Periodic minimal surfaces from finite element methods

Abstract A method has been developed for binding numerically the minimal (soap-film) surface bounded a skew quadrilateral. A general quartic is fitted to each patch in turn and the local curvature is adjusted appriately. 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 {ith, 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 generalisation.