### Abstract

A general algorithm for computing the potentials of a circular plate multipole system is developed based on the charge-density method. An efficient numerical integration algorithm for the superposition integrals is derived from integral asymptotic concepts. Utilization of system symmetry to reduce computation time and memory requirement is discussed in detail, particularly for storing the superposition integral matrix and for solving the charge-density vector. The Levinson algorithm for solving Toeplitz matrices is generalized to unravel the huge superposition matrices, yielding orders of magnitude savings in computational steps over the generic N^{3} matrix inversion schemes. Modification of the algorithms for studying ring multipole systems is considered. Sample computations are presented for demonstration and verification.

Original language | English (US) |
---|---|

Pages (from-to) | 272-281 |

Number of pages | 10 |

Journal | Journal of Electron Microscopy |

Volume | 43 |

Issue number | 5 |

State | Published - Oct 1994 |

### Fingerprint

### Keywords

- Charge-density method
- Integral asymptotic
- Levinson algorithm
- Multipole system
- Toeplitz matrices

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Physiology (medical)
- Infectious Diseases
- Pharmacology (medical)
- Instrumentation

### Cite this

*Journal of Electron Microscopy*,

*43*(5), 272-281.

**Improved charge-density method for studying circular-plate multipole systems.** / Szilagyi, Miklos N; Mui, P. H.

Research output: Contribution to journal › Article

*Journal of Electron Microscopy*, vol. 43, no. 5, pp. 272-281.

}

TY - JOUR

T1 - Improved charge-density method for studying circular-plate multipole systems

AU - Szilagyi, Miklos N

AU - Mui, P. H.

PY - 1994/10

Y1 - 1994/10

N2 - A general algorithm for computing the potentials of a circular plate multipole system is developed based on the charge-density method. An efficient numerical integration algorithm for the superposition integrals is derived from integral asymptotic concepts. Utilization of system symmetry to reduce computation time and memory requirement is discussed in detail, particularly for storing the superposition integral matrix and for solving the charge-density vector. The Levinson algorithm for solving Toeplitz matrices is generalized to unravel the huge superposition matrices, yielding orders of magnitude savings in computational steps over the generic N3 matrix inversion schemes. Modification of the algorithms for studying ring multipole systems is considered. Sample computations are presented for demonstration and verification.

AB - A general algorithm for computing the potentials of a circular plate multipole system is developed based on the charge-density method. An efficient numerical integration algorithm for the superposition integrals is derived from integral asymptotic concepts. Utilization of system symmetry to reduce computation time and memory requirement is discussed in detail, particularly for storing the superposition integral matrix and for solving the charge-density vector. The Levinson algorithm for solving Toeplitz matrices is generalized to unravel the huge superposition matrices, yielding orders of magnitude savings in computational steps over the generic N3 matrix inversion schemes. Modification of the algorithms for studying ring multipole systems is considered. Sample computations are presented for demonstration and verification.

KW - Charge-density method

KW - Integral asymptotic

KW - Levinson algorithm

KW - Multipole system

KW - Toeplitz matrices

UR - http://www.scopus.com/inward/record.url?scp=77958403500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958403500&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77958403500

VL - 43

SP - 272

EP - 281

JO - Microscopy (Oxford, England)

JF - Microscopy (Oxford, England)

SN - 2050-5698

IS - 5

ER -