, 04/18 [1 hr]: Conjugate gradient minimization.
• Lab8, 04/20 [1 hr]: Solution of Schrödinger's equation (in d>1 dimensions), convergence rates of non-linear minimization algorithms.

• Contents
• Infrastructure
  • Idag() and Jdag()
  • vector-vector product: pvector `*' pvector
  • sho()
• Physics and steepest descents: sch.C
  • Gathering data
• Line minimization
  • Theory of line minimization
  • Implementation
  • Debugging
  • Gathering data
• Conjugate gradients
  • Debugging
  • Gathering data
• Preconditioning
  • Implementation: K()
  • Debugging and Gathering data
  • Debugging
  • Gathering data
• About this document ...

Postscript Version

PDF Version