Bulk based preconditioning for quantum dot computations

ABSTRACT

This article describes how to accelerate the convergence of Preconditioned Conjugate Gradient (PCG) type eigensolvers for the computation of several states around the band gap of colloidal quantum dots. Our new approach uses the Hamiltonian from the bulk materials constituent for the quantum dot to design an efficient preconditioner for the folded spectrum PCG method. The technique described shows promising results when applied to CdSe quantum dot model problems. We show a decrease in the number of iteration steps by at least a factor of 4 compared to the previously used diagonal preconditioner.

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INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING

General Terms:
Algorithms

Keywords:
computational nanotechnology, preconditioned eigensolvers, quantum dots