20th GAMM-Seminar Leipzig on
Numerical Methods for Non-Local Operators

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
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  Abstract Reinhold Schneider, Thu, 14.00-15.00 Previous Contents Next  
  Density matrix computation for electronic structure calculation
Reinhold Schneider (University Kiel)

Numerical simulation of electronic structures, based on first principle methods derived from the multi-particle Schrödinger equation, play a fundamental role in quantum chemistry, molecular physics, solid physics etc. We present a short introduction into mean field calculation like Hartree-Fock models or Kohn-Sham equation in density functional theory. The computation of the ground state energy requires the self consistent computation of the first N eigenfunctions of a single particle Schrödinger operator. For large molecules the computational costs scale normaly like O(N3). Instead of computing the eigenfunctions one computes the projector onto the space spanned by these eigenfunctions. This projector is represented by the so-called density matrix. We present few possibilities to compute the density matrix. These algorithms require subsequent matrix-matrix multiplications or operator products. Most operators are nonlocal, which demands necessarily for fast matrix calculus. The analytical setting for density matrices will be established and the use of wavelet basis as systematic basis functions for the discretization will be discussed.

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Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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