Quadratic and cubic tetrahedron methods for Brillouin zone integration

The method of the division of the irreducible part of the Brillouin zone in tetrahedra in order to use them for the calculation of the integrals needed in electronic structure calculations is an efficient and well tested method. The integration inside each tetrahedron is usually carried out by approximating the integrated function with a linear function or with the quotient of two linear functions. In the present work a new method is presented for the integration inside each tetrahedron where the integrand is approximated with a quadratic or cubic function.