• As a mesh-less technique, it augments  design simulations to deepen “all our simulations say” conclusions.

• Edge functions are closed form solutions that
        • vary harmonically along the  associated side at
                • non-zero harmonic frequencies  associated with the side’s Fourier expansion
        • decay into the region

• The decay requirement may require that the region be decomposed into subregions with
            •  decaying edge functions

• Central functions are closed polar form solutions that
            • originate and grow from the center of each subregion
            • have positive integer harmonic numbers

• Corner functions are closed form polar solutions with
        • singular behaviour in the radial distance from the corner
        • non-singular behaviour on adjacent segments with prescribed boundary conditions

• The edge function basis for a subregion is its combined set of edge, central and corner functions

• Truncated bases are formed by omitting solutions with
        • harmonics greater a prescribed harmonic
        • singularities in radial derivatives greater than a prescribed order    

• A (truncated)solution is a sum of (truncated)basis solutions with multipliers found by matching
        • the prescribed boundary conditions
        • continuity at the same point on adjacent subregion boundaries.

• The superposition becomes the classical solution in the limit of vanishing matching errors.

• The inclusion of corner solutions yields relatively small basis with small matching errors.

• A traditional separation of variables basis can be used when the subregions are rectangles.