Foam: Multi-dimensional general purpose Monte Carlo generator with self-adapting simplical grid

Abstract

A new general purpose Monte Carlo event generator with self-adapting grid consisting of simplices is described. In the process of initialization, the simplex-shaped cells divide into daughter subcells in such a way that: (a) cell density is biggest in areas where integrand is peaked, (b) cells elongate themselves along hyperspaces where integrand is enhanced/singular. The grid is anisotropic, i.e. memory of the axes directions of the primary reference frame is lost. In particular, the algorithm is capable of dealing with distributions featuring strong correlation among variables (like ridge along diagonal). The presented algorithm is complementary to others known and commonly used in the Monte Carlo event generators. It is, in principle, more effective than any other one for distributions with very complicated patterns of singularities – the price to pay is that it is memory-hungry. It is therefore aimed at a small number of integration dimensions ( <10 ). It should be combined with other methods for higher dimension. The source code in Fortran 77 is available from http://home.cern.ch/ hadach.