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Cornell University
Department of Physics
Phys 480/680, Astro 690 April 15, 2001
Computational Physics, Spring 2001
Homework Assignment # 7
(Due Friday, April 13 at 8:00 am in Computer Lab.)
Agenda and readings for the weeks of April 2 & 9:
Goals: Gain experience calling LAPACK; solution of Poisson's
equation in d=3 using the FFT; learn to use overloading to express
scientific algorithms succinctly; solution of Poisson's equation in a
single line of code:
phi=I(Linv((-4*pi)*O(J(rho))));
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:
- Lec14, 03/26 [1 hr]: Relations among self-consistent iteration,
charge mixing, and Broyden's method; line optimization
- Lec15, 03/27 [1 hr]: Full, modified Broyden's method;
Introduction to Numerical linear algebra; benefits of LAPACK
- Lab 6, 03/29 [1 hr]: Analysis of convergence of charge mixing;
condition numbers; exploration of FLOP rates within inner loops.
Preview of coming two weeks:
- 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]:
Coding in C++
- Lec21, 04/10 [1 hr: evening, Clark 710]:
Optimization; Ahmdal's Law; inner loop tricks; memory hierarchy and cache
- Lec22, 04/11 [1 hr]:
Cache optimization; avoiding cache misses; BLAS1-3; blocked matrix multiplies
- Lab7, 04/13 [1 hr]:
More on flop rates; solution of Poisson's equation in d>1 dimensions
Tomas Arias
Sun Apr 15 19:43:40 EDT 2001
