PERIODIC MINIMAL-SURFACES FROM FINITE-ELEMENT METHODS

A method has been developed for binding numerically the minimal (soap- film) surface bounded a skew quadrilateral. A general quartic is fitte d to each patch in turn and the local curvature is adjusted appropriat ely. 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 Fo urier terms each corresponding to a set of planes {h, k, l} in the app ropriate space group. Thus, the exact minimal surface (or any other su rface such as an equipotential) can be expressed to any required accur acy as a sum of trigonometric functions which are readily calculable. The method is capable of generalisation.