Efficient algorithm for optimizing spectral partitions

We present an amelioration of current known algorithms for minimizing functions depending on the eigenvalues corresponding to a partition of a given domain. The idea is to use the advantage of a representation using density functions on a fixed grid 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 computations of optimal volumic 3D spectral partitions on sufficiently important discretizations.