TY - JOUR
T1 - Volumetric fast multipole method for modeling Schrödinger's equation
AU - Zhao, Zhiqin
AU - Kovvali, Narayan
AU - Lin, Wenbin
AU - Ahn, Chang Hoi
AU - Couchman, Luise
AU - Carin, Lawrence
N1 - Generated from Scopus record by KAUST IRTS on 2021-02-09
PY - 2007/6/10
Y1 - 2007/6/10
N2 - 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.
AB - 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.
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999106005596
UR - http://www.scopus.com/inward/record.url?scp=34248591330&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2006.11.003
DO - 10.1016/j.jcp.2006.11.003
M3 - Article
SN - 1090-2716
VL - 224
SP - 941
EP - 955
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -