  We present an amelioration of current known algorithms for optimal spectral
partitioning problems. The idea is to use the advantage of a representation
using density functions while decreasing the computational time. This is done
by restricting the computation to neighbourhoods of regions where the
associated densities are above a certain threshold. The algorithm extends and
improves known methods in the plane and on surfaces in dimension 3. It also
makes possible to make some of the first computations of volumic 3D spectral
partitions on sufficiently large discretizations.
