  Purpose: Magnetic polarizability tensors (MPTs) provide an economical
characterisation of conducting magnetic metallic objects and their spectral
signature can aid in the solution of metal detection inverse problems, such as
scrap metal sorting, searching for unexploded ordnance in areas of former
conflict, and security screening at event venues and transport hubs. In this
work, the authors discuss methods for efficiently building large dictionaries
for classification approaches. Design/methodology/approach: Previous work has
established explicit formulae for MPT coefficients, underpinned by a rigorous
mathematical theory. To assist with the efficient computation of MPTs at
differing parameters and objects of interest this work applies new observations
about the way the MPT coefficients can be computed. Furthermore, the authors
discuss discretisation strategies for hp-finite elements on meshes of
unstructured tetrahedra combined with prismatic boundary layer elements for
resolving thin skin depths and using an adaptive proper orthogonal
decomposition (POD) reduced order modelling methodology to accelerate
computations for varying parameters. Findings: The success of the proposed
methodologies is demonstrated using a series of examples. A significant
reduction in computational effort is observed across all examples. The authors
identify and recommend a simple discretisation strategy, and improved accuracy
is obtained using adaptive POD. Originality: The authors present novel
computations, timings, and error certificates of MPT characterisations of
realistic objects made of magnetic materials. A novel postprocessing
implementation is introduced, and an adaptive POD algorithm is demonstrated.
