Cornell University
Department of Physics
Phys 480/680, Astro 690 March 12, 2004
Computational Physics, Spring 2002
Homework Assignment # 5
(Due Thu, March 18)
Agenda and readings for the week of March 5:
Goal: Building upon the components you have built, 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
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:
- 03/02 NO LECTURE
- 03/04 Lec 11: Numerical interpolation; exchange and correlation energy
functionals; solution of many non-linear equations in many unknowns
via self-consistent iteration and mixing.
Readings: NR
3.0-3.2, 9.6-9.7; Sections ``Introduction,'' ``Procedure'' (you
can skip the relativistic part), ``Results,'' and ``The LDA
approximation,'' from
http://physics.nist.gov/PhysRefData/DFTdata/contents.html
- 05/05 NO LAB
- 03/09 Lec 12: Mixing as a general algorithm; analysis of convergence for
mixing, condition numbers; sophisticated algorithms, Netwon-Raphson,
Broyden; need for an alternative for large systems.
Reading: NR 9.6-9.7
- 03/11 Lec 13: Line optimization; modified Broyden
method; Introduction to Numerical linear algebra; benefits of
LAPACK; solution of linear equations through LU decomposition.
Reading: NR 2.0, 2.3
- 03/12 Lab 4: Convergence of energies; Energiess of simple
harmonic oscillator; ``hot-wired'' Hartree solver for atoms!
Preview of coming week:
- 03/16 Lec 14: Crout's algoritm for LU decomposition
Reading: NR 2.0, 2.3
- 03/18 Lec 15: Optimization: Amdahl's Law; inner loop tricks; Solution of Poisson's equation in d>1 dimensions; expressive software/DFT++
- 03/19 Lab 5: Full, self-consistent solutions for density functional
theory of atoms; using gprof; avoiding malloc; inlining optimizations.
Tomas Arias
2004-03-12
