The aim of this minisymposium is to discuss the role of Hilbert complexes and related structure-preserving discretizations in the analysis, and implementation of high order and high performance numerical methods for low-frequency electromagnetic simulations and related PDEs. We would like to cover a wide range of approaches: from methods well stablished in computational electromagnetism, like Whitney forms and finite element exterior calculus, discontinuous Galerkin or finite volume methods, to more recent approaches like polytopal methods, virtual element methods or isogeometric methods. Applications to other PDEs with geometric or topological structure, as well as computational aspects connected with structure preservation, such as domain decomposition, high-performance implementations, and model-reduction techniques, will also be considered.