  The unique properties of anisotropic and composite particles are increasingly
being leveraged in modern particulate products. However, tailored synthesis of
particles characterized by multi-dimensional dispersed properties remains in
its infancy and few mathematical models for their synthesis exist. Here, we
present a novel, accurate and highly efficient numerical approach to solve a
multi-dimensional population balance equation, based on the idea of the exact
method of moments for nucleation and growth \cite{pflug2020emom}. The
transformation of the multi-dimensional population balance equation into a set
of one-dimensional integro-differential equations allows us to exploit accurate
and extremely efficient numerical schemes that markedly outperform classical
methods (such as finite volume type methods) which is outlined by convergence
tests. Our approach not only provides information about complete particle size
distribution over time, but also offers insights into particle structure. The
presented scheme and its performance is exmplified based on coprecipitation of
nanoparticles. For this process, a generic growth law is derived and parameter
studies as well as convergence series are performed.
