Skip to main content
Journal cover image

Volumetric fast multipole method for modeling Schrödinger's equation

Publication ,  Journal Article
Zhao, Z; Kovvali, N; Lin, W; Ahn, CH; Couchman, L; Carin, L
Published in: Journal of Computational Physics
June 10, 2007

A volume integral equation method is presented for solving Schrödinger's equation for three-dimensional quantum structures. The method is applicable to problems with arbitrary geometry and potential distribution, with unknowns required only in the part of the computational domain for which the potential is different from the background. Two different Green's functions are investigated based on different choices of the background medium. It is demonstrated that one of these choices is particularly advantageous in that it significantly reduces the storage and computational complexity. Solving the volume integral equation directly involves O(N2) complexity. In this paper, the volume integral equation is solved efficiently via a multi-level fast multipole method (MLFMM) implementation, requiring O(N log N) memory and computational cost. We demonstrate the effectiveness of this method for rectangular and spherical quantum wells, and the quantum harmonic oscillator, and present preliminary results of interest for multi-atom quantum phenomena. © 2006 Elsevier Inc. All rights reserved.

Duke Scholars

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

June 10, 2007

Volume

224

Issue

2

Start / End Page

941 / 955

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Zhao, Z., Kovvali, N., Lin, W., Ahn, C. H., Couchman, L., & Carin, L. (2007). Volumetric fast multipole method for modeling Schrödinger's equation. Journal of Computational Physics, 224(2), 941–955. https://doi.org/10.1016/j.jcp.2006.11.003
Zhao, Z., N. Kovvali, W. Lin, C. H. Ahn, L. Couchman, and L. Carin. “Volumetric fast multipole method for modeling Schrödinger's equation.” Journal of Computational Physics 224, no. 2 (June 10, 2007): 941–55. https://doi.org/10.1016/j.jcp.2006.11.003.
Zhao Z, Kovvali N, Lin W, Ahn CH, Couchman L, Carin L. Volumetric fast multipole method for modeling Schrödinger's equation. Journal of Computational Physics. 2007 Jun 10;224(2):941–55.
Zhao, Z., et al. “Volumetric fast multipole method for modeling Schrödinger's equation.” Journal of Computational Physics, vol. 224, no. 2, June 2007, pp. 941–55. Scopus, doi:10.1016/j.jcp.2006.11.003.
Zhao Z, Kovvali N, Lin W, Ahn CH, Couchman L, Carin L. Volumetric fast multipole method for modeling Schrödinger's equation. Journal of Computational Physics. 2007 Jun 10;224(2):941–955.
Journal cover image

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

June 10, 2007

Volume

224

Issue

2

Start / End Page

941 / 955

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences