GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
The numerical solution of the N-body problem
Computers in Physics
Field Computation by Moment Methods
Field Computation by Moment Methods
Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
SIAM Journal on Numerical Analysis
The rapid evaluation of potential fields in particle systems
The rapid evaluation of potential fields in particle systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fast Evaluation of Volume Potentials in Boundary Element Methods
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
A volume integral equation method is presented for solving Schrodinger'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(N^2) complexity. In this paper, the volume integral equation is solved efficiently via a multi-level fast multipole method (MLFMM) implementation, requiring O(NlogN) 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.