An algebraic representation of the linear-analytic tetrahedron method Original Research Article

We present a new formulation of the tetrahedron method for calculating Lindhard sums in susceptibility calculations. Using an analytic approach rather than the usual geometric interpretation, we provide a general algebraic form for the integral. Our result is much more compact and less complicated than the geometric approach and involves the minimum of calculation. The ordering and subdivision of tetrahedra in the geometric approach is obviated. Our analytic approach may be readily applied to other microcell geometries and is demonstrated in this paper for both the tetrahedron microcell as well as the geometrically complex parallelepiped microcell.