An algebraic formulation of the simplex linear method for multiple integrals over the d-dimensional domain

作者：Kaprzyk S^*

来源：Computer Physics Communications, 2012, 183(1): 20-25.

DOI：10.1016/j.cpc.2011.08.006

• Simplex linear method
• Multiple integrals
• Brillouin zone

We present the systematic treatment of multiple integrals over a simplex of the dimensionality d (d-simplex). The integrand is an analytical function in a suitable domain, and the linear form was employed as an argument. Using the elements obtained from the values of the integrand at the vertices of the d-simplex, integral can be evaluated analytically and expressed as the quotient of two determinants. Potential applications of the results described in the present study include numerical computations of Green%26apos;s GF), and the response of quantum systems in terms of complex susceptibilities in multidimensional space.

• 出版日期2012-1