, Volume 79, Issue 2–4, pp 381–388 | Cite as

An analytic mapping of 3-D space to facilitate physical analysis



A method is presented for the solution of Laplace's equation in three dimensions through the use of a combination of polynomial and eigenfunction solutions. Results are presented comparing the method with an exact solution. Excellent agreement is obtained for economical solution representations. The aproximate analytic solution is supplemented by a correction term to ensure that the boundary conditions for the problem are satified exactly. In this form, the method is used to present calculations for the mapping of a hexahedral space to the unit cube.

AMS Subject Classifications

35J05 35J55 65Z05 


Mesh generation partial differential equation 


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Copyright information

© Springer-Verlag Wien 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of LeedsLeedsUK
  2. 2.Faculty of Mathematics and Physical Sciences, School of Physics and AstronomyUniversity of LeedsLeedsUK

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