A theory of special points in two-dimensional solid-state calculations

A theory of special points in solid-state calculations is developed using a finite-dimensional function space. This generalizes:many of the ideas of the present authors about Gaussian-type cubature since the special points are identified with the grid points of a quadrature. The theory is applied to planar square lattices with C-4v symmetry. By the systematic use of symmetry, substantial grids of points can be calculated economically. The accuracy of the sets of points is discussed and a redefinition of accuracy offered. Examples are given, some of which agree with those already known, but a new category of skew direct product grids is introduced which enables a large number of suitable grids to be generated. (C) 1999 John Wiley & Sons, Inc.