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The geometric solution of Laplace's equation

Publication ,  Journal Article
Bakhoum, EG; Board, JA
Published in: Journal of Computational Physics
January 1, 1996

A new numerical method for the rapid solution of Laplace's equation in exterior domains and in interior domains with complicated boundaries is presented. The method is based on a formula first stated by J. J. Thomson and later refined by the authors. The mathematical foundations presented allow for the solution of field problems by means of geometric construction principles. Specifically, the method utilizes the concept of representing equipotential surfaces by polynomials for the rapid tracing of these surfaces; and is, therefore, fundamentally different from previously known techniques which are based on discretizing the domain or the boundary of the problem. For the class of problems characterized by irregular domains, the fastest available techniques have traditionally required an O(M · N) computations, where M is the number of points inside the domain at which the solution is computed and N is the number of points used on the boundary. The new method requires an O(M) computations only and is, therefore, more advantageous in large scale calculations. This paper presents only the two-dimensional version of the geometric solution of Laplace's equation. © 1996 Academic Press, Inc.

Duke Scholars

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

January 1, 1996

Volume

123

Issue

2

Start / End Page

274 / 295

Related Subject Headings

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

Citation

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Bakhoum, E. G., & Board, J. A. (1996). The geometric solution of Laplace's equation. Journal of Computational Physics, 123(2), 274–295. https://doi.org/10.1006/jcph.1996.0024
Bakhoum, E. G., and J. A. Board. “The geometric solution of Laplace's equation.” Journal of Computational Physics 123, no. 2 (January 1, 1996): 274–95. https://doi.org/10.1006/jcph.1996.0024.
Bakhoum EG, Board JA. The geometric solution of Laplace's equation. Journal of Computational Physics. 1996 Jan 1;123(2):274–95.
Bakhoum, E. G., and J. A. Board. “The geometric solution of Laplace's equation.” Journal of Computational Physics, vol. 123, no. 2, Jan. 1996, pp. 274–95. Scopus, doi:10.1006/jcph.1996.0024.
Bakhoum EG, Board JA. The geometric solution of Laplace's equation. Journal of Computational Physics. 1996 Jan 1;123(2):274–295.
Journal cover image

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

January 1, 1996

Volume

123

Issue

2

Start / End Page

274 / 295

Related Subject Headings

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