  Microstructure reconstruction is an important and emerging aspect of
computational materials engineering and multiscale modeling and simulation.
Despite extensive research and fast progress in the field, the application of
descriptor-based reconstruction remains limited by computational resources.
Common methods for increasing the computational feasibility of descriptor-based
microstructure reconstruction lie in approximating the microstructure by simple
geometrical shapes and by utilizing differentiable descriptors to enable
gradient-based optimization. The present work combines these two ideas for
structures composed of non-overlapping ellipsoidal inclusions such as
magnetorheological elastomers. This requires to express the descriptors as a
function of the microstructure parametrization. Deriving these relations leads
to analytical solutions that further speed up the reconstruction procedure.
Based on these descriptors, microstructure reconstruction is formulated as a
multi-stage optimization procedure. The developed algorithm is validated by
means of different numerical experiments and advantages and limitations are
discussed in detail.
