  We present a new efficient numerical approach for representing anisotropic
physical quantities and/or matrix elements defined on the Fermi surface of
metallic materials. The method introduces a set of numerically calculated
generalized orthonormal functions which are the solutions of the Helmholtz
equation defined on the Fermi surface. Noteworthy, many properties of our
proposed basis set are also shared by the Fermi Surface Harmonics (FSH)
introduced by Philip B. Allen [Physical Review B 13, 1416 (1976)], proposed to
be constructed as polynomials of the cartesian components of the electronic
velocity. The main motivation of both approaches is identical, to handle
anisotropic problems efficiently. However, in our approach the basis set is
defined as the eigenfunctions of a differential operator and several desirable
properties are introduced by construction. The method demonstrates very robust
in handling problems with any crystal structure or topology of the Fermi
surface, and the periodicity of the reciprocal space is treated as a boundary
condition for our Helmholtz equation. We illustrate the method by analysing the
free-electron-like Lithium (Li), Sodium (Na), Copper (Cu), Lead(Pb), Tungsten
(W) and Magnesium diboride (MgB2).
