Cornell University

Department of Physics

Phys 480/680, Astro 690 March 7, 2005

Computational Physics, Spring 2005

Homework Assignment # 5

(Due Thu, March 31)

Agenda and readings for the week of March 5:

Goal: Building upon the components you have made, you will perform your own full density-functional-theory calculations of atoms. You will reproduce the accepted values to at least as much precision as published by the US Nationial Institute of Standards and Technology, the micro-hartree level!!!

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:

• Lec 11, 03/01: Solution of many non-linear equations in many unknowns, mixing method, convergence rates, condition numbers; Newton-Raphson and Broyden approaches; motivation for a ``modified'' Broyden's method for large systems of equations
  Readings: NR 9.6-9.7

• Lec 12, 03/03 Modified Broyden method

• Lab 4, 03/03 Failed attempt to ``hot-wire'' solver for atoms within Hartree theory!

Preview of coming weeks:

• 03/08 Lec 14: Recap modified Broyden method; Introduction to numerical linear algebra; Benefits of LAPACK; Solution of linear systems through LU decomposition; Crout's algoritm for LU decomposition
  Reading: NR 2.0, 2.3

• 03/10 Lec 15: Crout's Algorithm cont'd; Optimization: Amdahl's Law

• 03/10 Lab 5: Energies of harmonic oscillator; ``Hot-wired'' solver for atoms within Hartree theory.

• 03/15 Lec 16: Inner loop tricks; Cache optimization, avoiding cache misses; BLAS1-3; blocked matrix multiplies.

• 03/17 Lab 6 (Meet in Rock B3): Optimization of full atomic solvers

• 03/17 Lec 17 (in B3 after lab): Automated empirical optimization of software (AEOS), automatically tuned linear algebra software (ATLAS), FFTW

• 03/21-3/25 SPRING BREAK

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