Existence of Bernstein-Sato polynomials by using the analytic Grobner fan

In 1987, C. Sabbah proved the existence of Bernstein-Sato polynomials associated with several analytic functions. The purpose of this article is to give a more elementary and constructive proof of the result of C. Sabbah based on the notion of the analytic Gr"obner fan of a D-module.