  Brown-Resnick processes are max-stable processes that are associated to
Gaussian processes. Their simulation is often based on the corresponding
spectral representation which is not unique. We study to what extent simulation
accuracy and efficiency can be improved by minimizing the maximal variance of
the underlying Gaussian process. Such a minimization is a difficult
mathematical problem that also depends on the geometry of the simulation
domain. We extend Matheron's (1974) seminal contribution in two aspects: (i)
making his description of a minimal maximal variance explicit for convex
variograms on symmetric domains and (ii) proving that the same strategy reduces
the maximal variance also for a huge class of non-convex variograms
representable through a Bernstein function. A simulation study confirms that
our non-costly modification can lead to substantial improvements among Gaussian
representations. We also compare it with three other established algorithms.
