An analytic mapping of 3-D space to facilitate physical analysis |
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Authors: | M I G Bloor M J Wilson |
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Affiliation: | (1) Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK;(2) Faculty of Mathematics and Physical Sciences, School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK |
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Abstract: | 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. |
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Keywords: | 35J05 35J55 65Z05 |
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