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Periodic Minimal Surfaces from Finite Element Methods

A. Mackay
Journal / Anthology

Chemical Physics Letters
Year: 1994
Volume: 221
Page range: 317-321

A method has been developed for binding numerically the minimal (soap-film) surface bounded by a skew quadrilateral. A general quartic is fitted to each patch in turn and the local curvature is adjusted appropriately. Using this, the P and D periodic minimal surfaces have each been expressed as the nodal surface of an expression which is the sum of Fourier terms each corresponding to a set of planes {h,k,l} in the appropriate space group. Thus, the exact minimal surface (or any other surface such as an equipotential) can be expressed to any required accuracy as a sum of trigonometric functions which are readily calculable. The method is capable of generalization.

*Engineering > Finite Element Methods
*Mathematics > Geometry > Surfaces