Subject: Sonderforschungsbereich 611 - SFB-Seminar am 1. Oktober 2009
From: Astrid Link <[email-masked]>
To: Astrid Link <[email-masked]>
Date: Thu, 24 Sep 2009 09:41:24 +0200

Einladung zu einem Vortrag im SFB-Seminar

  Donnerstag, 1. Oktober 2009

    Wegelerstr. 10, Kleiner Hoersaal

  15.30  Uhr

   Prof. Dr. N. Sukumar, University of California, Davis, USA,
  spricht zum Thema

  Linear Scaling Finite Element Solution of the All-Electron Coulomb
  Problem in Periodic Solids

 
Abstract:
The computation of the electrostatic potential and total energy of 
crystalline solids has been an ongoing problem in solid state physics. 
In quantum mechanical calculations, the electrostatic potential is 
constructed as a sum of nuclear and electronic terms. In an infinite 
crystal, each of these terms diverges and the sum is only conditionally 
convergent due to the long-range 1/r nature of the Coulomb interaction. 
A common approach to such "all electron" Coulomb problems is to smear 
the nuclear point charges (distributed nucleus approximation) and solve 
the resulting smoothed but strongly inhomogeneous problem in a basis 
which can be concentrated in the vicinity of the nuclei. Accurate 
solutions require strongly localized nuclear charges and so highly 
refined basis sets in the vicinity of the nuclei. The most common 
approach in high-accuracy calculations employs a combined 
spherical-harmonic and Fourier representation and so has O (N log N) 
complexity.
In this talk, I will present a systematically improvable, O (N) (linear 
scaling) formulation for the all-electron Coulomb problem in periodic 
solids that avoids the need for distributed nucleus approximations. 
Ewald sums, and operations in reciprocal space. Linear scaling is 
achieved by introducing smooth, strictly local neutralizing densities to 
render interactions strictly local and solving the remaining neutral 
Poisson problem for the electrons in real space. The resulting 
formulation is amenable to solution using basis sets that are in H1. In 
the numerical computations, we employ finite element and enriched finite 
element methods to demonstrate the accuracy and convergence of the 
approach by direct comparison to standard Ewald sums and application to 
all-electron diamond.

  Tee: 16.30 h

-- 

Astrid Link
Sonderforschungsbereich 611
Universitaet Bonn
Poppelsdorfer Allee 82
53115 Bonn, Germany
Tel.: +49 228 73-4882 (-3858)
Fax:  +49 228 73-7864
[email-masked] 
www.sfb611.iam.uni-bonn.de