Cornell University

Department of Physics

Phys 480/680, Astro 690 April 8, 2002

Computational Physics, Spring 2002

Homework Assignment # 8

(Due Tuesday, April 16 at 8:40 am in Computer Lab.)

Agenda and readings for the week of April 9:

Goal: 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:

• Lec18, 04/02 (Tue: mini-lecture, 25mins): Solution of Poisson's equation in d>1 dimension in a single line of expressive software!
• Lab6, 04/02 (Tue): Fully optimized atomic software, FLOP rates of common operations
• Lec19, 04/04 (Thu): Implementation of expressive software for Poisson's equation: plane wave basis and coding in C++

Preview of coming week:

• Lec20, 04/09 (Tue: mini-lecture, 40mins): C++ continued, d=3 DFT and IDFT
• Lab7, 04/09 (Tue): Timing computer FLOP performance for BLAS/LAPACK operations
• Lec21, 04/11 (Thu): Solution of Schrödinger's equation in three-dimensions, steepest descents, line-minimization
  Reading: NR 10.0,10.5
• Lec22, 04/16 (Tue: mini-lecture, 25mins): preconditioning
• Lab8, 04/16 (Tue): Solving Poisson's equation in d>1 dimensions

• Contents
• Infrastructure
  • Working with classes
    • Using classes in the standard C++ library
    • Working with user defined classes: ``vec.C''
  • ``pvector'' class
    • C3tensor() and free_C3tensor()
      • Debugging
    • sum()
    • operator-(), operator*()
    • I()
    • J()
    • O() and Linv()
• Physics
  • evalr()
    • Debugging
  • Potential from a sum of two Gaussian distributions
    • GaussR()
      • Debugging:
    • Computation of total electrostatic potential energy U
      • Debugging:
    • Computation of potential field
      • For fun:
      • Challenge physics question:
• ``complex.C''
• ``vec.C''
• ``pvector.C''
• main() for ``physics.C''
• About this document ...

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