Universal matrices for the N-dimensional finite element

New universal matrices are presented for the n-dimensional simplex element. Their use recasts complex integrals into sums and products of universal matrices with coordinate-independent geometric factors. This formulation requires the use of a single family of polynomial interpolation functions for all quantities depending on space. Universal matrices are defined as a function of the spatial dimensionality and the polynomial order of the interpolation functions. The formulation is presented for the general n-dimensional element with applications to line and triangular elements (spatially one and two dimensions respectively). The procedure of assembling element contribution to the global matrix is then identical for any element shape or spatial dimension and polynomial order used in the interpolation functions. Application of the method to the computation of charge density distribution in a photoionization chamber is given.