@Article{Pandis:2015:NID,
  author =       "Vassilis Pandis",
  title =        "Numerical integration of discontinuous functions
                  in many dimensions",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "41",
  number =       "3",
  accepted =     "4 May 2014",
  upcoming =     "true", 
  abstract =     "
                  We consider the problem of numerically
                  integrating functions with hyperplane
                  discontinuities over the entire Euclidean
                  space in many dimensions. We describe
                  a simple process through which the
                  Euclidean space is partitioned into
                  simplices on which the integrand
                  is smooth, generalising the standard
                  practice of dividing the interval used in
                  one-dimensional problems. Our procedure
                  is combined with existing adaptive
                  cubature algorithms to significantly
                  reduce the necessary number of
                  function evaluations and memory
                  requirements of the integrator. The
                  method is embarrassingly parallel and
                  can be trivially scaled across many
                  cores with virtually no overhead. Our
                  method is particularly pertinent to the
                  integration of Green’s functions,
                  a problem directly related to the
                  perturbation theory of impurity
                  models. In three spatial dimensions we
                  observe a speed-up of order 100 which
                  increases with increasing dimensionality.",
}