Efficient computation of magnetic polarizability tensor spectral signatures for object characterisation in metal detection

Purpose:Magnetic polarizability tensors (MPTs) provide an economical characterisation of conductingmagnetic metallic objects and their spectral signature can aid in the solution of metal detection inverseproblems, such as scrap metal sorting, searching for unexploded ordnance in areas of former conflict, andsecurity  screening  at  event  venues  and  transport  hubs.   In  this  work,  the  authors  discuss  methods  forefficiently 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  atdiffering parameters and objects of interest this work applies new observations about the way the MPTcoefficients can be computed.  Furthermore, the authors discuss discretisation strategies forhp–finite ele-ments on meshes of unstructured tetrahedra combined with prismatic boundary layer elements for resolvingthin skin depths and using an adaptive proper orthogonal decomposition (POD) reduced order modellingmethodology to accelerate computations for varying parameters,Findings:The  success  of  the  proposed  methodologies  is  demonstrated  using  a  series  of  examples.   Asignificant  reduction  in  computational  effort  is  observed  across  all  examples.   The  authors  identify  andrecommend a simple discretisation strategy, and improved accuracy is obtained using adaptive POD.Originality:The authors present novel computations, timings, and error certificates of MPT characterisa-tions of realistic objects made of magnetic materials.  A novel postprocessing implementation is introduced,and an adaptive POD algorithm is demonstrated.