Cornell University

Department of Physics

Phys 480/680, Astro 690 March 17, 2000

Computational Physics, Spring 2000

Homework Assignment # 7

(Due Thursday, April 6 at 8:40 am in Lab.)

Agenda and readings for the week of March 27:

All readings from Numerical Recipes: The Art of Scientific Computing, 2 edition (in Fortran or C).

• Lec10, 03/28: Linear solvers; LAPACK Reading: 2.0-2.3
• Lec11, 03/30: Partial differential equations (PDEs) in multiple dimensions
• Lec12, 04/04: Fast Fourier Transform (FFT) Reading: 12.0-12.2, 12.4
• Lab6, 04/06: Optimization

Goal: This homework develops a powerful technique for solving the non-linear system of many equations in many unknowns which we face in the electronic structure of atoms.

• Contents
• Packaging
  • ``getg''
    • Debugging
  • ``ludcmpp480'' and ``lubksbp480''
    • Debugging
• Initial Performance
  • Convergence Rate
  • Run time
• Broyden Solver
  • Bookkeeping
    • Debugging
  • Improved initial guess
  • ``broyden''
    • Matrix G and vector u
      • Declarations:
      • Residual vector :
      • Formation:
    • Solution of G b = u
    • Formation of final Rho[it+1]
  • Convergence rate
• Optimization
  • Calls to dvector() and free_dvector()
  • Calls to rk4p480()
  • Calls to derivs_Schrodinger()
  • Calls to exc() and excp()
• Uranium
• ``test_getg.c''
• ``test_lu.c''
• About this document ...

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